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Research Papers

Therapeutic Equipment for Brain-Hyperthermia Using Convective Spray Cooling OPEN ACCESS

[+] Author and Article Information
Imran Mahmood

Department of Mechatronics and
Control Engineering,
University of Engineering and Technology,
Lahore 54890, Pakistan
e-mail: imran.mahmood@uet.edu.pk

Ali Raza

Department of Mechatronics and
Control Engineering,
University of Engineering and Technology,
Lahore 54890, Pakistan
e-mail: aliraza@uet.edu.pk

1Corresponding author.

Manuscript received October 22, 2016; final manuscript received April 7, 2017; published online June 27, 2017. Assoc. Editor: Matthew R. Myers.

J. Med. Devices 11(3), 031010 (Jun 27, 2017) (11 pages) Paper No: MED-16-1345; doi: 10.1115/1.4036652 History: Received October 22, 2016; Revised April 07, 2017

A new type of therapeutic equipment is designed herein, using concepts of convective heat transfer and spray cooling, to treat patients suffering from brain-hyperthermia. The equipment is aimed to provide emergency treatment in order to prevent disability or possible mortality because thermoregulatory system of the patients fails to maintain a homeostasis. The equipment uses noncontact method of forced convection, applied uniformly at body exteriors. The heat exchanger is designed to contain four independent pipe-sections with orifice openings around the body. The cool-air, maintained within ASHRAE’s thermal comfort bounds, is sprayed through the orifices. Design improvements have been made on the basis of image analysis of the flow. The boundary layer (BL) analysis has also been performed over a specially designed mannequin with induced hyperthermia characteristics. The testing indicates a decay of ∼6 °C in 280 min with a time constant of 2 h. Comparative to existing techniques, in addition to being a noncontact approach, the equipment shows better thermoregulatory performance along with a flexibility to accommodate different body contours.

FIGURES IN THIS ARTICLE
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Human body is a complex union of diverse biological organs and mechanisms, most of which are controlled by brain. Hypothalamus, for example, is a part of brain which controls the body temperature among other body functions. It maintains a homeostasis through thermoregulation. However, long-term heat exposures may bring the body to a pathological state called hyperthermia. Depending upon the intensity of the disease, the treatment is necessary and sometimes required on emergency basis. In this context, authors present a new therapeutic device for the treatment of hyperthermia.

Hyperthermia is an overheated state of body, where the core temperature rises above 40 °C [14]. It is life-threatening with risks of impairment of vital organs, unconsciousness, coma, and/or death in severe cases [5,6]. The treatments primarily rely on pharmacology. The studies reveal that the initial few hours are very crucial for hyperthermia patients [7], and a medicated treatment alone may become ineffective due to time delays [4]. In such situations, a physical cooling therapy may provide a suitable solution to deal with the situation [6,8,9].

Most of the published literature, however, emphasizes the occurrence, preventative measures, and pharmacological aspects [2,1012] of hyperthermia, instead of its mechanics. Only a few cooling therapy methods are documented, despite the evidence that a controlled-cooling therapy may be considered, the only viable survival option in the event of postcardiac arrest patients suffering with heat illness [10]. Wakamatsu et al. [13,14] performed series of experiments over the hyperthermia therapy based on air- and water-cooled blankets. The therapy highlights a fuzzy-based algorithm using induced hyperthermia (e.g., exercise-based, as in Refs. [1517]) characteristics. However, the authors neither discuss the underlying heat transfer parameters nor the desired thermal comfort standards. Moreover, the detailed analysis of thermal conductivity for the mannequin is not discussed along with the necessary design parameters of metabolic rate, respiratory mechanics, and heat flux estimation. Furthermore, the coolant flow through blanket makes it complicated to handle, and also the blankets are not efficient enough to ensure a proper contact with the body to maximize the heat transfer rate.

Another therapeutic attempt is reported by Gaohua and Kimura [18]. It is the first attempt to model the brain hyperthermia using the first-order model of body-temperatures. However, it excludes the pathological thresholds/parameters such as oxygen consumption rate, blood flow rate, and partial pressures of O2 and CO2. It is important to highlight that the real body-temperature characteristics are nonlinear functions of aforementioned thresholds/parameters and, therefore, are not truly represented by simpler first-order models.

The therapeutic equipment designed herein overcomes the aforementioned shortcomings in the reported literature by undergoing a detailed thermodynamic analysis. The equipment is noncontact and based on convective heat transfer using the spray-cooling methodology, while staying within ASHRAE’s thermal comfort standards [19]. At the core of this equipment is a multiturn helical heat-exchanger which makes use of different orifices to allow the cool air to diverge onto the surface. The cool air sweeps across the surface to take away the heat. A detailed boundary layer (BL) analysis has been done, assisted by an image-analysis technique to monitor the BL-velocity over the surface. The test subject is a specially designed mannequin. It has been developed after a detailed human-body heat-transfer analysis and is able to exhibit the induced hyperthermia characteristics. The results indicate that the new equipment is successful in effectively lowering the temperatures of the mannequin. Furthermore, the equipment is also able to increase the area of fluid divergence over the body surface, as compared to the blanket cooling methodology of Wakamatsu et al. [13,14]. It is, therefore, hoped that the non-contact-based equipment developed herein may be used in hospitals to save patients suffering from brain-hyperthermia.

Section 2 provides a detailed account of our methodology ranging from mannequin design to the heat-exchanger development. It is followed by the results including the vision-based velocimetry approach to monitor the convective heat transfer as well as the detailed testing of the therapeutic equipment. It is followed by sections on discussion and conclusion.

ASHRAE Thermal Comfort Standards.

It is important to highlight that any cooling therapy should remain bounded within the thermal comfort standards. Because within these comfort bounds, body’s physiological effort toward thermoregulation minimizes. This, in turn, supports the cooling therapy. Moreover, the therapy is a long procedure, and therefore, lowering the cooling temperatures below comfort levels for longer hours may lead to some complications [9], e.g., uncontrolled hypothermia induction or behavioral irritations for patients in subconscious state.

American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) has developed numerous standards for human well-being for the built environments. In this research, two important set of parameters are extracted from ASHRAE standards for human comfort in certain occupancy [19]. The first set corresponds to the size of mannequin, and adopts the length of 1.7 m and area of ∼1.8 m2 for the mannequin.

The second set, on the other hand, is composed of spray cooling parameters of mean air velocity, coolant temperature, and humidity. For typical hot climates, the air temperature for thermal comfort must fall in the range of 2228°C and mean air velocity should be kept <2m/s to avoid draft (i.e., undesired cooling effect due to higher air velocity). Therefore, the selected air-temperature for our research is 26±1°C, whereas the mean air velocity is 1.5 ± 0.5 m/s. These values are expected to improve the air-cooling therapy because of the reasons mentioned above, while staying within the comfort bounds at the same time. The humidity level in these studies is selected to be 50%. It is also pointed out that some other selective/whole body therapeutic studies have used a temperature range of 1935°C [9,13].

Mannequin Design.

The mannequin is designed herein to replicate the human-body’s thermal characteristics under hyperthermia conditions. The use of mannequin is done because of ethical considerations in experimental studies, against using human patients in pathological conditions [2].

In the literature, different thermal-mannequin designs [2022] have been reported within the paradigm of physiological thermal comfort analysis. The general limitation in these approaches is their inability to provide the data for pathological extremities, e.g., multinode thermal conductivity analysis, blood perfusion characteristics, etc. Any effective treatment of hyperthermia, such as the one presented herein, will require the data for pathological extremities. Therefore, a new thermal mannequin design has been accomplished to effectively mimic the heat illness.

Thermal Conductivity of the Mannequin.

Considering the fast cardiovascular response under hyperthermia and the maximum blood perfusion rate at peripheral tissues, only the surface heat transfer characteristics are simulated in this mannequin. The vasodilatation of the skin blood may enhance up to 15 times to evacuate the extreme heat-stress inside the body [19]. Thus, the outer skin layers named epidermis, dermis, subcutaneous, and inner tissues [23] are crucial for heat transfer and hence simulated in this study. In this context, a three-node mannequin model is developed, which is mainly responsible for accumulated thermal characteristics of a real body [24], as shown in Figs. 1 and 2.

The thermal conductivity data for each layer of skin is collected from various sources and mentioned in Table 1 [2527]. The resultant stack of skin layers can be considered as a circuit of thermal resistances in series. The mannequin materials selected hereby follow the approximated thermal conductivities of actual skin. However, the other thermal characteristics (i.e., specific heat and thickness) have relative tolerances which are adjusted by the volumetric flow rate (i.e., thickness of the heating fluid) inside the mannequin. While keeping the water flow rate at a threshold of 7L/min —which is the required blood perfusion rate for hyperthermia simulations [2]—the fluid thickness adjacent to the polyvinyl chloride (PVC) pipe’s inner surface is found to be 0.0045 m (almost half of the pipe diameter, i.e., 1 cm). With that fluid thickness (l), series thermal conductivity (k), and surface area (A), overall absolute thermal resistance (R) is found by a relationship, i.e., R=l/k×A. The net thermal resistance is found to be 0.0573 (K/W) in the case of our mannequin, whereas it is 0.064 (K/W) for real body. Moreover, the mannequin layers have low specific heat; the net thermal diffusivity (α=k/(D×C)) is 15% surplus comparative to the real body data. The thermal tolerances are encapsulated by 11.5% less thermal resistance and 15% more thermal diffusivity at the mannequin surface. The thermal thresholds inside the mannequin are attempted to achieve an approximation to that of real body thermal characteristics; however, the exact resemblance is difficult using artificial materials. Total length of mannequin is achieved at 1.72 m with a 1.77 m2 surface area.

Mannequin Working.

As mentioned earlier, the mannequin is designed by following the ASHRAE standards. It is divided into two sections: the upper body containing head, arms, chest and upper abdomen, and the lower body consisting of lower abdomen and legs. The geometrical proportions of these sections are calculated following those of an ideal man [28]. Polyester is used for the core of the dummy over which peripheral layers are placed to simulate the three node resistance model. PVC soft pipe is coiled over the whole surface of the polyester-core, without any voids/spaces. This pipe will construct two layers of the mannequin-skin: one with water to mimic blood-circulation and the other with its PVC material to represent subcutaneous tissue. The pipe windings are also covered with a polyethylene sheet in order to complete the three-resistance series circuit.

The mannequin fluid supply is also divided in patches (head, arms, chest, abdomen-and-thighs, and legs) and corresponding gate valves are adjusted in order to establish uniform thermal gradients at peripheries. The fluid pressure is maintained at 0.3 bar using in-series pumps, whereas the flow rate is kept consistent at 7L/min. Maximum blood perfusion rate, simulated hereby, follows the hyperthermia thresholds, and thus, the arteries-to-veins blood volume is maintained at 5 L inside the supply reservoir.

The working fluid is heated from 29°C to 50°C by an electric heater (1000 W), and the energy required to raise the mannequin temperature is 5952W/m2 (computed using Q=mcpΔT for an area of 1.77m2). Thus, the mannequin peripheral temperature rises from 35°C to 44±0.5°C —a desired milestone for hyperthermia induction. Following the Fourier’s Law of thermal conduction (Q=kAT/x ; k= net thermal conductivity and x= thickness of outer layers), the accumulated heat flux generated by hot water at mannequin outer peripheries (polyethylene plus PVC) has a magnitude of 3294W/m2 under a steady-state condition. Thus, the mannequin successfully exhibits the desired thermal characteristics and is fully prepared to perform the cooling therapies. The fluid-flow network is completely insulated as well. The whole setup is shown in Fig. 2.

Heat Exchanger Design.

In the reported cooling therapies, the surface-conduction methodology is generally applied, e.g., air/water-based cooling blankets, ice baths, cooling garments, cooling helmets, etc., [9,13,14,29]. This method has limited effectiveness, because it requires a full contact between the body and the equipment, in addition to the limitations of time delays and energy-conversion losses. The method being designed herein, on the other hand, is non-contact-based and relies on the convective heat transfer methodology within ASHRAE’s comfort bounds. This design technique has been implemented in the following steps.

Spray Cooling.

The heat transfer methodology adopted in this research falls in the category of spray cooling. The literature indicates that a modified version of spray cooling has been applied on human skin during laser treatments [30], but not for therapeutic equipment. It was decided that small openings (orifices) will be provided on the helical turns around the body in order to provide the desired spray cooling characteristics.

It is important to visualize the spray cooling effect on the body/mannequin. Equally important is to identify the orifice geometry versus flow divergence, which is vital to select the best suited orifice-geometry for the therapy. The parameter of flow divergence indicates the fluid’s ability to spread over a neighboring area. Therefore, an image-processing technique is required for this purpose. In order to facilitate the flow visualization, smoke-incense was used, and the resulting air flow was captured by a camera (Sony DSC-WX9), as shown in Fig. 3. For analysis, an open source java-based image-processing software called imagej [31] was used. The detailed results are discussed in Sec. 3.1 on visualization results. The velocity measurements were made by software’s particle image velocimetry (PIV) technique as well as by using a calibrated digital anemometer.

Orifice Design.

The flow visualization and velocimetry, as detailed above, helped in selecting the most suited orifices among a number of different options. It was also revealed that different orifices suit different body sections. The selected orifice geometry along with their location and flow characteristics are tabulated in Table 2, whereas the setup is illustrated in Fig. 3. The bottom of orifice openings is inclined at 45 deg to assist the exiting fluid. The incident flow makes a 45 deg impact considering the corresponding mannequin-patch as a flat surface. The flow then scatters over the adjacent areas with controlled velocity BL, discussed later in the results section, transferring the heat.

The selected material for helical pipe, coiled around the mannequin, is a flexible PVC. A galvanized wire-frame helps in retaining the helix shape, as shown in Fig. 3. The coil is made of insulator material which prevents the cool air from ambient effects and also offers a low friction. Four parallel helix turns (each with orifice openings as detailed in Table 2) behave like independent pressurized chambers with an ability to spray the air.

Air Supply Network.

Pressurized cool air is required to generate the said velocities at each orifice. An air supply unit, consisting of compressor, reservoir, and all the necessary peripherals, is used to maintain the air pressure of 7 bar. The compressed air temperature was recorded initially at 36°C. Following the thermal comfort standards discussed earlier, the temperature is required in the neighborhood of 26°C and the air velocity around 1.5 m/s. An air-cooler is, therefore, required to cool down the pressurized air. To serve the purpose, a simple copper helical coil of 10-ft length was dipped inside the hydraulic basin, carrying ice cold water at 10°C. This arrangement lowers the air temperature from 36°C to 26°C with a velocity drop, i.e., 0.5 m/s. The cooler is shown between the compressor and air supply network in Fig. 4. Alternatively, one can use other methods to cool down the air, e.g., refrigeration cycle air cooler and dryers. Generally, the hospitals have facilities for compressed air generation which can be used here, provided the supply is maintained at the desired comfort levels.

From the main pressure line, the cool air is supplied to four parallel coils through gate valves. Each valve is tuned to meet the average velocity requirement over the respective mannequin patches. Along with the mannequin body, heat exchanger and its supply network are insulated by a polyester sheet. The complete process is shown in Fig. 4.

Measurements and Uncertainties.

The performance of the heat exchanger is tested, over the mannequin surface with induced hyperthermia. The temperature readings are recorded at fluid outlet of the mannequin using digital thermometer. A typical therapy span can prolong over 6 h. During cooling, temperature versus time data is logged for each 0.1°C drop. During heating, the temperature of mannequin’s reservoir is observed using K-type thermocouple. Maximum fluid temperature was recorded to be 50°C to achieve a 44°C mannequin temperature. The temperatures of the cooler and the environment are also measured regularly. The air film produced by the orifices absorbs the heat by making a thermal boundary layer and diffuse outward from the mannequin-periphery due to stack effect (i.e., the air rising up due to temperature difference). Hot air is evacuated by an exhaust fan to the ambient environment.

Experimentation was done at an outdoor temperature of 45°C, whereas the indoor temperature varied in a range of 35–37 °C with humidity levels of 50–60%. The environmental conditions were deliberately selected in harsher season because heat strokes are frequently observed in similar conditions. Water temperature in the cooling tower was recorded as 29°C at the inlet and 10±1°C after getting it ice cooled. The compressed air was cooled from 36°C to 26±1°C, at an outlet pressure of 7±1bar. Air velocity was recorded at 7.5 m/s at the inlet of the cooling tower and 7 m/s at the outlet. Mannequin’s hyperthermic thresholds were found at 44±0.5°C temperature, with blood perfusion rate of 7±0.5L/min at a pressure 0.35±0.05bar.

Visualization Results.

Figures 58 illustrate the visualization frames captured during experimentation. The spray characteristics of previously designed orifices are analyzed here using BL analysis. Spray cooling patterns are recorded using the experimental setup mentioned in Fig. 3. Hydrodynamic BL parameters, i.e., velocity distribution and BL thickness are vital for heat transfer analysis, and are therefore established hereby. For brevity, only two frames are shown in the figure, i.e., one at the start and the other at the end (where the fluid has fully covered a certain patch). The velocity measurements are considered just after the air flow incident, and hence, the velocity boundary layer thickness is observed as nonzero at leading edge. This effect also depends on the considered frame number and increases toward trailing edge due to decrease in air velocity and stack effect.

The assumptions while considering the turbulent boundary layer for the flow over these patches are: (1) the boundary layer analysis is performed by assuming each patch as flat plate with incident fluid at some angle (not parallel to the patch) and (2) the heat absorption effect over the velocity boundary layer growth is negligible. The observations in this context are: (1) the velocity fluctuations along the longitudinal axis for respective patch show the turbulent nature of the flow. Turbulent eddies create fluctuations in velocity [4]. (2) The pressurized orifice fluid flow, incident with an impact, splash the fluid toward longitudinal axis implying a negligible transitional length for laminar to turbulence conversion.

Head Patch.

An aggressive spray cooling at the head patch can be disturbing to the patient. Therefore, staying within the thermal comfort bounds is of vital importance. The designed orifices are successful in creating a thin film over the patch. Out of three orifices for the head-patch, one is positioned at the forehead, and the other two are directed at both the temples. The film is able to accommodate the surface irregularities with maximum area of flow convergence in minimum time (surface renewal takes 460 ms for the head patch). Detailed video analysis provides a better glimpse of the process of film creation. The orifice flow indicates turbulence over the surface once the impact angle is increased above 45 deg, which is exhibited by the nonuniform velocity profile as well. The net incident velocity generated by these orifices lies in the range of 1.8–2.2 m/s. The BL thickness for this velocity profile lies in the range of 1–2.8 cm. For 22 cm head patch, the average velocity is achieved to be 1.9 m/s and BL thickness to be 2 cm. Smaller length versus head-area flow-convergence is met by 26% more velocity. However, average velocity for whole body remains within the set value. Selected frames are shown in Fig. 5.

The heat transfer parameters for head patch have been summarized in Table 3, i.e., with average velocity (1.9 m/s), boundary layer thickness, cool air flux renewal time, average convective heat transfer, and average convective heat transfer coefficient (CHTC). The blood perfusion taking place in other patches also plays a significant role in transferring the heat from the brain during hyperthermia. As the cardiovascular cycle maintains a continuous blood circulation in/out of heart, every time it gushes a fresh blood stream toward the brain; some temperature has already been lowered because of the perfusion in other patches (almost 63% heat transfer takes place in other patches). Furthermore, the current convection-based method provides cooler air flux to the lungs and hence to the blood stream—thus providing oxygen to brain which is one of the critical requirements under these circumstances [12]. This was not possible with the previous conduction-based approaches. However, the exact quantitative measurement requires a direct experimentation on physical patients which is beyond the scope of current research.

The maximum convective heat transferred (CHT) from head patch is 228 W which is in resemblance to the helmet-based conductive heat transfer approach, i.e., 220 W [9]. The average convective heat transfer coefficient for head patch is 12.67W/m2K and found to be in range to that of previous convective heat transfer studies for human body, i.e., 10–11.7W/m2K [32,33].

Chest and Upper Abdomen Patch.

The next area to be analyzed is that of upper body. It contains the chest patch and one arm patch (assuming symmetry). Flow characteristics are examined at Frame 25 with three vector lines marked in Fig. 6. Video analysis depicts a clear growth of turbulent boundary layer. The particles scatter along the length (50 cm) with nonuniform velocity drops, and the thickness of the wavy boundary layer increases downstream. The slow motion analysis of the frames shows a D-shape thin film produced just at the incident orifice flow. Afterward, surface roughness, drag effect, and shear stress between the particles become prominent. As a result, the particle-velocity drops, and clothing friction further submerges the fluid layers. Meanwhile flux renewal provides a momentum at the mixing length and generates slight sweep toward sublayers of low velocity. The mixing length means the length where the interaction among the fresh and diffused fluxes takes place. It takes 704 ms to cover the entire area prior to fresh influx. Compared to the conventional air blanket cooling methods [13], it provides direct convection with better coverage, optimized film creation, and takes less time for heat evacuation. Average velocity is found to be 1.5 m/s, and BL thickness is 7 cm.

Patch for Lower Abdomen and Thighs.

The patch-length for lower abdomen and thighs is approximately equal to that of chest and upper abdomen. The orifice-shapes are also same. Hence, the spray cooling characteristics are observed to be similar. Turbulent boundary layer is observed. However, the flux renewal time is lower, i.e., 640 ms due to fewer surface irregularities and frictional area. Flow patterns show that the area of flow divergence out of orifice has a D-shaped high velocity thin-film initially, and later, a wavy thicker flow. For each patch, the flux of cool air diffuses its energy and absorbs the heat as it moves downstream. Fresh supply of cool air replaces the previous flux which rises above the surface due to difference in densities called stack effect. Warm air, raised above the mannequin surface, is removed from the chamber by the exhaust fan. Velocity and its BL thickness analysis is performed for the two vector lines shown in Frame 25. The average velocity comes out to be about 1.7 m/s, and the BL thickness is observed to be 5 cm, as shown in Fig. 7.

Legs Patch.

Considering the natural geometry of legs (reducing diametrically), a separate orifice was used for each leg, as shown in Fig. 8. The incident flow is tangent to the knee position. The resultant flow-field splashes in the form of thin film at the upper area, and thereafter a low velocity thicker flow goes 50 cm to the downstream (as observed from slow motion video analysis). The orifices create thin BL thickness by maximizing the area of flow divergence in lowest time, i.e., 577 ms. The boundary layer grows turbulent later in the downstream, increases its thickness, and later decreases radially toward the edges. The turbulence is generated by surface roughness, irregular geometry, shear stress between fluid layers, and getting mixed with natural atmosphere. The resultant average velocity is 1.2 m/s. and BL thickness is 2 cm, as computed in Fig. 8.

Boundary Layer Analysis of the Results.

In the context of forced convective mode of heat transfer, the investigation of boundary layer parameters is of prime importance. The orifices placed over the mannequin generate laminar flow initially which turns turbulent just after the incident. The velocity profiles showed the sharp fluctuations as smoke incense flow downstream. But these flows are ensured with low velocity gradients in order to meet the necessary needs of thermal comfort. Turbulent flow with low velocity gradients—the one exhibited in this research—is an active area of research [34]. For detailed findings on fluid flow across an oblique (45 deg) flat plat, including Reynolds number of 20,000, the reader referred to Ref. [35]. In this context, the amount of convective heat transferred (CHT) and convective heat transfer coefficient (CHTC) are important parameters and are computed using the experimental data tabulated in Table 3. For turbulent flow, the following relationship [36] holds good for average convective heat transfer coefficient assuming that the body surface behaves like a flat one Display Formula

(1)ha=0.036×(k/L)×ReL0×8×Pr1/3

where k is the thermal conductivity, L is the characteristic length for each patch, ReL is the Reynolds number (U×x/υ), U is the free stream velocity, x is the characteristic length along the surface, υ is the kinematic viscosity, and Pr is Prandtl number found to be 0.712 for air at 26°C (varies 0.7–0.8 for air, however, for operating temperature, the value is considered to be 0.712) [36,37]. Since inlet air temperature, spray height, and velocity are uniform throughout experimentation, CHTC is assumed to be constant for each patch. Under the steady-state conditions, maximum convective heat Q absorbed by air flux over the mannequin patch is computed by the following equation: Display Formula

(2)Q=haA(TsTair)

where Ts is the mannequin surface temperature, Tair is the cool air temperature, and A is the mannequin surface area.

Overall, BL-creation exhibited the heat evacuation capacity of the heat exchanger as indicated by CHTCavg=9.833W/m2/K. The values of CHTC of individual patches are tabulated in Table 3. The values lie in close neighborhood of each other except for the head patch which is 20% higher due to higher velocity versus area-to-length ratio. However, this is supportive for brain cooling considering its sensitivity to thermal defense. The value of CHTC for legs is found to be 24% below the average value because of reducing diameters with respect to the lengths.

Under steady-state conditions, the mannequin’s peripheral exergy was found to be 3294W/m2 (or energy 5832W), and the heat exchanger’s max CHT was found to be 313W (Eq. (2)). Thus, the designed therapy has heat removal capacity of 5% to that of maximum energy conducted from the body. Under body-hyperthermia, accumulated heat capacity was 5952W/m2, and max net evacuation (from Table 3, by adding values for all the patches) was found to be 708W. Out of that 33% of average convective heat is released from the head patch which is within the range of a helmet-based head-cooling therapy, i.e., 220 W [9]. In total, the heat exchanger removed 13% of total stored heat, with an average flux renewal time of 600 ms for the coolant.

At this stage, it is still difficult to predict the total therapeutic time due to transient heat generation, surface nonlinearity, and temperature-dependent parametric variations. Thus, the steady-state behaviors effectively define the maximum thresholds of the heat exchanger, whereas the transient behaviors (discussed in Sec. 3.3) best depict the therapeutic effectiveness over time.

Transient Cooling Results.

With all the experimentation details discussed earlier, the drop in mannequin’s temperature and heat flux versus the time of therapy is plotted in Figs. 9(a)9(f). Multiple scans were performed to gradually improve the process parameters. For brevity, two scans are presented here. The first scan prolonged about 6 h. The drop in mannequin-temperature was recorded from 44°C to 38.5°C. The first scan illustrates the transient behavior of the heat exchanger over the mannequin assembly, which also carries the reservoir-volume along with it. The volume is essential for priming and heating purposes, but counteracts in establishing the thermal gradients at the same time. Therefore, a second scan was done after some minor modifications in the setup, e.g., a three-way control valve was added between drain and suction of the tank. While the mannequin’s fluid was being heated, the valve remained open so that the fluid routed through the reservoir. Once the desired thermal characteristics were induced in the mannequin, the valve was closed to bypass the reservoir. The second test was conducted with these minor adjustments, and the results are being shown in Fig. 9(b). By keeping the spray characteristics constant, body’s heat transfer is entirely time-dependent. Since the heat transfer is a function of body-temperature (variant with respect to time), it follows a similar curve with an average value of 265±50 (W), as shown in Fig. 9(d). Both in temperature and heat transfer curves, the nonlinear thermal characteristics of the mannequin, similar to those in real body, are also visible.

Temperature comparison in Fig. 9(c) shows that the second scan has a sharper decay during first few hours, and afterward the curves are almost similar. Initially, the higher temperature difference between surface and coolant (TsTair) indicates better effect of spray cooling, and hence, the heat transfer becomes more prominent, as illustrated in Fig. 9(f) as well. Later, as the mannequin surface approaches near-room temperatures, the coolant gets less effective because of ambient effects. This has happened due to reduced temperature gradient between the exhaust inlet and outlet. Though the mannequin periphery is insulated yet the chamber is not completely air-tight. Thus, the decrease in temperature difference (TsTair) makes the cooling less effective (Fourier’s law of thermal conductivity). This is also illustrated by convective heat transfer versus ambient temperature plot in Fig. 9(e). It implies that a rise in indoor-temperature during experimentation reduces the equipment’s ability to transfer heat.

Temperature gradient in Fig. 9(b), once extended to 37°C, indicates the time constant τ to be 122 min (2 h). Comparatively, the equipment developed herein performs better than the air-cooled blanket [13] which has a time constant of 2.5 h. As compared to the water-cooled blanket with a time constant of 2 h [14], the equipment performs equally good. This is in addition to being a noncontact method. The benefits of being a noncontact method outweigh those of any contact-based approaches. First of all, in the water-cooled blanket, it is difficult to control the requisite fluid flow vis–vis the surface contact area, and avoid leakages or other uncertainties. Moreover, it is difficult to keep the head and face covered with a blanket for hours-long therapy. Convection, on the other hand, provides fresh and relatively cool air for inhaling which may also assist in supplying oxygen to the brain. This may, in return, also help in treating the hyperthermia. It is emphasized that the heat exchanger and the mannequin were designed in this study following the real-time human-body heat transfer thresholds and tested under steady-state conditions. The testing of equipment under variable fluid temperature will be done in future which is expected to show further improvements in the results.

Normally, the body has a natural thermoregulation system to evacuate the surplus heat. But, under brain-hyperthermia, this ability gets impaired partially or completely, and a persistent condition may turn out to be life threatening. In this context, we have presented a life saving device that may provide therapy both in prehospital and hospital environments. The major outcomes achieved here are concluded briefly.

  1. (1)In order to stay within biomedical ethics while taking full privilege of experimentation, a thermal mannequin is constructed. Based on the detailed thermal conductivity analysis, a three node model is replicated, induced with above-thermal norms at mannequin peripheries.
  2. (2)A new heat exchanger is presented hereby which is based on forced convective heat transfer method. Helical turns with orifice openings (for each body patch) provide cool air to flow across the body. The orifice-based design also enables the flow to diverge, increasing the area covered by the coolant.
  3. (3)Visual tools have been used to improve the spray cooling heat transfer performance. Recordings show that a controlled boundary layer is created within human thermal comfort standards, i.e., with average air velocity of ¡2 m/s and therapeutic temperature of around 26°C.
  4. (4)The therapeutic device successfully evacuates the body heat with convective heat transfer of ∼313 W, convective heat transfer coefficient of 9.83W/m2/K, and net heat absorption of ∼704 W with respect to respective air flux renewal (e.g., 600 ms). Therapy’s transient behavior shows an improvement in time constant (i.e., 2 h) comparative to conductive cooling methods developed so far.
  5. (5)The cooling therapy results provide valuable data for other therapeutic designs for similar heat illnesses. It may also be useful for controlled-environment-design in health care units like burn care centers, cardiac trauma units, and for prolonged anesthesia surgeries.

The therapeutic equipment developed, and duly tested, in this research provides a comprehensive, full-body, noncontact-based approach as compared to the other cooling procedures. In future, authors aim to design an adaptive controller for the equipment with a range of different pathophysiological behaviors.

The authors will like to acknowledge the Thermal Sciences Lab at the University of Engineering and Technology, Lahore (Faisalabad Campus) for sparing some equipment for the experimentation.

Wade, C. E. , Salinas, J. , Eastridge, B. J. , McManus, J. G. , and Holcomb, J. B. , 2011, “ Admission Hypo- or Hyperthermia and Survival After Trauma in Civilian and Military Environments,” Int. J. Emerg. Med., 4(1), p. 35. [CrossRef] [PubMed]
Kiyatkin, E. A. , 2004, “ Brain Hyperthermia During Physiological and Pathological Conditions: Causes, Mechanisms, and Functional Implications,” Curr. Neurovasc. Res., 1(1), pp. 77–90. [CrossRef] [PubMed]
Zhu, L. , 2000, “ Theoretical Evaluation of Contributions of Heat Conduction and Countercurrent Heat Exchange in Selective Brain Cooling in Humans,” Ann. Biomed. Eng., 28(3), pp. 269–277. [CrossRef] [PubMed]
Bouchama, A. , Dehbi, M. , and Chaves-Carballo, E. , 2007, “ Cooling and Hemodynamic Management in Heatstroke: Practical Recommendations,” Crit. Care, 11(3), p. R54. [CrossRef] [PubMed]
Badjatia, N. , 2009, “ Hyperthermia and Fever Control in Brain Injury,” Crit. Care Med., 37(7), pp. S250–S257.
Kasper, D. , Fauci, A. , Hauser, S. , Longo, D. , Jameson, J. , and Loscalzo, J. , 2015, Harrison’s Principles of Internal Medicine, 19th ed., McGraw-Hill, New York.
Moore, F. , Rhee, P. , Tisherman, S. , and Fulda, G. , 2012, Surgical Critical Care and Emergency Surgery: Clinical Questions and Answers, Wiley, Hoboken, NJ.
Dewhirst, M. W. , Viglianti, B. L. , Lora-Michiels, M. , Hanson, M. , and Hoopes, P. J. , 2003, “ Basic Principles of Thermal Dosimetry and Thermal Thresholds for Tissue Damage From Hyperthermia,” Int. J. Hyperthermia, 19(3), pp. 267–294. [CrossRef] [PubMed]
Gladen, A. , Iaizzo, P. A. , Bischof, J. C. , Erdman, A. G. , and Divani, A. A. , 2013, “ A Head and Neck Support Device for Inducing Local Hypothermia,” ASME J. Med. Devices, 8(1), p. 011002. [CrossRef]
Rhoades, R. , and Bell, D. , 2012, Medical Physiology: Principles for Clinical Medicine, Wolters Kluwer Health, Philadelphia, PA.
Cheuvront, S. N. , Kenefick, R. W. , Montain, S. J. , and Sawka, M. N. , 2010, “ Mechanisms of Aerobic Performance Impairment With Heat Stress and Dehydration,” J. Appl. Physiol., 109(6), pp. 1989–1995. [CrossRef] [PubMed]
Hargreaves, M. , 2008, “ Fatigue Mechanisms Determining Exercise Performance: Integrative Physiology is Systems Biology,” J. Appl. Physiol., 104(5), pp. 1541–1542. [CrossRef] [PubMed]
Wakamatsu, H. , and Utsuki, T. , 2009, “ Development of a Basic Air-Cooling Fuzzy Control System for Hypothermia,” Artif. Life Rob., 14(3), p. 311. [CrossRef]
Wakamatsu, H. , Wakatsuki, T. , and Utsuki, T. , 2007, “ Comparison of Fuzzy Control Systems for Hypothermal Brain Temperature Regulation,” Artif. Life Rob., 11(2), pp. 183–189. [CrossRef]
Mikulski, T. , Ziemba, A. , and Nazar, K. , 2008, “ Influence of Body Carbohydrate Store Modification on Catecholamine and Lactate Responses to Graded Exercise in Sedentary and Physically Active Subjects,” J. Physiol. Pharmacol., 59(3), pp. 603–616. https://www.ncbi.nlm.nih.gov/pubmed/18953101
Folch, N. , Peronnet, F. , Massicotte, D. , Charpentier, S. , and Lavoie, C. , 2003, “ Metabolic Response to a Large Starch Meal After Rest and Exercise: Comparison Between Men and Women,” Eur. J. Clin. Nutr., 57(9), pp. 1107–1115. [CrossRef] [PubMed]
Nybo, L. , Secher, N. H. , and Nielsen, B. , 2002, “ Inadequate Heat Release From the Human Brain During Prolonged Exercise With Hyperthermia,” J. Physiol., 545(2), pp. 697–704. [CrossRef] [PubMed]
Gaohua, L. , and Kimura, H. , 2008, “ A Mathematical Model of Respiratory and Biothermal Dynamics in Brain Hypothermia Treatment,” IEEE Trans. Biomed. Eng., 55(4), pp. 1266–1278. [CrossRef] [PubMed]
Handbook, A. , 2009, Fundamentals, Ashrae, Atlanta, GA.
Huizenga, C. , Hui, Z. , and Arens, E. , 2001, “ A Model of Human Physiology and Comfort for Assessing Complex Thermal Environments,” Build. Environ., 36(6), pp. 691–699. [CrossRef]
Nilsson, H. O. , and Holmr, I. , 2003, “ Comfort Climate Evaluation With Thermal Manikin Methods and Computer Simulation Models,” Indoor Air, 13(1), pp. 28–37. [CrossRef] [PubMed]
Farrington, R. B. , Rugh, J. P. , Bharathan, D. , and Burke, R. , 2004, “ Use of a Thermal Manikin to Evaluate Human Thermoregulatory Responses in Transient, Non-Uniform, Thermal Environments,” SAE Paper No. 2004-01-2345.
Zolfaghari, A. , and Maerefat, M. , 2010, “ A New Simplified Thermoregulatory Bioheat Model for Evaluating Thermal Response of the Human Body to Transient Environments,” Build. Environ., 45(10), pp. 2068–2076. [CrossRef]
Bulcao, C. F. , Frank, S. M. , Raja, S. N. , Tran, K. M. , and Goldstein, D. S. , 2000, “ Relative Contribution of Core and Skin Temperatures to Thermal Comfort in Humans,” J. Therm. Biol., 25(12), pp. 147–150. [CrossRef]
Jiang, S. , Ma, N. , Li, H. , and Zhang, X. , 2002, “ Effects of Thermal Properties and Geometrical Dimensions on Skin Burn Injuries,” Burns, 28(8), pp. 713–717. [CrossRef] [PubMed]
Kutz, M. , 2002, Handbook of Materials Selection, Wiley, New York.
Harper, C. A. , 2002, Handbook of Plastics, Elastomers, and Composites, McGraw-Hill, New York.
Bogin, B. , and Varela-Silva, M. I. , 2010, “ Leg Length, Body Proportion, and Health: A Review With a Note on Beauty,” Int. J. Environ. Res. Public Health, 7(3), pp. 1047–1075. [CrossRef] [PubMed]
Rothmaier, M. , Weder, M. , Meyer-Heim, A. , and Kesselring, J. , 2008, “ Design and Performance of Personal Cooling Garments Based on Three-Layer Laminates,” Med. Biol. Eng. Comput., 46(8), pp. 825–832. [CrossRef] [PubMed]
Kim, J. , 2007, “ Spray Cooling Heat Transfer: The State of the Art,” Int. J. Heat Fluid Flow, 28(4), pp. 753–767. [CrossRef]
Schindelin, J. , Rueden, C. T. , Hiner, M. C. , and Eliceiri, K. W. , 2015, “ The ImageJ Ecosystem: An Open Platform for Biomedical Image Analysis,” Mol. Reprod. Dev., 82(7–8), pp. 518–529. [CrossRef] [PubMed]
de Dear, R. J. , Arens, E. , Hui, Z. , and Oguro, M. , 1997, “ Convective and Radiative Heat Transfer Coefficients for Individual Human Body Segments,” Int. J. Biometeorol., 40(3), pp. 141–156. [CrossRef] [PubMed]
Defraeye, T. , Blocken, B. , Koninckx, E. , Hespel, P. , and Carmeliet, J. , 2011, “ Computational Fluid Dynamics Analysis of Drag and Convective Heat Transfer of Individual Body Segments for Different Cyclist Positions,” J. Biomech., 44(9), pp. 1695–1701. [CrossRef] [PubMed]
Marusic, I. , McKeon, B. J. , Monkewitz, P. A. , Nagib, H. M. , Smits, A. J. , and Sreenivasan, K. R. , 2010, “ Wall-Bounded Turbulent Flows at High Reynolds Numbers: Recent Advances and Key Issues,” Phys. Fluids, 22(6), p. 065103. [CrossRef]
Afgan, I. , Benhamadouche, S. , Han, X. , Sagaut, P. , and Laurence, D. , 2013, “ Flow Over a Flat Plate With Uniform Inlet and Incident Coherent Gusts,” J. Fluid Mech., 720, p. 457485. [CrossRef]
Thirumaleshwar, M. , 2009, Fundamentals of Heat and Mass Transfer (Always Learning), Pearson Education, New Delhi, India.
Rogers, G. F. C. , and Mayhew, Y. R. , 1995, Thermodynamic and Transport Properties of Fluids, Blackwell, Oxford, UK.
Copyright © 2017 by ASME
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References

Wade, C. E. , Salinas, J. , Eastridge, B. J. , McManus, J. G. , and Holcomb, J. B. , 2011, “ Admission Hypo- or Hyperthermia and Survival After Trauma in Civilian and Military Environments,” Int. J. Emerg. Med., 4(1), p. 35. [CrossRef] [PubMed]
Kiyatkin, E. A. , 2004, “ Brain Hyperthermia During Physiological and Pathological Conditions: Causes, Mechanisms, and Functional Implications,” Curr. Neurovasc. Res., 1(1), pp. 77–90. [CrossRef] [PubMed]
Zhu, L. , 2000, “ Theoretical Evaluation of Contributions of Heat Conduction and Countercurrent Heat Exchange in Selective Brain Cooling in Humans,” Ann. Biomed. Eng., 28(3), pp. 269–277. [CrossRef] [PubMed]
Bouchama, A. , Dehbi, M. , and Chaves-Carballo, E. , 2007, “ Cooling and Hemodynamic Management in Heatstroke: Practical Recommendations,” Crit. Care, 11(3), p. R54. [CrossRef] [PubMed]
Badjatia, N. , 2009, “ Hyperthermia and Fever Control in Brain Injury,” Crit. Care Med., 37(7), pp. S250–S257.
Kasper, D. , Fauci, A. , Hauser, S. , Longo, D. , Jameson, J. , and Loscalzo, J. , 2015, Harrison’s Principles of Internal Medicine, 19th ed., McGraw-Hill, New York.
Moore, F. , Rhee, P. , Tisherman, S. , and Fulda, G. , 2012, Surgical Critical Care and Emergency Surgery: Clinical Questions and Answers, Wiley, Hoboken, NJ.
Dewhirst, M. W. , Viglianti, B. L. , Lora-Michiels, M. , Hanson, M. , and Hoopes, P. J. , 2003, “ Basic Principles of Thermal Dosimetry and Thermal Thresholds for Tissue Damage From Hyperthermia,” Int. J. Hyperthermia, 19(3), pp. 267–294. [CrossRef] [PubMed]
Gladen, A. , Iaizzo, P. A. , Bischof, J. C. , Erdman, A. G. , and Divani, A. A. , 2013, “ A Head and Neck Support Device for Inducing Local Hypothermia,” ASME J. Med. Devices, 8(1), p. 011002. [CrossRef]
Rhoades, R. , and Bell, D. , 2012, Medical Physiology: Principles for Clinical Medicine, Wolters Kluwer Health, Philadelphia, PA.
Cheuvront, S. N. , Kenefick, R. W. , Montain, S. J. , and Sawka, M. N. , 2010, “ Mechanisms of Aerobic Performance Impairment With Heat Stress and Dehydration,” J. Appl. Physiol., 109(6), pp. 1989–1995. [CrossRef] [PubMed]
Hargreaves, M. , 2008, “ Fatigue Mechanisms Determining Exercise Performance: Integrative Physiology is Systems Biology,” J. Appl. Physiol., 104(5), pp. 1541–1542. [CrossRef] [PubMed]
Wakamatsu, H. , and Utsuki, T. , 2009, “ Development of a Basic Air-Cooling Fuzzy Control System for Hypothermia,” Artif. Life Rob., 14(3), p. 311. [CrossRef]
Wakamatsu, H. , Wakatsuki, T. , and Utsuki, T. , 2007, “ Comparison of Fuzzy Control Systems for Hypothermal Brain Temperature Regulation,” Artif. Life Rob., 11(2), pp. 183–189. [CrossRef]
Mikulski, T. , Ziemba, A. , and Nazar, K. , 2008, “ Influence of Body Carbohydrate Store Modification on Catecholamine and Lactate Responses to Graded Exercise in Sedentary and Physically Active Subjects,” J. Physiol. Pharmacol., 59(3), pp. 603–616. https://www.ncbi.nlm.nih.gov/pubmed/18953101
Folch, N. , Peronnet, F. , Massicotte, D. , Charpentier, S. , and Lavoie, C. , 2003, “ Metabolic Response to a Large Starch Meal After Rest and Exercise: Comparison Between Men and Women,” Eur. J. Clin. Nutr., 57(9), pp. 1107–1115. [CrossRef] [PubMed]
Nybo, L. , Secher, N. H. , and Nielsen, B. , 2002, “ Inadequate Heat Release From the Human Brain During Prolonged Exercise With Hyperthermia,” J. Physiol., 545(2), pp. 697–704. [CrossRef] [PubMed]
Gaohua, L. , and Kimura, H. , 2008, “ A Mathematical Model of Respiratory and Biothermal Dynamics in Brain Hypothermia Treatment,” IEEE Trans. Biomed. Eng., 55(4), pp. 1266–1278. [CrossRef] [PubMed]
Handbook, A. , 2009, Fundamentals, Ashrae, Atlanta, GA.
Huizenga, C. , Hui, Z. , and Arens, E. , 2001, “ A Model of Human Physiology and Comfort for Assessing Complex Thermal Environments,” Build. Environ., 36(6), pp. 691–699. [CrossRef]
Nilsson, H. O. , and Holmr, I. , 2003, “ Comfort Climate Evaluation With Thermal Manikin Methods and Computer Simulation Models,” Indoor Air, 13(1), pp. 28–37. [CrossRef] [PubMed]
Farrington, R. B. , Rugh, J. P. , Bharathan, D. , and Burke, R. , 2004, “ Use of a Thermal Manikin to Evaluate Human Thermoregulatory Responses in Transient, Non-Uniform, Thermal Environments,” SAE Paper No. 2004-01-2345.
Zolfaghari, A. , and Maerefat, M. , 2010, “ A New Simplified Thermoregulatory Bioheat Model for Evaluating Thermal Response of the Human Body to Transient Environments,” Build. Environ., 45(10), pp. 2068–2076. [CrossRef]
Bulcao, C. F. , Frank, S. M. , Raja, S. N. , Tran, K. M. , and Goldstein, D. S. , 2000, “ Relative Contribution of Core and Skin Temperatures to Thermal Comfort in Humans,” J. Therm. Biol., 25(12), pp. 147–150. [CrossRef]
Jiang, S. , Ma, N. , Li, H. , and Zhang, X. , 2002, “ Effects of Thermal Properties and Geometrical Dimensions on Skin Burn Injuries,” Burns, 28(8), pp. 713–717. [CrossRef] [PubMed]
Kutz, M. , 2002, Handbook of Materials Selection, Wiley, New York.
Harper, C. A. , 2002, Handbook of Plastics, Elastomers, and Composites, McGraw-Hill, New York.
Bogin, B. , and Varela-Silva, M. I. , 2010, “ Leg Length, Body Proportion, and Health: A Review With a Note on Beauty,” Int. J. Environ. Res. Public Health, 7(3), pp. 1047–1075. [CrossRef] [PubMed]
Rothmaier, M. , Weder, M. , Meyer-Heim, A. , and Kesselring, J. , 2008, “ Design and Performance of Personal Cooling Garments Based on Three-Layer Laminates,” Med. Biol. Eng. Comput., 46(8), pp. 825–832. [CrossRef] [PubMed]
Kim, J. , 2007, “ Spray Cooling Heat Transfer: The State of the Art,” Int. J. Heat Fluid Flow, 28(4), pp. 753–767. [CrossRef]
Schindelin, J. , Rueden, C. T. , Hiner, M. C. , and Eliceiri, K. W. , 2015, “ The ImageJ Ecosystem: An Open Platform for Biomedical Image Analysis,” Mol. Reprod. Dev., 82(7–8), pp. 518–529. [CrossRef] [PubMed]
de Dear, R. J. , Arens, E. , Hui, Z. , and Oguro, M. , 1997, “ Convective and Radiative Heat Transfer Coefficients for Individual Human Body Segments,” Int. J. Biometeorol., 40(3), pp. 141–156. [CrossRef] [PubMed]
Defraeye, T. , Blocken, B. , Koninckx, E. , Hespel, P. , and Carmeliet, J. , 2011, “ Computational Fluid Dynamics Analysis of Drag and Convective Heat Transfer of Individual Body Segments for Different Cyclist Positions,” J. Biomech., 44(9), pp. 1695–1701. [CrossRef] [PubMed]
Marusic, I. , McKeon, B. J. , Monkewitz, P. A. , Nagib, H. M. , Smits, A. J. , and Sreenivasan, K. R. , 2010, “ Wall-Bounded Turbulent Flows at High Reynolds Numbers: Recent Advances and Key Issues,” Phys. Fluids, 22(6), p. 065103. [CrossRef]
Afgan, I. , Benhamadouche, S. , Han, X. , Sagaut, P. , and Laurence, D. , 2013, “ Flow Over a Flat Plate With Uniform Inlet and Incident Coherent Gusts,” J. Fluid Mech., 720, p. 457485. [CrossRef]
Thirumaleshwar, M. , 2009, Fundamentals of Heat and Mass Transfer (Always Learning), Pearson Education, New Delhi, India.
Rogers, G. F. C. , and Mayhew, Y. R. , 1995, Thermodynamic and Transport Properties of Fluids, Blackwell, Oxford, UK.

Figures

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Fig. 1

Three-node mannequin skin model

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Fig. 2

Mannequin’s working fluid assembly

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Fig. 3

Setup for air supply and visual analysis with different orifices

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Fig. 4

Experimental setup with cool-air supply and distribution assembly

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Fig. 5

Boundary layer analysis over the head surface

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Fig. 6

Boundary layer analysis over the chest and upper abdomen surfaces

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Fig. 7

Boundary layer analysis over the lower abdomen and thighs surfaces

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Fig. 8

Boundary layer analysis over the legs surface

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Fig. 9

Therapeutic equipment active cooling results

Tables

Table Grahic Jump Location
Table 1 Thermal characteristics of a mannequin and a real body
Table Footer NoteNote: K, thermal conductivity; T, thickness; D, density; C, specific heat; R, absolute thermal resistance.
Table Grahic Jump Location
Table 2 Orifice design specifications
Table Footer NoteaFor side orifice, also notice the reduced incident air–velocity for the head patch for greater comfort in long therapy sessions.
Table Grahic Jump Location
Table 3 Hydrodynamic boundary layer analysis results
Table Footer NoteaThe Reynolds number is calculated at respective patch length from the corresponding leading edge.

Errata

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