Consider the conditions of Example 3–14 in the text for two different environments of air and water with convective heat transfer coefficient of 2 W/m² · K and 20 W/m² · K, respectively. The ambient (T_∞) and surrounding temperature (T_surr) for both air and water may be assumed to be 15°C. What would be the metabolic heat generation rate required to maintain the skin temperature at 34°C?

Example 3-14

Transcribed Image Text:

EXAMPLE 3-14 Application of Bioheat Transfer Equation We are interested in heat transfer analysis from a human body subjected to certain environmental conditions. For this purpose consider a region of muscle with a skin/ fat layer over it under steady state conditions as shown in Fig. 3-51. For simplicity approximate this region as a one-dimensional plane wall with surface area A. The muscle thickness is Lm covered by a layer of skin/fat with a thickness Lsf. The met- abolic heat generation rate (em) and perfusion rate (p) are both constant throughout the muscle. The blood density and specific heat are p, and cb, respectively. The core body temperate (T) and the arterial blood temperature (T₂) are both assumed to be the same and constant. The muscle and the skin/fat layer thermal conduc- tivities are km and ks, respectively. The skin has an emissivity of & and the body is subjected to an air environment with a temperature of To, a convection heat trans- fer coefficient of hconv, and a radiation heat transfer coefficient of hrad. Assuming blood properties and thermal conductivities are all constant, (a) develop an expres- sion for the interface temperature (T) between the muscle and the outer skin/fat layer, and (b) determine the temperature T, and the rate of heat loss from the body (Q), and the skin temperature (T) for the following conditions: