Essential Role of Blood Flow in Cooling the Human Body: Heat Transfer Problem

[chohocvo]

Homework Statement

The human body must maintain its core temperature inside a rather narrow range around 37°C. Metabolic processes, notably muscular exertion, convert chemical energy into internal energy deep in the interior. From the interior, energy must flow out to the skin or lungs to be expelled to the environment. During moderate exercise,an 80 kg man can metabolize food energy at the rate 300 kcal/h, do60 kcal/h of mechanical work, and put out the remaining 240 kcal/h of energy by heat. Most of the energy is carried from the body interior out to the skin by forced convection (as a plumber would say), whereby blood is warmed in the interior and then cooled at the skin, which is a few degrees cooler than the body core. Without blood flow, living tissue is a good thermal insulator, with thermal conductivity about 0.210 W/m·°C. Show that blood flow is essential to cool the man's body by calculating the rate of energy conduction in kcal/h through the tissue layer under his skin.Assume that its area is 1.20m2, its thickness is 2.50 cm, and it is maintained at37.0°C on one side and at 34.0°C on the other side.

Homework Equations

P = kA(T_h - T_c) / L

The Attempt at a Solution

I calculated the P using the last information given and get 35.25 J/s = 532 kcal/h
but the answer is 30.3 kcal/h
*"an 80 kg man can metabolize food energy at the rate 300 kcal/h, do60 kcal/h of mechanical work, and put out the remaining 240 kcal/h of energy by heat." I don't know how this is related to the problem!

 

[Filip Larsen]

Welcome to PF!

With the given numbers I get P = 30.24 W = 26.02 kcal/h. Not sure how you got 35.25 W, but your conversion of 35.25 W to kcal/h is clearly wrong (1 W = 3600/4184 kcal/h). Also not sure why the result should be 30.3 kcal/h. Perhaps you got a number or a unit wrong somewhere?

 

[chohocvo]

Welcome to PF!

With the given numbers I get P = 30.24 W = 26.02 kcal/h. Not sure how you got 35.25 W, but your conversion of 35.25 W to kcal/h is clearly wrong (1 W = 3600/4184 kcal/h). Also not sure why the result should be 30.3 kcal/h. Perhaps you got a number or a unit wrong somewhere?

THAX a lot! I did my conversion wrong. I was thinking 1J = 4.186cal :p. After I converse 35.28W to kcal/h, I get 30.3kcal/h.
Your answer is right for the problems. In my book it says the A is 1.4m2. The problem above was a similar problem I found on internet. I forgot to change the value.