Heat transfer from the human head can be quite different from heat transfer from

ID: 1859096 • Letter: H

Question

Heat transfer from the human head can be quite different from heat

transfer from the human hand. To evaluate the heat transfer rate, surface temperatures of

the head and hand are measured. It turns out that surface temperature of the head (35C)

is much higher than that of the hand (29%uF0B0C) during winter time. Heat transfer coefficient

h is 15 W/m2 %uF0B0C and the total hemispherical emissivity of the head surface is 0.9.

(A) Assume that the surface temperature of the head is uniform and the head can be

approximated as a sphere of radius of r0 (estimate r0 from your own head). What is the

surface area of the head? Calculate the convection and radiation heat transfer rates from

the head to the surrounding environment if the environment temperature is 5C and the

air temperature is 7C.

(B) Determine the convection and radiation heat transfer rates from the hands assuming

that the hands have the same surface area as the head.

convection and radiation? What is the total heat loss from the hands to the surrounding,

considering both convection and radiation? What is the ratio of total heat loss of the head

to that of the hands?

q =e %u03C3 T4 A

where

q = heat transfer per unit time (W)

%u03C3 = 5.6703 10-8 (W/m2K4) - The Stefan-Boltzmann Constant

T = absolute temperature Kelvin (K)

A = area of the emitting body (m2)

a)my head's radius ia around 5 cm

area of the head = 4*pi * r0^2 = .0314 m^2

heat transfer due to radiation = 0.9*5.67*10^-8 * .0314* ( 308^4 - 278^4) W

= 4.85 W

due to convection = h * A * ( t1 - t2) = 15 * .0314 * (35-7) = 13.188 W

b) from hands heat loss due to radiation = 0.9 * 5.67 * 10 ^ -8 * .0314 * (302^4 - 278^4) = 3.76 W

due to convection = h * A * ( t1 - t2 ) = 15 * .0314 * (29 - 7) = 10.362 W

c) total heat loss from

head = 4.85 + 13.188 = 18.038W

hands = 3.76 + 10.362 = 14.122 W

d) ratio = 18.038 / 14.122 = 1.277

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