Answer to Question #300748 in Molecular Physics | Thermodynamics for Heri

Question

A non-insulated pipe passes through a room in which air and walls are at 25°C. The outside

diameter of the pipe is 70 mm, and its surface temperature and emissivity are 200°C and 0.8,

respectively. What are the surface emissive power and irradiation? If the coefficient associated

with free convection heat transfer from the surface is 15W/m2K, what is the rate of heat loss

from the surface per unit length of the pipe?

(E = 2270.48 W/m2

, G = 447.14 W/m2

, Q/l = 997.90 W/m)

Answer 1

Solution;

Given;

$T_{surr}=25°c=298K$

$T_w=200°c=473K$

$\epsilon=0.8$

$D=70mm=0.07m$

$h=15W/m^2K$

Emmissive power;

$E=\epsilon\sigma T_w^4$

Where;

$\sigma=5.67×10^{-8}W/m^2K^4$

Substitute;

$E=0.8×5.67×10^{-8}×473^4$

$E=2270.48W/m^2$

The irradiation,G;

$G=\sigma T_{surr}^4$

$G=5.67×10^{-8}×298^4$

$G=447.14W/m^2$

Rate of heat loss;

$Q=Q_{conv}+Q_{rad}$

$Q=hA(T_w-T_{surr})+\epsilon\sigma A(T_w^4-T_{surr}^4)$

Substitute;

$Q=15×π×0.07(200-25)+0.8×5.67×10^{-8}×π×0.07(473^4-298^4)$

$Q=577.268+420.639=997.91W/m$