Page 150 - Industrial Ventilation Design Guidebook

i I 2 CHAPTER 4 PHYSICAL FUNDAMENTALS

FIGURE 4.28 Cylindrical and spherical coordinates.

4.3,3.2 One-Dimensional Steady-State Heat Conduction
Infinite Plate
A simple case of heat conduction is a plate of finite thickness but infinite
in other directions. If the temperature is constant around the plate, the mate-
rial is assumed to have a constant thermal conductivity. In this case the linear
temperature distribution and the heat flow through the plate is easy to deter-
mine from Fourier's law (Eq. (4.154)).
In a case similar to Fig. 4.23 the heat conduction equation (Eq. (4.180))
becomes

In steady-state conditions the right side of Eq. (4.180) is zero, and no heat genera-
tion takes place; the thermal conductivity in the one-dimensional case is constant.
The solution of Eq. (4.182) is

with boundary conditions

This gives the linear temperature distribution

Substituting the above equation into Eq. (4.154) gives the heat flow through
the plate:

Axial-Symmetric Case
For the axial-symmetric case the equation is