STEADY HEAT CONDUCTION IN PLANE WALLS

1) Heat flow through a wall is one dimensional when the temperature of the wall varies in one direction only.

a) The small thickness of the wall causes the temperature gradient in that direction to be large. Further, if the air temperatures in and outside the house remain constant, and then heat transfer through the wall of a house can be modeled as steady and one-dimensional.

b) The temperature of the wall in this case will depend on one direction only (say the x-direction) and can be expressed as T(x).

c) But  for steady operation, since there is no change in the temperature of the wall with time at any point. Therefore, the rate of heat transfer into the wall must be equal to the rate of heat transfer out of it. In other words, the rate of heat transfer through the wall must be constant.

d) Fourier’s Law of heat conduction

e) Consider a plane wall of thickness L and average thermal conductivity k. The two surfaces of the wall are maintained at constant temperatures of T₁ and T₂