The rate of conduction heat transfer through a plane wall of dimensions , and , thermal conductivity , and temperatures and on the faces can be determined as

Answer is explained in the explanation section below.

Explanation:

It can be determined by the use of Fourier's law of heat conduction.

Fourier's Law of Heat Conduction: States that, the rate of heat transfer is directly proportional to the temperature change from higher temperature to lower temperature. And it is directly proportional to the area perpendicular to the direction of the heat flow.

Through this statement, we can write the equation of the Fourier's law:

Q = Rate of Heat transfer.

A = Area

dT = Change in Temperature from Higher to Lower = T1 - T2, where T1 is assumed to be higher temperature.

dx = thickness of the wall, through which heat is transferring.

So,

Q is directly proportional to Area perpendicular to the direction of the heat flow.

So, we can write:

Q A

And

Q is directly proportional to temperature change.

So, we can write

Q dT/dx

So, in order to remove the proportionality sign, we need to introduce a constant, which is ( -K) here, Thermal conductivity material of the plane wall.

So,

Q  = - K.A . dT/dx

or

Q = - K . (H.W) . (T1-T2)/L

where, H = height of the wall

W = width of the wall

L = length of the wall.

So, by using the above equation, we can definitely determine the rate of heat transfer through a plane -wall.

Note: for your ease, I have drawn a schematic of the plane-wall and attached in the attachment.

a straight line sloped