STEADY -STATE HEAT CONDUCTION

Steady state means that temperature in an object may vary by location but it does not change with time.

Conduction in rectangular objects

Fourier's law describes the rate of heat conduction in a solid.

Boundary Conditions

x = x₁ T = T₁

x = x₂ T = T₂

Separating the variables,

Integrating from x₁ to x (some interior location within the slab)

if integrated from x₁ to x₂

where L = thickness of the slab.

Thermal Resistance concept:

In the flow of electricity, the electrical resistance is determined from the ratio of electric potential divided by the electric current. Similarly, we may consider heat resistance as a ratio of the driving potential (temperature difference) divided by the rate of heat transfer.

Thus,

or,

units of resistance = °C/W