Answer to Question #181919 in Physics for Knight

Question

For a temperature difference ΔT = 20C, one slab of material conducts 10W/m2.

What is the rate of heat flow per m2

of surface area when the slabs are placed side

by side with ΔTtot = 20C?

Answer 1

For one slab, for a temperature difference ΔT = 20ºC, the rate of heat flow per unit area is 10 W/m². We know that for one slab $\Delta x$ thick, the rate can be expressed as

$$q=k\frac{\Delta T_\text{tot}}{n\Delta x}=\frac{20k}{\Delta x}=10\text{ W/K m}^2,\\\space\\ \frac{k}{\Delta x}=0.5.$$

So, for n slabs

$$q_n=k\frac{\Delta T_\text{tot}}{n\Delta x}=\frac{10}{n}\text{ W/m}^2.$$