Question

derive an expression for net thermal resistance --------

1. if two bodies having thermal connectivity K1 and K2 connected in series .and parallel

Answer 1

Thermal resistance:

It is the measure of opposition to the flow of heat.

$R_{Th}=\frac{d}{kA}$

Here, d is length of the rod, A is cross-sectional area, and k is coefficient of thermal conductivity.

Series combination:

$$\begin{gathered} R_s=R_1+R_2 \\ =\frac{d_1}{k_1{A}_1}+\frac{d_2}{k_2{A}_2} \\ =\frac{d_1{k}_2{A}_2+d_2{k}_1{A}_1}{k_1{k}_2{A}_1{A}_2} \end{gathered}$$

Parallel combination:

$$\begin{gathered} \frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2} \\ =\frac{k_1{A}_1}{d_1}+\frac{k_2{A}_2}{d_2} \\ {R}_p=\frac{d_1{d}_2}{k_1{d}_2{A}_1+k_2{d}_1{A}_2} \end{gathered}$$