Question

A cylindrical rod of length $l$, thermal conductivity $K$ and area of cross section $A$ has one end in the furnace at temperature $T_1$ and the other end in surrounding at temperature $T_2$. Surface of the rod exposed to the surrounding has emissivity $e$. Also $T_2=T_s+\Delta T$ and $T_s \gg$ $\Delta T$. If $T_1-T_s \propto \Delta T$, then the proportionality constant is

• A. $\left(\frac{1+2 e \sigma \ell T_s^3}{k}\right)$
• B. $\left(1+\frac{4 e \sigma \ell T_s^2}{k}\right)$
• C. $\left(1+\frac{4 e \sigma \ell T_s^3}{k}\right)$
• D. $k\left(1+4 e \sigma 1 T_s\right)$

Answer 1

Answer: (C)

Correct answer is (c) $\left(1+\frac{4 e \sigma \ell T_s^3}{k}\right)$