Question

A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of $5^{\circ }C.$ The tube wall has inner and outer radii of 25 and 75 mm, respectively, and a thermal conductivity of 10 W/m-K. The thermal contact resistance between the heater and the outer surface of the tube (per unit length of the tube) is 0.01 mK/W. The outer surface of the heater is exposed to a fluid with $T_{\infty }={10}^{\circ }C$ and a convection coefficient of $h=100W/m^{2}K$. The heater power per unit length of the tube (W/m) required to maintain the heater at a uniform temperature of ${25}^{\circ }C$ is :

• A. 2377
• B. 706.38
• C. 727.67
• D. 1434.85

Answer 1

The correct option is D 1434.85




Thermal circuit:



Total heat transfer rate $\left(Q\right)=Q_1+Q_2$

$=\frac{(T_0-T_{\infty })}{\frac{1}{h{A}_0}}+\frac{(T_0-T_1)}{\frac{ln\left(\frac{r_2}{r_1}\right)}{2\pi kL}+0.01}$

$=\frac{(25-10)}{\frac{1}{100\times 2\pi \times 0.075}}+\frac{(25-5)}{\frac{ln\left(\frac{75}{25}\right)}{2\pi \times 10}+0.01}$

= 706.38 +727.67

Q = 1434.52 W/m