Question

A sample water heating system consists of a thick-walled tube of I.D. 25 mm, O.D 40 mm, and length 2.274 m. Water at the rate of 5 kg/min enters at ${20}^{\circ }C$ and leaves at ${70}^{\circ }C.$ Electrical heating within the wall of the tube generates heat at a uniform rate of ${10}^{7}W/m^3.$ If the inner surface temperature of the tube is ${80}^{\circ }C,$ the heat transfer coefficient at the outlet is

• A. $97500W/m^{2}K$
• B. $9275000W/m^{2}K$
• C. $9.27W/m^{2}K$
• D. $9750W/m^{2}K$

Answer 1

The correct option is D $9750W/m^{2}K$


$\begin{array}{cc}{q}_{g}volume& =q{A}_s\\ q_g\frac{\pi }{4}(D_0^2-D_i^2)L& =q\pi D_{i}L\\ q& =\frac{q_g(D_0^2-D_i^2)}{4D_i}\\ q& =\frac{{10}^7\times ({0.04}^2-{0.025}^2)}{4\times 0.025}=97500W/m^2\\ q& =h(T_s-T_0)\\ h& =\frac{q}{T_s-T_0}=\frac{97500}{80-70}=9750W/m^{2}K\end{array}$