Water at 20C and a flow rate of 0.1 kg/s enters a

Chapter 8, Problem 8.24

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Water at 20C and a flow rate of 0.1 kg/s enters a heated,thin-walled tube with a diameter of 15 mm and length of2 m. The wall heat flux provided by the heating ele-ments depends on the wall temperature according to therelationwhere qs,o?104W/m2, ??0.2 K?1, Tref?20C, andTsis the wall temperature in C. Assume fully devel-oped flow and thermal conditions with a convectioncoefficient of 3000 W/m2?K.(a) Beginning with a properly defined differential con-trol volume in the tube, derive expressions for thevariation of the water, Tm(x), and the wall, Ts(x), temperatures as a function of distance from thetube inlet.(b) Using a numerical integration scheme, calculateand plot the temperature distributions, Tm(x) andTs(x), on the same graph. Identify and comment onthe main features of the distributions. Hint: TheIHTintegral function DER(Tm,x) can be used toperform the integration along the length of the tube.(c) Calculate the total rate of heat transfer to the water.