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

Chapter , Problem 8.24

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Water at 20 C and a flow rate of 0.1 kg/s enters a heated, thin-walled tube with a diameter of 15 mm and length of 2 m. The wall heat flux provided by the heating elements depends on the wall temperature according to the relation where q s,o 104 W/m2 , 0.2 K1 , Tref 20 C, and Ts is the wall temperature in C. Assume fully developed flow and thermal conditions with a convection coefficient of 3000 W/m2 K. (a) Beginning with a properly defined differential control volume in the tube, derive expressions for the variation of the water, Tm(x), and the wall, Ts(x), q temperatures as a function of distance from the tube inlet. (b) Using a numerical integration scheme, calculate and plot the temperature distributions, Tm(x) and Ts(x), on the same graph. Identify and comment on the main features of the distributions. Hint: The IHT integral function DER(Tm, x) can be used to perform the integration along the length of the tube. (c) Calculate the total rate of heat transfer to the water.