7.3 Text Problem 8.24 in 7th Ed, 8.19 in 8th Ed. 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 of 2 m. The wall heat flux provided by the heating ele- ments depends on the wall temperature according to the relation q?(x) = 9,[1 + a(T. - Tred)] where ". = 104 W/m, a = 0.2 K-!, Tref = 20C, and T, is the wall temperature in C. Assume fully devel- oped flow and thermal conditions with a convection coefficient of 3000 W/m.K. (a) Beginning with a properly defined differential con- trol volume in the tube, derive expressions for the variation of the water, Tm(x), and the wall, T.(x), temperatures as a function of distance from the tube inlet. (b) Using a numerical integration scheme, calculate and plot the temperature distributions, T.(x) and T.(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. Hints: For part a, I got: dTm = TTDH [hTmn +75.0(1 a Tres) h - aqs. - Tm dx mCp For part b, try using an ODE solver in Matlab to solve part b. (Ts(x) and Tm(x) can be determined analytically, but you don't need to do that.)