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Q: Steady-state temperatures at selected nodal points of the symmetrical section of a flow channel are known to be T2 = 95.47°C, T3 = 117.3°C, T5 = 79.79°C, T6 = 77.29°C, T8 = 87.28°C, and T10 = 77.65°C. The wall experiences uniform volumetric heat generation of q = 106 W/m3 and has a thermal conductivity of k = 10W/m · K. The inner and outer surfaces of the channel experience convection with fluid temperatures of T8,i = 50°C and T8,o = 25°C and convection coefficients of hi = 500 W/m2 · K and ho = 250 W/m2 · K.
(a) Determine the temperatures at nodes 1, 4, 7, and 9.
(b) Calculate the heat rate per unit length (W/m) from the outer surface A to the adjacent fluid.
(c) Calculate the heat rate per unit length from the inner fluid to surface B.
(d) Verify that your results are consistent with an overall energy balance on the channel section.
