1. (6 pts) Fluid at velocity U and temperature To flows into a long, isothermal circular...

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1. (6 pts) Fluid at velocity U and temperature To flows into a long, isothermal circular tube at temperate Tw (with Tw> T). Assume Rep = 200 and Pr = 5. a. Sketch qualitative velocity profiles (u(r)) at multiple axial locations along the tube, illustrating how the flow transitions toward a hydrodynamically fully developed profile. b. Sketch qualitative temperature profiles (T(r)) at multiple axial locations along the tube. Clearly indicate how the thermal development length compares with the hydrodynamic development length. c. Plot the axial profile of the mean temperature of the fluid (T(z)) along the length of the tube. 1. (6 pts) Fluid at velocity U and temperature To flows into a long, isothermal circular tube at temperate Tw (with Tw> T). Assume Rep = 200 and Pr = 5. a. Sketch qualitative velocity profiles (u(r)) at multiple axial locations along the tube, illustrating how the flow transitions toward a hydrodynamically fully developed profile. b. Sketch qualitative temperature profiles (T(r)) at multiple axial locations along the tube. Clearly indicate how the thermal development length compares with the hydrodynamic development length. c. Plot the axial profile of the mean temperature of the fluid (T(z)) along the length of the tube.