3.) Consider the flow through a circular pipe which is both hydrodynamically and thermally fully- developed....

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3.) Consider the flow through a circular pipe which is both hydrodynamically and thermally fully- developed. This flow is pressure-driven, laminar, with a parabolic velocity profile. A uniform heat transfer rate is supplied along the entire length. A sketch of the situation is given below: 8.0m Uniform heat flux, h 10 cm Thick oil is being pumped through this pipe with the following pertaining: The thermophysical properties remain constant throughout the entire flow. The density of the fluid, p = 870 kg/m The kinematic viscosity, v = 3 10-3 m/s The specific heat, cp = 1.70 kJ/kg-K The thermal conductivity of the fluid, k = 0.146 W/m-K The volumetric flowrate through the pipe, Q = 7.8 10-4 m3/s The wall temperature at the cross section labelled as "1" is equal to Tw1 = 150.0 C The wall temperature at the cross section labelled as "2" is equal to Tw2 = 160.0 C a.) Determine the approximate mean temperature of the fluid, Tm1, at cross-section "1" ? b.) What is the rate of heat input to the fluid, q, between "1" and "2" ? c.) Confirm that the flow regime of this problem is suitable for the technique used to make your calculations. Show this and explain. 3.) Consider the flow through a circular pipe which is both hydrodynamically and thermally fully- developed. This flow is pressure-driven, laminar, with a parabolic velocity profile. A uniform heat transfer rate is supplied along the entire length. A sketch of the situation is given below: 8.0m Uniform heat flux, h 10 cm Thick oil is being pumped through this pipe with the following pertaining: The thermophysical properties remain constant throughout the entire flow. The density of the fluid, p = 870 kg/m The kinematic viscosity, v = 3 10-3 m/s The specific heat, cp = 1.70 kJ/kg-K The thermal conductivity of the fluid, k = 0.146 W/m-K The volumetric flowrate through the pipe, Q = 7.8 10-4 m3/s The wall temperature at the cross section labelled as "1" is equal to Tw1 = 150.0 C The wall temperature at the cross section labelled as "2" is equal to Tw2 = 160.0 C a.) Determine the approximate mean temperature of the fluid, Tm1, at cross-section "1" ? b.) What is the rate of heat input to the fluid, q, between "1" and "2" ? c.) Confirm that the flow regime of this problem is suitable for the technique used to make your calculations. Show this and explain.