Question

Water enters a large circular pipe of diameter D with a mean temperature of Tmi and mass flow rate of ml . The pipe is half-embedded in insulation as shown in the figure below. Conditions are such that a linearly- increasing heat flux is applied to the exposed top half of the pipe. a. If the heat flux profile is q-q + Or , derive an equation that describes the mean temperature of the water as a function of its distance x along the pipe. Qualitatively plot on Tm vs. x axes the b. If m-0.2 kg/s, Tm-30°C, q-800 W/m, 0-10,000W/m/m, and D- 0.25m, calculate the c. If the pipe is 10 m long, will the flow reach hydrodynamic and thermal fully-developed expected variation in the mean temperature mean fluid temperature at x=2m. conditions?

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