hw1 - a constant wall temperature. Let / s T T = and * / r...

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Transport in Thermofluids ME220B Homework #1 Problem 1: Consider the problem illustrated in Figure 27-3, in which an invisid fluid of initial temperature i T is directed between parallel plates that (each) deliver a constant heat flux s q to the fluid. Using the dimensionless temperature and spatial variables: ( ) / ( / ) i s T T aq k ϑ = - , * / x x a = and * / y y a = , show that the heat equation may be expressed in dimensionless form as: 2 2 * * Ua x y α = . with the boundary conditions: * * 0 / 0 y y = = , * * 1/2 / 1 y y = = , * ( 0) 0 x = = . Solve the heat equation to demonstrate the solution given by Eq. (7) in the notes. Problem 2: Solve the described in Problem 1 and show that the local Nusselt for heat transfer to the flow is given by Eq. (8) in the notes. Problem 3: Derive the heat equation for pipe flow for fully-developed heat transfer with
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Unformatted text preview: a constant wall temperature. Let / s T T = and * / r r R = . Numerically solve the heat equation for pipe flow with a constant wall temperature to determine the D Nu . Solve for the downstream mean fluid temperature variation in terms of / s T T = , D Nu , m , and . Show that the mean dimensionless temperature is given by 1 * * 2 ( / ) m z m r dr = . Let * ( 0) r = = when z = , and determine ( 0) m z = . Consider fluid, = 0.15x10-6 m 2 /s, flowing with a mean velocity of 30 cm/s, through a constant wall temperature pipe having a 1 cm interior diameter (ID). Plot the dimensionless temperature distribution through the pipe at the distances z = 0, 1, 2 and 5 m....
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