SolutionHW_C8 - Homework Set#8 Due date by 11:00 am Problem...

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Homework Set #8: Due date: 11/17/06, by 11:00 am. Problem # 1: The crude oil with temperature-independent physical properties is in fully developed laminar flow between two flat surfaces placed a distance 2B apart (see the figure in Problem 1, homework set # 7.) For z < 0 the fluid is uniform at T = T 1 . For z > 0 heat is added at a constant, uniform flux q 0 at both walls. It is assumed that heat conduction in the flow direction is negligible compared to energy convection, and that the viscous works is negligible. a. State necessary assumptions. b. Obtain a partial differential equation for temperature distribution in the crude oil, using the equation of energy in terms of temperature in the lecture slides or in Table B.9 of BSL, and the assumptions in (a). You do NOT need to solve this equation. But you need to show how your assumptions can be used to simplify the general equation of energy. Answer: 1. Assumptions a. The heat conduction in the z-direction is negligible compared to energy convection b. Works done by viscous stresses are negligible. c. The oil is incompressible d. Steady state heating 2. Set up a partial differential equation for temperature from the general equation of energy 2 ˆ p x y z T T
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