HW_C7 - oil You do NOT need to solve this equation c State boundary conditions Problem 2 Consider a crude oil flowing in an annular space of a

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Homework Set #7: Due date: 11/10/06, by 11:00 am. Problem # 1: A crude oil rich in wax must be heated to enable its transportation in an annular space of a production well. If the clearance between the two coaxial casings forming the annulus is significantly smaller than the radius of the inner casing, one can treat flow in this annulus as that between two flat surfaces. In this sense, the crude oil with temperature-independent physical properties is in fully developed laminar flow between two flat surfaces placed a distance 2B apart, as shown in the below figure. 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. Derive a partial differential equation describing temperature distribution in the crude
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Unformatted text preview: oil. You do NOT need to solve this equation. c. State boundary conditions. Problem # 2: Consider a crude oil flowing in an annular space of a horizontal production well. The two coaxial casings forming the annulus have inner and outer radii κ R and R, respectively. Heat is added to the fluid through the inner cylinder wall at the rate q (heat per unit are per unit time), and the outer cylinder wall is thermally insulated. Note that in this problem you must use a cylindrical coordinate system. It is assumed that heat conduction in the flow direction is negligible compared to energy convection, and that the viscous works is negligible. d. State necessary assumptions. e. Derive a partial differential equation describing temperature distribution in the crude oil. You do NOT need to solve this equation. f. State boundary conditions....
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This note was uploaded on 12/14/2011 for the course PGE 312 taught by Professor Peters during the Spring '08 term at University of Texas at Austin.

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