Solution_HW7 - Solution for homework Set#7 Consider a crude...

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Solution for homework Set #7: 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 0 (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. a. State necessary assumptions. b. Derive a partial differential equation describing temperature distribution in the crude oil. You do NOT need to solve this equation. c. State boundary conditions. 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.
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