Thermodynamics HW Solutions 531

Thermodynamics HW Solutions 531 - 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛...

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Chapter 6 Fundamentals of Convection 6-44 The flow of fluid between two large parallel plates is considered. Using the results of Problem 6-43, a relation for the volumetric heat generation rate is to be obtained using the conduction problem, and the result is to be verified. Assumptions 1 Steady operating conditions exist. 2 The fluid has constant properties. 3 Body forces such as gravity are negligible. V Fluid L T 0 Analysis The energy equation in Prob. 6-44 was determined to be 2 2 2 = L dy T d k V μ (1) The steady one-dimensional heat conduction equation with constant heat generation is 0 0 2 2 = + k g dy T d (2) Comparing the two equation above, the volumetric heat generation rate is determined to be
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Unformatted text preview: 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = L g V & Integrating Eq. (2) twice gives 4 3 2 3 2 ) ( C y C y k g y T C y k g dy dT + + − = + − = & & Applying the two boundary conditions give B.C. 1: y =0 3 = ⎯→ ⎯ = − = C dy dT k y B.C. 2: y = L 2 4 2 ) ( L k g T C T L T & + = ⎯→ ⎯ = Substituting, the temperature distribution becomes ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + = 2 2 2 1 2 ) ( L y k L g T y T & Maximum temperature occurs at y = 0, and it value is k L g T T T 2 ) ( 2 max & + = = which is equivalent to the result k T T T 2 ) ( 2 max V + = = obtained in Prob. 6-43. 6-20...
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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