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1. Consider a Couette flow problem in which a fluid of viscosity u is flowing in between two plates. The top plate is moving with a speed of u, and has a temperature of Te whereas the bottom plate is fixed and has a temperature of Tw. In addition, a pressure gradient exists along the length of the plate, in the direction of the flow. Determine the enthalpy profile. Plot it with a suitable choice of numerical values a. for a non-zero pressure gradient and b. for zero pressure gradient and compare the two profiles, commenting on the physical impact of the pressure gradient. Answer: y ap D² D ax 2µ Pr h(y) = hw + (h, – hw)+ už (y+ Dy D3y 24 Pr dp y Dy Pr 6D 12 24

1. Consider a Couette flow problem in which a fluid of viscosity u is flowing in between two plates. The top plate is moving with a speed of u, and has a temperature of Te whereas the bottom plate is fixed and has a temperature of Tw. In addition, a pressure gradient exists along the length of the plate, in the direction of the flow. Determine the enthalpy profile. Plot it with a suitable choice of numerical values a. for a non-zero pressure gradient and b. for zero pressure gradient and compare the two profiles, commenting on the physical impact of the pressure gradient. Answer: y ap D² D ax 2µ Pr h(y) = hw + (h, – hw)+ už (y+ Dy D3y 24 Pr dp y Dy Pr 6D 12 24

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. Consider a Couette flow problem in which a fluid of viscosity u is flowing in between two plates. The top plate is moving with a speed of u, and has a temperature of Te whereas the bottom plate is fixed and has a temperature of Tw. In addition, a pressure gradient exists along the length of the plate, in the direction of the flow. Determine the enthalpy profile. Plot it with a suitable choice of numerical values a. for a non-zero pressure gradient and b. for zero pressure gradient and compare the two profiles, commenting on the physical impact of the pressure gradient. Answer: G-O) (-)-G-呢,) y ap D2 ax 2µ (y Dy3 D3y 24 h(y) = hw + (he - hw)+ Pr u? Ue D. (y3 Dy 2 Pr dp Pr (dp 6D 12 24
Transcribed Image Text:1. Consider a Couette flow problem in which a fluid of viscosity u is flowing in between two plates. The top plate is moving with a speed of u, and has a temperature of Te whereas the bottom plate is fixed and has a temperature of Tw. In addition, a pressure gradient exists along the length of the plate, in the direction of the flow. Determine the enthalpy profile. Plot it with a suitable choice of numerical values a. for a non-zero pressure gradient and b. for zero pressure gradient and compare the two profiles, commenting on the physical impact of the pressure gradient. Answer: G-O) (-)-G-呢,) y ap D2 ax 2µ (y Dy3 D3y 24 h(y) = hw + (he - hw)+ Pr u? Ue D. (y3 Dy 2 Pr dp Pr (dp 6D 12 24
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