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
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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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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