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1. The challenge of convection is that our flow geometry is often too complex to determine the exact velocity profile, u(y), and temperature profile, T(y). This is why we will later use simplified correlations to determine h. However, there are a few very simple geometries where these solutions exist. Consider a laminar fluid flow over the top of a flat plate. Assume that the flow has the velocity and temperature profiles listed below at one x-location on the plate, where A through G are constants. Answer the questions below: u(y) = Ay+ By² - Cy³ T(y) = D + Ey + Fy² - Gy³ a) Using the above profiles, obtain the exact expressions for the wall shear stress, 7, and the heat transfer coefficient, hx, at this location on the plate. b) Compare the heat transfer coefficients and wall shear stresses you would obtain if the fluid with the above profiles were air vs. water (both at T = 300K) by looking up relevant properties from the back of the book. For your comparison, calculate the ratio of Twater/ Tair and hx, water/hx,air. Assume the u and I profiles are unchanged and that the plate and fluids have the same temperatures (T, and T.) for both cases.

1. The challenge of convection is that our flow geometry is often too complex to determine the exact velocity profile, u(y), and temperature profile, T(y). This is why we will later use simplified correlations to determine h. However, there are a few very simple geometries where these solutions exist. Consider a laminar fluid flow over the top of a flat plate. Assume that the flow has the velocity and temperature profiles listed below at one x-location on the plate, where A through G are constants. Answer the questions below: u(y) = Ay+ By² - Cy³ T(y) = D + Ey + Fy² - Gy³ a) Using the above profiles, obtain the exact expressions for the wall shear stress, 7, and the heat transfer coefficient, hx, at this location on the plate. b) Compare the heat transfer coefficients and wall shear stresses you would obtain if the fluid with the above profiles were air vs. water (both at T = 300K) by looking up relevant properties from the back of the book. For your comparison, calculate the ratio of Twater/ Tair and hx, water/hx,air. Assume the u and I profiles are unchanged and that the plate and fluids have the same temperatures (T, and T.) for both cases.

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. The challenge of convection is that our flow geometry is often too complex to determine the exact velocity profile, u(y), and temperature profile, T(y). This is why we will later use simplified correlations to determine h. However, there are a few very simple geometries where these solutions exist. Consider a laminar fluid flow over the top of a flat plate. Assume that the flow has the velocity and temperature profiles listed below at one x-location on the plate, where A through G are constants. Answer the questions below: u(y) = Ay+By² - Cy³ T(y) = D + Ey + Fy² - Gy³ a) Using the above profiles, obtain the exact expressions for the wall shear stress, 7, and the heat transfer coefficient, hx, at this location on the plate. b) Compare the heat transfer coefficients and wall shear stresses you would obtain if the fluid with the above profiles were air vs. water (both at T = 300K) by looking up relevant properties from the back of the book. For your comparison, calculate the ratio of Twater/ Tair and hx, water/hx, air. Assume the u and I profiles are unchanged and that the plate and fluids have the same temperatures (T, and T) for both cases.
Transcribed Image Text:1. The challenge of convection is that our flow geometry is often too complex to determine the exact velocity profile, u(y), and temperature profile, T(y). This is why we will later use simplified correlations to determine h. However, there are a few very simple geometries where these solutions exist. Consider a laminar fluid flow over the top of a flat plate. Assume that the flow has the velocity and temperature profiles listed below at one x-location on the plate, where A through G are constants. Answer the questions below: u(y) = Ay+By² - Cy³ T(y) = D + Ey + Fy² - Gy³ a) Using the above profiles, obtain the exact expressions for the wall shear stress, 7, and the heat transfer coefficient, hx, at this location on the plate. b) Compare the heat transfer coefficients and wall shear stresses you would obtain if the fluid with the above profiles were air vs. water (both at T = 300K) by looking up relevant properties from the back of the book. For your comparison, calculate the ratio of Twater/ Tair and hx, water/hx, air. Assume the u and I profiles are unchanged and that the plate and fluids have the same temperatures (T, and T) for both cases.
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