1. A film has a length L = 8 cm (x direction) and width W =...
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1. A film has a length L = 8 cm (x direction) and width W = 10 cm (y direction) with a temperature T = 50C fixed at the upper boundary and T. = 25C fixed at the remaining 3 boundaries. The film is 0.1 cm thick and insulated on its z planes, so you may assume the heat flow is 2 dimensional. In class, we derived an equation for the steady-state, 2-dimensional temperature profile for this type of geometry. The material has a thermal conductivity k = 100 W/(m*K). T(x, y) = Tc + (T - Tc) 2[1 cos(nn)] (TTX) -sin (nV n=in sinh| )sinh("[) a. Determine the rate of heat flow at steady-state into the system at the upper boundary (y=W). The heat flow in the y direction is defined as Qy = fqydA, where q, is the flux in the y- direction. Use a value of at least n=50. b. Determine the rate of heat flow at steady-state out of the system at the right boundary (x=L). Note that Qx = f qxdA Use a value of at least n=50. T8 C. If you were to instead determine the temperature profile numerically by T7 discretizing the domain as shown to the right, what would be the values of the unknown temperatures? d. Bonus (+4): If the bottom of the system was insulated such that the boundary condition changed from T(x, 0) = Tc to = 0, what would be the new equation for the temperature profile? yly=0 T1 T4 T2 T5 T3 T6 1. A film has a length L = 8 cm (x direction) and width W = 10 cm (y direction) with a temperature T = 50C fixed at the upper boundary and T. = 25C fixed at the remaining 3 boundaries. The film is 0.1 cm thick and insulated on its z planes, so you may assume the heat flow is 2 dimensional. In class, we derived an equation for the steady-state, 2-dimensional temperature profile for this type of geometry. The material has a thermal conductivity k = 100 W/(m*K). T(x, y) = Tc + (T - Tc) 2[1 cos(nn)] (TTX) -sin (nV n=in sinh| )sinh("[) a. Determine the rate of heat flow at steady-state into the system at the upper boundary (y=W). The heat flow in the y direction is defined as Qy = fqydA, where q, is the flux in the y- direction. Use a value of at least n=50. b. Determine the rate of heat flow at steady-state out of the system at the right boundary (x=L). Note that Qx = f qxdA Use a value of at least n=50. T8 C. If you were to instead determine the temperature profile numerically by T7 discretizing the domain as shown to the right, what would be the values of the unknown temperatures? d. Bonus (+4): If the bottom of the system was insulated such that the boundary condition changed from T(x, 0) = Tc to = 0, what would be the new equation for the temperature profile? yly=0 T1 T4 T2 T5 T3 T6
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Related Book For
Fundamentals Of Momentum Heat And Mass Transfer
ISBN: 9781118947463
6th Edition
Authors: James Welty, Gregory L. Rorrer, David G. Foster
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