Functionally graded materials are intentionally
Chapter 4, Problem 4.56(choose chapter or problem)
Functionally graded materials are intentionally fabri-cated to establish a spatial distribution of properties inthe final product. Consider an L?Ltwo-dimensionalobject with L?20 mm. The thermal conductivity dis-tribution of the functionally graded material is k(x)?20 W/m?K?(7070 W/m5/2?K) x3/2. Two sets of boundaryconditions, denoted as cases 1 and 2, are applied.Case Surface Boundary Condition11T?100C2T?50C3Adiabatic4Adiabatic21Adiabatic2Adiabatic3T?50C4T?100C(a) Determine the spatially averaged value of the ther-mal conductivity . Use this value to estimate theheat rate per unit length for cases 1 and 2.(b) Using a grid spacing of 2 mm, determine the heatrate per unit depth for case 1. Compare your resultto the estimated value calculated in part (a).(c) Using a grid spacing of 2 mm, determine the heatrate per unit depth for case 2. Compare your resultto the estimated value calculated in part (a).
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