Functionally graded materials are intentionally fabricated to establish a spatial distribution of properties in the final product. Consider an L x L two-dimensional object with L = 20 mm. The thermal conductivity distribution of the functionally graded material is k(x) = 20 W/m ·
K+ (7070 W/m^5/2  · K) x^3/2. Two sets of boundary conditions, denoted as cases 1 and 2, are applied.

(a) Determine the spatially averaged value of the thermal conductivity . Use this value to estimate the heat rate per unit length for cases 1 and 2.
(b) Using a grid spacing of 2 mm, determine the heat rate per unit depth for case 1. Compare your result to the estimated value calculated in part (a).
(c) Using a grid spacing of 2 mm, determine the heat rate per unit depth for case 2. Compare your result to the estimated value calculated in part (a).

Transcribed Image Text:

Surface 1 Surface 3. y Surface 4 Surface 2 -k(x)