Consider a long has of rectangular cross section and of dimensions a and b on th

Question

Consider a long has of rectangular cross section and of dimensions a and b on the x and y directions, respectively. The thermal conductivity of the material of the has is direction depends such that the thermal conductivity is the x direction, kx is two lines greater than the thermal conductivity is the direction ky. The surfaces at x=0, x=a and y=0 are all maintained at a constant temperature Y1, While the surface at y=b in kept at constant T2. There are no heat sources or sinks in the bar. Given the formulation of the problem for the steady-state temperature distribution T(x, y ). A slab which extends from x = -L to x = L, is initially at a uniform temperature T1. For times I 0, internal energy is generated in the slab at an exponential decay rate per unit values according to phi = phi 0 e-beta r. Where phi 0 and beta are two given positive constants, while the surface at x = L, are kept at the initial temperature T1. Assuming constant thermophysical properties, formulate the protection the unsteady-state temperature distribution T(x, t)in the slab for times t>0.

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