Surface temperature at o qccc x0 t is t initially the plate

Question

Radiation is suddenly directed at the surface of a semi-infinite plate of conductivity k and thermal diffusivity D. Due to the thermal absorption characteristics of the material the radiation results in a variable energy generation rate given by

q^m(x) = q^m₀ e^-bx,

Where and b are constants and x is distance along the plate. Surface temperature at o qccc x₀. T. is T Initially the plate is at uniform temperature Write the heat equation and boundary conditions.