Dimensional Thermal Diffusion into Two Different Phases

APPENDIX ONE-DIMENSIONAL THERMAL DIFFUSION INTO TWO DIFFERENT PHASES 

Assume that a quantity of heat,, is initially deposited as a spatial and temporal delta function at x = 0 and t = 0. The subsequent onedimensional diffusion of heat into a homogeneous medium and the resultant temperature change as a function of x (distance from the position 

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Note that when 1 then aj = 1/2 and Eq. (118) becomes identical to Eq. (115) when x = 0. 

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