Pseudo-similarity solutions of the one-dimensional diffusion equation with applications to the phase change problem

Abstract

New solutions of the diffusion equation may be used to prescribe both the diffusion potential and the diffusional flow rate, along the moving curve X = α ( 1 + β ⋅ T ) 1 / 2 X = \alpha {\left ( {1 + \beta \cdot T} \right )^{1/2}} , as arbitrary power series in the variable ( α ( 1 + β ⋅ T ) 1 / 2 ) \left ( {\alpha {{\left ( {1 + \beta \cdot T} \right )}^{1/2}}} \right ) , where α \alpha and β \beta are arbitrary constants and T T is time.