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

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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.

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