On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature

In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Bessel composite function in space and time of the first order and first kind. This is when τ > X. For X > τ the solution is in terms of the Bessel composite function in space and time of the first order and first kind. The wave temperature is a decaying exponential in time when X = τ. An approximate expression for dimensionless temperature was obtained by expanding the binomial series in the exponent in the Laplace domain and after neglecting fourthand higher-order terms before inversion from the Laplace domain. The Fourier model, the damped wave model and the a capite ad calcem in temperature/concentration model solutions are compared side by side in the form of a graph. The a capite ad calcem model solution is seen to undergo the convex to concave transition sooner than the damped wave model. The results of the a capite ad calcem temperature model for distances further from the surface are closer to the Fourier model solution.