Solids Laplace transform technique

Transient heat conduction or mass transfer in solids with constant physical properties (diffusion coefficient, thermal diffusivity, thermal conductivity, etc.) is usually represented by a parabolic partial differential equation. For steady state heat or mass transfer in solids, potential distribution in electrochemical cells is usually represented by elliptic partial differential equations. In this chapter, we describe how one can arrive at the analytical solutions for linear parabolic partial differential equations and elliptic partial differential equations in semi-infinite domains using the Laplace transform technique, a similarity solution technique and Maple. In addition, we describe how numerical similarity solutions can be obtained for nonlinear partial differential equations in semi-infinite domains. 

This problem requires specific techniques not developed in this chapter, such as Laplace transforms, and the reader interested in the derivation of the solution may refer to the textbook of Crank (1976). Defining a as the final distribution ratio, i.e., the amount of solute contained in the solid divided by the amount contained in the liquid when t- co... 

Fig. 2,17. Pressure and temperature dependence of reaction (24). The solid lines are a calculated fit using an inverse Laplace transform/Master Equation technique described in...

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