Simple solutions of the partial differential equation for diffusion (or heat conduction)

It is shown that simple approximate solutions of the partial differential equation for diffusion in finite solids of various shapes and under various conditions can be derived from the simple solutions which are rigorously applicable to linear diffusion in a semi-infinite slab

2006

Scholarcy highlights

  • It is shown that simple approximate solutions of the partial differential equation for diffusion in finite solids of various shapes and under various conditions can be derived from the simple solutions which are rigorously applicable to linear diffusion in a semi-infinite slab
  • For linear diffusion in a finite slab, the solutions show that each end of the slab can be regarded as functioning as the end of a semi-infinite slab for a time during which the central and the average fractional concentrations fall to 0·6 and 0·3, respectively
  • Very simple expressions for the concentration distribution or for average concentration in solids of various shapes are obtained without using any special mathematical method
  • All expressions are obtained in terms of a dimensionless parameter, and it is shown that; the concentration distribution in solids of any material and of various shapes can be derived from one single universal curve
  • Tables and graphs are given showing the relation between the numerical values calculated from the present simple solutions and those obtained by other much more laborious methods
  • Please contact the Royal Society if you find an error you would like to see corrected

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