الفهرس 
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Abstract
In this thesis, a careful study of the general theory of heat conduction through isotropic solids is presented. The author reviewed the main mathematical methods used for the solution of transient heat conduction problems including exact analytical methods for linear problems as well as approximate and numerical methods for non-linear problems. The application of the variational principles to heat conduction problems is given.
The Gauss principle of least constraint, which is a restricted variational principle applied in mechanics, is presented and applied for the solution of both linear and non-linear problems of heat conduction through a semi-infinite body and an infinite circular solid cylinder. The Gauss principle of least constraint is a true minimum principle, its basic point is a functional which is attached to the differential equation and whose minimum is zero.
Results of the problems are illustrated in figures and tables, and are compared with those of other authors, when available.
Discussion of the error produced by the approximate method and how it is minimized is given.