 Recent mathematical development in the Thermal field for application in Engineering & Technology The heat conduction through solids is a very important and interesting problem for its applicability in engineering and technology. The classical theory in this area provides governing equations for the distribution of strain in an elastic medium subject to temperature gradients. In the field equations the heat conduction equation is of parabolic type whereas the equations of motion are of hyperbolic type. As such the coupled problem predicts a finite speed of propagation for predominantly elastic disturbances but an infinite speed for predominantly thermal disturbances which are coupled together. This means that a part of every solution of the equations extends to infinity. Obviously, this result is physically unrealistic but sufficient evidence is available in literature to show that thermal disturbance do propagate in finite speeds.

In order to overcome this paradox there are mainly three different theories put forward by three eminent researchers.

These theories are known as generalized theory of thermo elasticity. During the last four decades there are significant researches following the generalized theory for several application in the field of engineering. The solutions of the governing equations are very unwieldy and the researchers follow various mathematical techniques to deal with the equations for solutions. Recently, the decoupling of the field variables has been made by eigenvalue approach methodology and various problems have been solved and published in esteemed international journals.

In order to cite a few applications, we may mention that thermal shocks and very high temperature inevitably give rise to severe thermal stresses causing catastrophic failure of structural components such as aircraft engines, turbines, space vehicles etc. A sound theory and procedure on thermal stresses are necessary to overcome these failures. It is recognized that the theory of thermal stresses are of great practical utility in the field of engineering and technology like acoustics, aeronautics, chemical and nuclear engineering.

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