Some investigations on steady and unsteady flow of second order thermo viscous fluids

Abstract

The non-Newtonian behavior of fluid flows has been a subject of serious concern to both experimental and theoretical sciences for over one and half centuries. More particularly there has been much activity in this direction between first and second world wars of the last century. During which the subject Continuum Mechanics has been put on rational mathematical newlinefoundation to explain the typical behavior of materials of industry and military newlineimportance. The linear theories based on linear constitutive relations are found to be inadequate to predict the interaction between the mechanical and thermal newlineresponses individually or severally of materials like liquid polymers, fluid newlineplastic, the molten metals etc subjected to stresses has been the motivating newlineforce behind study of the non-linear theories for material description. A non- newlinelinear generalization of the Voigt type materials was proposed by Rivlin and newlineErignen. Some of the non-liner theories proposed so far ( listed in references) newlinehave not taken into account the strong dependence of visco-elastic behavior newlineupon thermal conduction i.e. interaction /interrelation between mechanical and newlinenon mechanical (such as thermal, chemical, electromagnetic etc ) effects even newlinethough the large of amount data of experimental evidence indicate a strong newlinedependence of visco-elastic nature of the fluid upon thermal behavior (Ferry).For example materials such as solid Propellants exhibit a mechanical newlinebehavior at moderate temperature variations , where as a little or no correlation between them would be observed with that under the isothermal condition.