Heat transfer and flow of a modified second grade fluid

TLDR: In this paper, the authors examined the fully developed flow of a generalized fluid of second grade between heated parallel plates, due to a pressure gradient along the plate, and obtained the solution for the case when the temperature changes only in the direction normal to the plates for the two most commonly used viscosity models.

Abstract: We examine the fully developed flow of a generalized fluid of second grade between heated parallel plates, due to a pressure gradient along the plate. The constant coefficient coefficient of shear viscosity of a fluid of second grade is replaced by a shear dependent viscosity with an exponent m. If the normal stress coefficients are set equal to zero, this reduces to the standard power-law model. We obtain the solution for the case when the temperature changes only in the direction normal to the plates for the two most commonly used viscosity models, i.e. (i) when the viscosity does not depend on temperature, and (ii) when the viscosity is an exponentially decaying function of temperature.