A study of quadratic thermal radiation and quadratic convection on viscoelastic material flow with two different heat source modulations

Abstract

In many practical applications such as plastic manufacturing and the polymer industries, the temperature difference is substantially large as a result the density of the working fluid alters nonlinearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, as it has a considerable impact on the flow and heat transport characteristics of the working fluid. Here, the non-Newtonian viscoelastic material flow driven by stretching of elastic sheet subjected to NBA and quadratic form of Rosseland thermal radiation is investigated. Two different heat source modulations, viz., exponential space-dependent heat source, and a temperature-related heat source are analyzed. The viscoelastic material obeys the quadratic Boussinesq approximation. The fluctuation of plate temperature is linear and the transpiration (plate mass suction) is also accounted. The Darcy law is employed for a porous medium. The dimensionless profiles of the velocity, heat transport rate, and temperature are simulated by solving the nonlinear two-point boundary value system by employing the finite difference-based routine. The significance of key parameters involved in the problem is studied on various flow fields via surface and streamline plots. It is found that the quadratic convection mechanism enhanced the Nusselt number; however, the quadratic thermal radiation aspect reduced the Nusselt number. The higher velocities are captured in the case of quadratic thermal convection as compared with its absence. Whereas this trend is quite opposite for the thermal field. The velocity of viscoelastic material positively correlated with the viscoelastic material parameter. Further, the outcome of this investigation helps in determining the key parameters which facilitate the desired heat transport rate.