Optimization of non-uniform heat source/sink in a viscoplastic nanofluid with thermal radiation: the case of Bingham-Papanastasiou rheological theory

Abstract

Viscoplasticity is defined by a yield stress where materials exhibit no deformation below this yield stress, while above it, they undergo deformation and flow in accordance with various constitutive relations. The application of viscoplastic fluid in manufacturing procedures necessitates the inclusion of stress-strain relations of Bingham rheological for the simulation of thermal transfer in these fluids. The theoretical framework is developed by utilizing the Bingham-Papanastasiou model in conjunction with the laws of momentum and energy equations through a cylindrical surface saturated in a requisite porous medium. In addition, the radiation and irregular heat source/sink effects by incorporating ethylene-glycol-based ZnO nanofluid are also involved in the current exploration. The bvp4c solver is used to numerically solve a set of non-linear transformed equations that result from the suggested theoretical framework. The profile of temperature distribution is lowered, as a result, of the suppression of convective transport and shear-induced heating with a superior impact of the local Bingham number, ${\Sigma }_a$. In addition, larger values of ${\Sigma }_a$ indicate that the gap between the curves of the velocity field is higher compared to the plot shown for the temperature field. Moreover, the expansion or stretching rate of the cylindrical surface becomes stronger owing to greater values of the local growth parameter.