Application of PEST and PEHF in magneto-Williamson nanofluid depending on the suction/injection

Abstract This article investigates the flow properties of two-dimensional steady incompressible Williamson nanofluid moving over a stretched exponential surface with the features of both suction/injections. The coupled boundary conditions introduce the influence of thermophoresis boundary as well as the Brownian motion. The assessment of heat transfer is conducted for the two conditions of prescribed exponential order heat flux (PEHF) and prescribed exponential order surface temperature (PEST). The fundamental laws of heat transfer and motion have been implemented mathematically to model the existing flow situations. The non-dimensional variables have been assigned to put the main equations of the current problem into a dimensionless ordinary differential equation (ODEs). This dimensionless system of nonlinear ODEs has been solved on the basis of Homotopy analysis method (HAM). The results under various flow parameters have been graphically plotted in the form of temperature, velocity, and concentration profiles. The three profiles correspondingly modify for the increase in suction/injection parameter, thermophoresis parameter, and Lewis number both in PEST and PEHF case. Moreover, the escalation in the values of Brownian motion parameter, and the thermophoresis parameter respectively causes to enhance and decline the temperature and concentration profile only in case of PEST whereas a respective drop and development is detected in case of PEHF.