Nonlinear sensitivity and optimization of heat transfer and drag in power law fluid flow over a permeable wedge with variable magnetic field and thermal radiation effects

One of the UN Sustainable Development Goals (SDGs) focuses on preventing energy waste while meeting human energy demands. To contribute to this goal, we optimize the drag force and heat transfer rate in the boundary layer flow of a power-law fluid under the influence of a variable magnetic field and thermal radiation along a nonlinear stretching/shrinking permeable wedge. This optimization is achieved through sensitivity analysis using response surface methodology (RSM). Initially, data is collected using the built-in numerical scheme bvp4c to solve the nonlinear local non-similar problem derived from the Navier-Stokes and the energy equations. The impact of stretching/shrinking wedge along with thermal radiation in both pseudoplastic and dilatant fluids on velocity and temperature profiles, Nusselt number, and skin friction coefficient are discussed graphically. RSM is employed to perform regression analysis and develop expressions for the skin friction and Nusselt number as functions of the coded variables A, B, and C (representing the power law index n, thermal radiation parameter Rd, and velocity ratio parameter ϕ). The optimal impact of these factors is presented in graphs that discuss the sensitivity of skin friction and Nusselt number. From the results, it is revealed that skin friction coefficient is more sensitive to the velocity ratio parameter and Nusselt number is more sensitive to radiation parameter at low and medium levels of power law index and radiation, but it becomes more sensitive to velocity ratio parameter at high level.