Effects of variable magnetic field and partial slips on the dynamics of Sutterby nanofluid due to biaxially exponential and nonlinear stretchable sheets

Based on both the characteristics of shear thinning and shear thickening fluids, the Sutterby fluid has various applications in engineering and industrial fields. Due to the dual nature of the Sutterby fluid, the motive of the current study is to scrutinize the variable physical effects on the Sutterby nanofluid flow subject to shear thickening and shear thinning behavior over biaxially stretchable exponential and nonlinear sheets. The steady flow mechanism with the variable magnetic field, partial slip effects, and variable heat source/sink is examined over both stretchable sheets. The analysis of mass and heat transfer is carried out with the mutual impacts of thermophoresis and Brownian motion through the Buongiorno model. Suitable transformations for both exponential and nonlinear sheets are implemented on the problem's constitutive equations. As a result, the nonlinear setup of ordinary differential equations is acquired which is further numerically analyzed through the bvp4c technique in MATLAB. The graphical explanation of temperature, velocity, and concentration distributions exhibits that the exponential sheet provides more significant results as compared to the nonlinear sheet. Further, this study revealed that for the shear thickening behavior of Sutterby nanofluid, the increasing values of Deborah number increase the axial velocity.