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In this analysis, the stability of MHD stagnation point flow and heat transfer of an electrically conducting viscous incompressible fluid on a horizontally stretching/shrinking permeable cylinder with volumetric heat source are investigated. The cylindrical surface is subjected to a cross flow and a heat flux. This analysis finds applications in the areas of polymeric processing unit due to stretching/shrinking of surface and biofluid flows with therapeutic effects through the arteries, vein and digestive system that have a tube-like structure. Other aspects of the analysis are: magnetic field intensity whose strength can be remotely controlled and embodied generating/absorbing thermal power. The solution of the boundary value problems (BVP) is carried out with MATLAB’s inbuilt solver bvp4c. The most significant findings are recorded as: an increase in magnetic field strength increases the skin friction at the solid surface which is consistent with progressive thinning of boundary layer. This striking result is of interest in industrial applications because it is easy to regulate the magnetic field strength by electromagnetic devices such as controlling the voltage in the electric circuit. There is a point of neutrality of thermal energy distribution during the high fluctuation of temperature irrespective of the presence of heat generation or absorption. This can be attributed to the dominating effect of stretching/shrinking of the surface. The first solution provides stability of the flow with an increase in velocity in the presence of heat sink that is commensurate with the strength.

This study investigates analytically the stability analysis of a nonlinear convective boundary layer (BL) flow of the nanofluids GO-EG and GO-W on a shrinking surface in the presence of a magnetic field and viscous dissipation. We provide a second-order nonlinear ordinary differential equation (NODE) for temperature distribution (TD) and a third-order NODE for velocity profile (VP) coupling based on the thermophysical characteristics of the base fluid and nanofluid as well as similarity transformations (STs) in the fundamental governing equations of momentum and energy. The analytical method HAM is used to answer the equations that have been gathered. In many different industries, such as manufacturing, automotive, microelectronics, and defense, cooling of various types of equipment and devices has very important challenges. To fulfill the demands of the engineering and industrial industries, it is hoped that this issue would significantly improve the heat transformation ratio.