Stability analysis of inclined MHD and Joule effects in Ti-alloy and MWCNT/water hybrid nanofluid: Flow separation

Abstract

This research article explains the Joule heating and inclined magnetic field effects on Ti6Al4V-MWCNT/[Formula: see text] hybrid nanofluids toward an exponentially shrinking surface. The system of flow governing equations, which is a coupled system of non-linear PDE’s, are transformed into a system of non-dimensional ODE’s by using suitable similarity transformations. The shooting method along with a fourth order Runge-Kutta approach is used to solve the system of resultant ODE’s. As a result, the dual solutions are identified for this problem. By utilizing the least eigenvalue approach, the first solution is found to be realistic and stable whereas the second solution is not stable. In order to verify the accuracy of outcomes, it is compared with the previously published results, and it is found that the present analysis is accurate upto four decimal places. Further, the streamline profiles are also provided in addition to the least eigenvalue profiles to understand the flow patterns. Finally, the flow separation point is identified. The velocity profiles improves in the case of first solution but it declines in the case of second solution with a rise in the shrinking strength parameter, however the temperature profiles behave in opposite manner. The skin friction coefficient and heat transfer rate of Ti6Al4V-MWCNT/[Formula: see text] based hybrid nanofluids are found to be better with higher values of inclined MHD [Formula: see text] and incline angle [Formula: see text].