Multiple solutions of melting heat transfer of MHD hybrid based nanofluid flow influenced by heat generation/absorption

This paper presents a hybrid based nanofluid flow past over a stretching/shrinking surface. The magnetic field effect is applied normal to the surface. Additionally, the melting heat transfer effect is also taken into considerations. For the performance of heat transport phenomenon, the heat generation/absorption effect is added. The suitable similarity transformations are used to transform the partial differential equations into dimensionless form of ordinary differential equations. For obtaining solutions of the problem, a bvp4c technique is used to handle the transformed differential equations along with boundary conditions. Dual nature study is performed which is the first and second solutions of the problem. In the first solution, increasing the melting temperature improves the rate of heat transfer. Higher values of the shrinking parameter cause an increase in the velocity profile in the first solution and decreases in the second solution. Further, the temperature of the liquid improves as the thermal radiation and heat generation parameters increase, respectively. The temporal stability analysis represents that only one of the two solutions is stable as time evolves. The numerical results are acquired in the form of tabulated data and graphical structures.

Automated summary

This paper presents a study on the impact of magnetic field effect and melting heat transfer effect on the nanofluid flow over a stretching/shrinking surface. By applying suitable similarity transformations, the partial differential equations are transformed into dimensionless ordinary differential equations, which are then solved using the bvp4c technique. The analysis shows that increasing the melting temperature improves the heat transfer rate. The velocity profile increases with higher values of the shrinking parameter in the first solution and decreases in the second solution. Additionally, the liquid temperature increases with the increase of thermal radiation and heat generation parameters, respectively. The temporal stability analysis reveals that only one of the two solutions is stable as time evolves.