Quadruple solutions of mixed convection flow of magnetohydrodynamic nanofluid over exponentially vertical shrinking and stretching surfaces: Stability analysis

Background and objective: The last two and half decades are witnessed a great surge in the use convective fluids for enhancement of heat transfer of minerals ethylene glycol, oil and water due to their numerous applications in the industrial segments including chemical production, microelectronics, power generation, transportation, and air-conditioning. For this purpose, different procedures were applied to upgrade the thermal conductivity of common fluid but could not. Further, Choi and Eastman in 1995 introduced nanofluid which has good thermal properties as compared to common fluids. After that, it can be seen that researchers, mathematicians, and scientists tried to understand the principles of nanofluids and how to implicate them in many different practical applications. In this work, the Buongiorno model has been considered for nanofluid. One of the prime objectives is to consider all possible multiple solutions of the model because these solutions cannot be seen experimentally.

Methods: The governing equations of fluid flow have been transformed in the form of ordinary differential equations. These equations have been solved by two methods namely, shooting method and three-stage Lobatto IIIa formula.

Results: The effects of different parameters on temperature, velocity, concentration profiles, skin friction coefficient, Sherwood number, and reduced Nusselt number were obtained and presented graphically. It was noticed that four solutions existed at definite ranges of the parameters for high suction over both surfaces for the first time. The results of the stability analysis revealed that only the first solution is more stable and possess physical reliability compared to the remaining solutions.

Conclusion: The graphs also indicated that the fluid velocity decreases as the thermophoresis parameter increases but the opposite behavior observed for both temperature and concentration profiles in the first solution. Furthermore, it was detected that the concentration profile declined at the higher values of the Brownian motion parameter.