Mixed Convection Flow of Powell–Eyring Nanofluid near a Stagnation Point along a Vertical Stretching Sheet

Nadhirah Abdul Halim,Noor Fadiya Mohd Noor

doi:10.3390/math9040364

Abstract

A stagnation-point flow of a Powell–Eyring nanofluid along a vertical stretching surface is examined. The buoyancy force effect due to mixed convection is taken into consideration along with the Brownian motion and thermophoresis effect. The flow is investigated under active and passive controls of nanoparticles at the surface. The associating partial differential equations are converted into a set of nonlinear, ordinary differential equations using similarity conversions. Then, the equations are reduced to first-order differential equations before further being solved using the shooting method and bvp4c function in MATLAB. All results are presented in graphical and tabular forms. The buoyancy parameter causes the skin friction coefficient to increase in opposing flows but to decrease in assisting flows. In the absence of buoyancy force, there is no difference in the magnitude of the skin friction coefficient between active and passive controls of the nanoparticles. Stagnation has a bigger influence under passive control in enhancing the heat transfer rate as compared to when the fluid is under active control. Assisting flows have better heat and mass transfer rates with a lower magnitude of skin friction coefficient as compared to opposing flows. In this case, the nanofluid parameters, the Brownian motion, and thermophoresis altogether reduce the overall heat transfer rates of the non-Newtonian nanofluid.

Highlights

Mixed convection flow occurs when effects from forced convection and natural convection mechanisms contribute significantly to heat transfer
According to Chen et al [1], the buoyancy force that arises from the temperature difference will instigate a longitudinal pressure gradient
Their study shows that a dual solution exists for the opposing flow whilst a unique solution is available for the assisting flow

Summary

Introduction

Mixed convection flow occurs when effects from forced convection and natural convection mechanisms contribute significantly to heat transfer. Hayat et al [7] applied the homotopy analysis method (HAM) in their study on the influence of thermal radiation on the MHD stagnation point flow with mixed convection Both thermal radiation and magnetic parameter are found to improve the heat transfer rate of the fluid in assisting flows as well as in opposing flows. Abbas et al [9] discussed the stagnation point flow of a Maxwell fluid on a stretching vertical surface with mixed convection They found that increasing the fluid relaxation time represented by the Deborah number will increase the heat transfer rate in opposing flow but will decrease it in assisting flow. Hayat et al [10]

Methods

Discussion

Conclusion