Numerical Solution of Magnetized Williamson Nanofluid Flow over an Exponentially Stretching Permeable Surface with Temperature Dependent Viscosity and Thermal Conductivity

Muhammad Amjad; Iftikhar Ahmed; Kamran Ahmed; Marei Saeed Alqarni; Tanvir Akbar; Taseer Muhammad

doi:10.3390/nano12203661

Numerical Solution of Magnetized Williamson Nanofluid Flow over an Exponentially Stretching Permeable Surface with Temperature Dependent Viscosity and Thermal Conductivity

Nanomaterials (Basel). 2022 Oct 18;12(20):3661. doi: 10.3390/nano12203661.

Authors

Muhammad Amjad¹, Iftikhar Ahmed¹, Kamran Ahmed¹, Marei Saeed Alqarni², Tanvir Akbar¹, Taseer Muhammad²

Affiliations

¹ Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan.
² Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia.

Abstract

This research work describes and investigates Williamson nanofluid flow over an exponentially stretching permeable vertical plate with temperature-dependent thermal conductivity and viscosity. The governing non-linear partial differential equations (PDEs) are metamorphosed into coupled non-linear ordinary differential equations (ODEs) by using similarity transformation. The succeeding equations were numerically solved using MATLAB function bvp4c for various values of parameters. For velocity, temperature, concentration, the skin friction coefficient, and the local Nusselt number, data are presented in the form of graphs and tables. It is noted that for increasing values of magnetic parameter M, Williamson parameter λ, and viscosity parameter α, the boundary layer thickness of the velocity profile decreases, while it increases for the temperature profile. The findings of the present work are validated through the published results.

Keywords: MHD; Williamson fluid; exponential stretching; nanofluids; variable thermal conductivity and viscosity.

Grants and funding

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia for funding this work through Large Groups Project under grant number RGP.2/206/43.