Analysis of Nonlinear Convection Flow of Williamson Nanofluid with Melting Heat Transfer in Porous Medium


Published: 2023-11-08

Page: 444-472

Markus A. *

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Olanrewaju P. O.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

Nwaokolo M. A.

Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.

*Author to whom correspondence should be addressed.


Williamson nanofluids have the potential to improve the efficiency and performance of a wide range of thermal system. In this current study, analysis of nonlinear convection flow of Williamson Nano fluid with melting heat transfer in porous medium has been carried out. The governing boundary layer Partial Differential Equations (PDEs) were transformed into a system of Ordinary Differential Equations (ODEs) by using similarity transformation and then solved numerically by shooting technique alongside with the fifth order Runge-Kutta method for various values of the dimensionless parameters of the modeled problems. Velocity, temperature and concentration profiles were presented graphically. The effects of various dimensionless parameters were analyzed. The outcomes demonstrate that the velocity profile enlarges as the value of Non-Newtonian Williamson parameter, nonlinear convection parameter and Heat source term are upgraded and decrease the velocity profile as the value of Magnetic parameter and Porosity are increased. The temperature profile increases when the value of the following parameters are increased; Magnetic parameter, Eckert number and Porosity. It decreases when the value of Local Grashof number are upgraded. Meanwhile the concentration profile is engulf with a boost as the value of Local Grashof number and Radiation parameter are increased. It decreases when the value of chemical reaction parameter, Relative temperature, and Activation energy are increased respectively .Interestingly, the effect of embedded fluid flow parameters on the skin friction, heat transfer rate and mass transfer rate were established for engineering/industrial purpose.

Keywords: Nonlinear convection flow, thermal system, differential equations, Williamson Nanofluid

How to Cite

Markus A., Olanrewaju P. O., & Nwaokolo M. A. (2023). Analysis of Nonlinear Convection Flow of Williamson Nanofluid with Melting Heat Transfer in Porous Medium. Asian Journal of Pure and Applied Mathematics, 5(1), 444–472. Retrieved from


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