The application of non-Fourier and Fick's laws to the flow of temperature-dependent thermal conductivity generalized Newtonian liquids: A 3D computational study

Document Type : Article


1 Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.

2 Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.; Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal Upper Dir 18000, Pakistan.

3 Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.;Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan.

4 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.


The current article presents a numerical study for local solutions of Sisko liquid flow by bidirectional stretched surface. Additionally, the analysis of relaxation times for the heat and mass transfer mechanisms are made by utilizing modified heat flux and mass diffusion models. These improved relations are the generalized form of Fourier's and Fick's laws in which the time space upper-convected derivative are employed to portray the heat conduction and mass diffusion mechanisms. Appropriate transformations lead to a strongly nonlinear differential system of equations which is then solved numerically by employing the applications of bvp4c package in Matlab software. Another numerical method namely shooting technique with RK45 Fehlberg and Newton-Raphson method is utilized to authenticate the results. Graphical illustrations demonstrating the impacts of sundry physical parameters with required discussion highlighting their physical effect are also a part of this exploration. It is perceived that the temperature and concentration of Sisko liquid are diminishing functions of relaxation times for the heat and mass transfer mechanisms. It is also fascinating to perceive that the temperature and concentration of Sisko liquid are higher in case of classical form in comparison with an improved constitutive relations.


Main Subjects

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