Abstract
The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.
Highlights
The numerous application of non-Newtonian fluids in industry and commerce has prompted researchers to do study in this area
In the heat transfer mechanism, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers
We investigated the 2D boundary layer flow of a MHD Carreau fluid along a permeable shrinking sheet in the presence of Joule heating, Ohmic dissipation, and non-uniform heat source/sink effects
Summary
The numerous application of non-Newtonian fluids in industry and commerce has prompted researchers to do study in this area. Important applications of these types of fluids include the chemical industry, such as paint manufacture, palm oil production, and shampoo production, as well as the food sector, such as mayonnaise production. The highly driven authors are interested in the study of the rheology of non-Newtonian liquids. As the complicated numerical and analytical relationship between the shear rate and stress is represented by the non-Newtonian liquid substance, they are graded into dilatant, shear thinning, and shear thickening properties. While different fluid simulations are used in this respect to analyze the inherent advantages from the above components, there is no single scheme in this respect. The organized effort by Carreau (1972) [1]
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