Abstract
In this article, we aim to analyze the dual solutions for the flow of non-Newtonian material (Carreau fluid) over a radially shrinking surface. Magnetohydrodynamics fluid is considered. Concept of Stefan Boltzmann constant and mean absorption coefficient is used in the mathematical modeling of energy expression. Mass transfer is discussed. The upper and lower branch solutions for the Sherwood number, skin friction coefficient, and Nusselt number are calculated for different pertinent flow variables. Appropriate transformation variables are employed for reduction of partial differential equations system into ordinary differential equations. Dual solutions are obtained for the non-dimensional concentration, temperature, velocity, gradient of concentration, gradient of temperature, and gradient of velocity. The critical values for each upper and lower solutions are obtained for the case of gradient of velocity, gradient of temperature, and gradient of concentration. It is formed that concentration and temperature fields display same impact regarding both upper and lower branch solutions for velocity ratio and temperature ratio parameters.
Highlights
It is very well recognized that the non-Newtonian materials are more applicable than viscous materials in processes of engineering, geophysics, and biomechanics.[1,2]
Many non-Newtonian materials exist in nature for their different characteristics. The difference between these materials can be distinguished from the functional relation between shear stress, the force per unit area mandatory to tolerate a constant rate of shear rate and liquid movement, and rate of velocity change when different layers of fluid or one layer passes through an adjacent layer
That for lower l, the upper branch solution of velocity increases while a decay is noticed in lower branch solution
Summary
It is very well recognized that the non-Newtonian materials are more applicable than viscous materials in processes of engineering, geophysics, and biomechanics.[1,2] Many non-Newtonian materials exist in nature for their different characteristics. The difference between these materials can be distinguished from the functional relation between shear stress, the force per unit area mandatory to tolerate a constant rate of shear rate and liquid movement, and rate of velocity change when different layers of fluid or one layer passes through an adjacent layer.
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