A note on the similar and non-similar solutions of powell-eyring fluid flow model and heat transfer over a horizontal stretchable surface

Deliberation on the dynamics of non-Newtonian fluids, most especially Powell-Eyring fluid flow can be described as an open question. In this investigation, the flow and heat transfer characteristics are examined numerically by means of similarity analysis for a Powell-Eyring fluid moving over an isothermal stretched surface along the horizontal direction, whose velocity varies nonlinearly as a function of xx and follows a specified power-law degree formula. In order to solve the problem under consideration, the resulting system of coupled nonlinear partial differential equations with their corresponding boundary conditions is transformed into a correct similar form by utilizing appropriate similarity transformations, which are exceptionally acceptable for a particular form of the power-law stretching velocity, whose exponent is equal to 1⁄3. From the mathematical point of view, the similar equations of the studied flow cannot be obtained for any form of the powerlaw surface stretching velocity. As a result, it was found that the use of a general power-law stretching velocity results in non-similar equations. Also, appropriate numerical methods for similar and nonsimilar equations are used to discuss the results of engineering significance. Furthermore, correlation expressions for the skin friction and Nusselt number have been derived by applying the linear regression on the data outputted from the used computational methods. On the contrary to the heat transfer rate, it was found that the local skin friction coefficient is a decreasing property of powerlaw stretching.