Abstract
An analysis for the steady two-dimensional boundary-layer stagnation-point flow of Rivlin–Ericksen fluid of second grade with a uniform suction is carried out via symmetry analysis. By employing Lie-group method to the given system of nonlinear partial differential equations, the symmetries of the equations are determined. Using these symmetries, the solution of the given equations is found. The effect of the viscoelastic parameter k and the suction parameter R on the tangential and normal velocities, temperature profiles, heat transfer coefficient and the wall shear stress, have been studied. Also, the effect of the Prandtl number Pr on the temperature and the heat transfer coefficient has been studied.
Highlights
The two-dimensional stagnation point flow of an incompressible viscous fluid appears in several manufacturing processes of industry such as the extrusion of polymers, the cooling of metallic plates, the aerodynamic extrusion of plastic sheets, etc
Laminar two-dimensional flow of an incompressible Rivlin–Ericksen fluid of second grade impinging perpendicular on a permeable wall and flows away along the x-axis
Lie-group method is applicable to both linear and non-linear partial differential equations, which leads to similarity variables that used to reduce the number of independent variables in partial differential equations
Summary
The two-dimensional stagnation point flow of an incompressible viscous fluid appears in several manufacturing processes of industry such as the extrusion of polymers, the cooling of metallic plates, the aerodynamic extrusion of plastic sheets, etc. The effect of the non-Newtonian nature of the fluid on the velocity profile and heat transfer coefficient at the wall for different Prandtl numbers and wall surface flux variation was investigated He concluded that, the smaller the Prendtl number, the thicker is the thermal boundary layer. Temperature distribution in the boundary layer is determined when the surface is held at constant temperature giving the so called surface heat flux In their analysis, they used the finite-differences scheme along with the Thomas algorithm to solve the resulting system of ordinary differential equations. At the second case (prescribed surface temperature), his study included both viscous dissipation and work due to deformation He analyzed the effect on both temperature and temperature-gradient profiles when the contribution of heat due to elastic deformation is taken into account in the energy equation. The resulting system of nonlinear differential equations is solved numerically using shooting method coupled with Runge–Kutta scheme
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