Abstract
A numerical investigation is made to study the thermal boundary layer for flow of incompressible Newtonian fluid over an exponentially stretching sheet with an exponentially moving free stream. The governing partial differential equations are transformed into self-similar ordinary differential equations using similarity transformations in exponential forms. Then those are solved numerically by shooting technique using Runge-Kutta method. The study reveals that the momentum boundary layer thickness for this flow is considerably smaller than the linear stagnation point flow past a linearly stretching sheet. The momentum and thermal boundary layer thicknesses reduce when the velocity ratio parameter increases. For the temperature distribution, in addition to the heat transfer from the sheet, the heat absorption at the sheet also occurs in certain situations and both heat transfer and absorption increase with the velocity ratio parameter and the Prandtl number. The temperature inside the boundary layer significantly decreases with higher values of velocity ratio parameter and the Prandtl number.
Highlights
The viscous fluid flow due to a stretching sheet is very significant problem in fluid dynamics due to its huge applications in many manufacturing processes, for example, the cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheets, the boundary layer along a liquid film in the condensation processes, hot rolling, paper production, metal spinning, glass-fiber production, and drawing of plastic films
The heat transfer from a stretching surface is of interest in polymer extrusion processes where the object, after passing through a die, enters the fluid for cooling below a certain temperature
The mixed convection for the flow due to linearly stretching sheet with mass suction/injection was studied by Ali and Al-Yousef [7]
Summary
The viscous fluid flow due to a stretching sheet is very significant problem in fluid dynamics due to its huge applications in many manufacturing processes, for example, the cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyers, the aerodynamic extrusion of plastic sheets, the boundary layer along a liquid film in the condensation processes, hot rolling, paper production, metal spinning, glass-fiber production, and drawing of plastic films. The heat transfer from a stretching surface is of interest in polymer extrusion processes where the object, after passing through a die, enters the fluid for cooling below a certain temperature. The quality of the final product depends on the rate of heat transfer from the stretching surface. Crane [1] first investigated the steady boundary layer flow of an incompressible viscous fluid over a linearly stretching plate and gave an exact similarity solution in closed analytical form. Ali [8] investigated the buoyancy effects on the boundary layers induced by a rapidly stretching surface. Tsai et al [9] discussed the effect of nonuniform heat source/sink on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity. Bhattacharyya [12, 13] presented effect of heat source/sink
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