Analytical and numerical study of Heat transfer and fluid flow of Jeffrey fluid over a stretching or shrinking sheet

In this article, the effect of elastic properties of non-Newtonian (Jeffrey) fluid that passes on a stretching or shrinking sheet is studied analytically and numerically for various values of Deborah number ( )and ratio of relaxation to retardation times ( ) and Prandtl number (Pr) is compared by effect of Newtonian fluid on the moving sheet. Similarity transformation is used to convert the governing partial differential equations to nonlinear ordinary differential equations. The converted governing equations are solved by using the shooting and central finite difference methods. The results show that elastic properties of Jeffrey fluid cause decreasing in boundary layer thickness. Behavior of and in velocity distribution is inversely at elastic return. In viscoelastic fluid, two phenomena affect synchronously at boundary layer thickness which are stress release and vertical stresses appearance. The first phenomenon causes increasing the boundary layer thickness, while the second phenomenon causes decreasing it. The results show that fluid particles acceleration at moving sheet vicinity is negative and it increases for stretching sheet and inversely decreases for shrinking sheet. In sheet length, f( ) (similarity function) and f ''( ) (acceleration) is continuously decreasing while f '( ) (velocity) is increasing for stretching sheet for Deborah number and ratio of relaxation to retardation times and are inversely for shrinking sheet. Variations of the above parameters are inversely for shrinking sheet. Effects of Pr on ( ) (temperature profile) are decreasing. Since Pr is ratio of viscous diffusion rate to the thermal diffusion rate, higher Prandtl number reduces the thermal diffusivity

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Study of non-Newtonian fluids flow over a stretching or shrinking surface achieved greatattention [1-15] due to its large number of applications in engineering and various industries suchas expansion and contracting of surfaces , hot rolling , wire rolling , glass fiber , large metal platescooling in the cold water flow and the metal packaging and aluminum bottle manufacturingprocesses , etc. The effects of non-Newtonian behavior can be calculated due to their elasticity ,