Stagnation Point Flow of a Non-Newtonian Second Order Fluid

Abstract

In this paper the flow near a two-dimensional stagnation point for a particular non-Newtonian fluid has been studied. For a second order fluid the equation of motion for the stream function has been solved by using a similarity approach. A new parameter which is a combination of the Weissenberg number and the Reynolds number characterizes the visco-elastic effects. A fourth order differential equation has to be solved numerically. Only three boundary conditions are necessary. Results for various cases will be shown. In addition an approxamation theory has been derived in order to recognize the influence of the new parameter.

Stagnation-point flow of upper-convected Maxwell fluids

“…Frater [13] appears to be the first to suggest that the overshoot of the velocity in the boundary layer might be due to seeking a regular perturbation solution of the problem in terms of an elasticity number. Recent findings by Teipel [14], Garg and Rajagopal [15], and Pakdemirli and Suhubi [16] have demonstrated that the perturbation technique may not render satisfactory results when dealing with viscoelastic fluids. The shortcomings of the perturbation method in dealing with stagnation-point flows of second-grade fluids has beautifully been demonstrated by Ariel [17].…”

Diffusion of Chemically Reactive Species in Stagnation-Point Flow of a Third Grade Fluid: a Hybrid Numerical Method

“…Rajagopal et al (1984) have presented the Falkner-Skan flows of an incompressible second grade fluid. Later, numerous attempts for stagnation point flow in a viscoelastic fluid using various techniques were made by Teipel (1988), Garg and Rajagopal (1990Rajagopal ( , 1991, and Pakdemirli and Suhubi (1992). Ariel (1995) studied the stagnation point flow of a second grade fluid with and without suction velocity at the wall numerically using a hybrid method.…”

Two dimensional stagnation point flow of an elastico‐viscous fluid with partial slip

“…Beard and Walters [1] in their seminal work attempted to overcome the aforementioned dilemma by seeking a first order perturbation solution in which the primary flow was taken as the Newtonian flow, and the secondary flow represented the effects of viscoelasticity. Later researches by Sarpkaya and Riley [2], Serth [3], and Teipel [4] exposed the limitations of the perturbation solution by showing that as the value of k, the non-Newtonian fluid parameter was increased even to a value as small as 0.3, the perturbation solution failed to describe the flow adequately. Not only there are oscillations in the flow for any positive value of k, but there is a sharp increase in the stress at the wall for values of k near 0.3.…”

“…Not only there are oscillations in the flow for any positive value of k, but there is a sharp increase in the stress at the wall for values of k near 0.3. Using the celebrated von Karman-Polhausen method, Teipel [4] concluded that the stress becomes infinite for some critical value k c of k near 0.3. In an interesting development Ariel [5] formulated an efficient algorithm to compute the flow of elasticoviscous fluids in semi-infinite domains.…”