On thermal boundary layer of a non-Newtonian fluid on a power-law stretched surface of variable temperature with suction or injection

Abstract

Heat transfer characteristics of a non-Newtonian uid on a power-law stretched surface of variable temperature with suction or injection were investigated. Similarity solutions of the laminar boundary layer equations describing heat transfer and¯uid¯ow in a quiescent uid were obtained and solved numerically. Velocity and temperature pro®les as well as the Nusselt number, Nu, were studied for two thermal boundary conditions; uniform surface temperature and variable surface temperature, for different parameters; Prandtl number Pr, temperature exponent b, velocity exponent m, injection parameter d and power-law index n. It was found that decreasing injection parameter d, and power-law index n and increasing Prandtl number Pr and surface temperature exponent b enhance the heat transfer coef®cient.

Non‐Newtonian boundary layer flow induced by a permeable surface stretched with prescribed skin velocity

“…In Figure 5 there is shown the variation of the skin friction with the power of the stretching velocity. It is an interesting dependence, not yet presented in the papers dealing with this subject, at our best knowledge:Our curves labeled with m =1 (linear stretched surface) in Figure 5 shows the same behavior, not only for impermeable surface (Tashtoush et al , 2001), but also for suction and injection.One remarks also the increase of S with m for any kind of fluids, but clearly those with n <1 are more affected by the intensification of the stretching. For these fluids the curves are almost linear and this direct proportionality between skin friction and power of stretching is a new interesting finding.The effect of injection to increase the skin friction as compared to the impermeable plate is the same as discussed for previous figures.The velocity profiles shown in Figures 6‐8 support a feature already reported in the literature, namely that the momentum boundary layer thickness decreases with increase in the power‐law index, see for instance Prasad et al (2009).…”

“…Comparisons with Tashtoush et al (2001) on the skin friction behavior are not possible since they did not report such results. However, in Prasad et al (2009) there is found that the skin friction decreases as the power-law index n increases (their Table II) and this is also our conclusion (for m ¼ 1 in Figure 3).…”

“…The analysis of Figure 3 shows the following facts:large rates of injection lead to very large values of the skin friction, the effect being more intense for small n (shear thinning fluids);at the same rate of injection/suction, S is increased when the surface is stretched linearly than uniformly; andwhen m =1, massive suction is supported by the boundary layer, which becomes more stable in such conditions.The following comments are pertinent for Figure 4:At same rates of mass transfer through the permeable stretching surface, the skin friction is higher for linear stretching velocity than in the case of uniform stretching.Except for uniform stretching with suction or no suction/injection, skin friction decreases continuously as we move from dilatants to pure Newtonian and further to pseudoplastic fluids.Injection produces smaller friction at the wall than in the case of impermeable wall. This effect is opposite for suction and is generally known from the literature.Comparisons with Tashtoush et al (2001) on the skin friction behavior are not possible since they did not report such results. However, in Prasad et al (2009) there is found that the skin friction decreases as the power‐law index n increases (their Table II) and this is also our conclusion (for m =1 in Figure 3).…”

“…A more recent contribution is that by Tashtoush et al (2001) who analyzed the thermal boundary layer on a power‐law stretched surface of variable temperature with suction or injection. Their energy equation was uncoupled from the momentum equation and their presentation was focused more on the heat transfer characteristics than on the flow ones.…”

“…A recent paper by Prasad et al (2009) focuses on a magnetohydrodynamic (MHD) power‐law fluid flow and heat transfer over a non‐isothermal stretching sheet driven with a velocity u w ( x )∼ x . As in Tashtoush et al (2001), the energy equation is uncoupled from the momentum equation. Along a slight different direction, Postelnicu and Pop (2011) analyzed the steady two‐dimensional laminar boundary layer flow of a power‐law fluid past a permeable stretching wedge beneath a variable free stream.…”