Skin friction and heat transfer in power-law fluid laminar boundary layer along a moving surface. (English) Zbl 1101.76323

Summary: Analytical and numerical solutions are presented for momentum and energy laminar boundary layer along a moving plate in power-law fluids utilizing a similarity transformation and shooting technique. The results indicate that for a given power-law exponent \(n\) (\(0<n\leqslant 1\)) or velocity ratio parameter \(\xi\) , the skin friction \(\sigma\) decreases with the increasing in \(\xi\) or \(n\). The shear force decreases with the increasing in dimensionless tangential velocity \(t\). When Prandtl number \(N_{\text{Pr}}=1\), the dimensionless temperature \(w(t)\) is a linear function of \(t\), and the viscous boundary layer is similar to that of thermal boundary layer. In particular, \(w(t)=t\) if \(\xi=0\), i.e., the velocity distribution in viscous boundary layer has the same pattern as the temperature distribution in the thermal boundary and \(\delta=\delta _T\). For \(N_{\text{Pr}}\geqslant 1\), the increase of viscous diffusion is larger than that of thermal diffusion with the increasing in \(N_{\text{Pr}}\), and \(\delta_T(t)<\delta (t)\). The thermal diffusion ratio increases with the increasing in \(n\) (\(0<n \leqslant 1\)) and \(\xi\).


76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76A05 Non-Newtonian fluids
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
80A20 Heat and mass transfer, heat flow (MSC2010)
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