×

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 \(\xi\).

MSC:

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)
PDFBibTeX XMLCite
Full Text: DOI