On energy boundary layer equations in power law non-Newtonian fluids

Abstract

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated. Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer. The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group. One model was assumed that Prandtl number is a constant, and the other model was assumed that viscosity diffusion is analogous to thermal diffusion. The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

Keywords

power law fluids / heat transfer / similarity solution / nonlinear boundary value problem

References

[1] SchlichtingH.Boundary layer theory [M], 1979, New York, McGraw-Hill

[2] SchowalterW. R.. The Application of boundary-layer theory to power-law pseudoplastic fluids: Similar solutions [J]. AIChE Journal, 1960, 6: 24-28

[3] AcrivosA., ShahM. J., PetersenE. E.. Momentum and heat transfer in laminar boundary-layer flows of non-Newtonian fluids past external surfaces [J]. AIChE Journal, 1960, 6: 312-317

[4] HadyF. M.. Mixed convection boundary-layer flow of non-Newtonian fluids on a horizontal plate [J]. Applied Mathematics and Computation, 1995, 68: 105-112

[5] HowellT. G., JengD. R., de WittK. J.. Momentum and heat transfer on a continuous moving surface in power law fluid [J]. Int J Heat Mass Transfer, 1997, 40: 1853-1861

[6] ChenC.-H.. Effect of viscous dissipation on heat transfer in non-Newtonian liquid film over an unsteady stretching sheet [J]. Journal of Non-Newtonian Fluid Mechanics, 2005, 135: 128-135

[7] WangC., PopI.. Analysis of the flow of a power law fluid film on an unsteady stretching surface by means of homotopy analysis method [J]. Journal of Non-Newtonian Fluid Mechanics, 2006, 138: 161-172

[8] ZhengL.-c., ZhangX.-x., HeJ.-cheng.. Existence and estimate of positive solutions to a nonlinear singular boundary value problem in the theory of dilatant non-Newtonian fluids [J]. Math Comp Model, 2007, 45: 387-393

[9] ZhengL.-c., ZhangX.-x., LuC.-qing.. Heat transfer of power law non-Newtonian [J]. Chin Phys Lett, 2006, 23(12): 3301-3304