Suitable heat transfer model for self-similar laminar boundary layer in power law fluids

2004 ◽  
Vol 13 (2) ◽  
pp. 150-154 ◽  
Author(s):  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Jicheng He
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Power Law ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Power Law Fluids ◽  
Self Similar

Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation

2018 ◽  
Vol 19 (3-4) ◽  
pp. 415-426 ◽  
Author(s):  
G.C. Layek ◽  
Bidyut Mandal ◽  
Krishnendu Bhattacharyya ◽  
Astick Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Power Law ◽  
Stretching Sheet ◽  
Symmetry Analysis ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Self Similar

AbstractA symmetry analysis of steady two-dimensional boundary layer stagnation-point flow and heat transfer of viscous incompressible non-Newtonian power-law fluids over a nonlinearly shrinking/stretching sheet with thermal radiation effect is presented. Lie group of continuous symmetry transformations is employed to the boundary layer flow and heat transfer equations, that gives scaling laws and self-similar equations for a special type of shrinking/stretching velocity ($c{x^{1/3}}$) and free-stream straining velocity ($a{x^{1/3}}$) along the axial direction to the sheet. The self-similar equations are solved numerically using very efficient shooting method. For the above nonlinear velocities, the unique self-similar solution is obtained for straining velocity being always less than the shrinking/stretching velocity for Newtonian and non-Newtonian power-law fluids. The thickness of velocity boundary layer becomes thinner with power-law index for shrinking as well as stretching sheet cases. Also, the thermal boundary layer thickness decreases with increasing values the Prandtl number and the radiation parameter.

scholarly journals Group Invariant Solutions for Flow and Heat Transfer of Power-Law Nanofluid in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Saba Javaid ◽  
Asim Aziz
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Power Law ◽  
Internal Heat ◽  
Shear Thickening ◽  
Internal Heat Source ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Flow And Heat Transfer ◽  
Power Law Nanofluid

The present work covers the flow and heat transfer model for the power-law nanofluid in the presence of a porous medium over the penetrable plate. The flow is caused by the impulsive movement of the plate embedded in Darcy’s type porous medium. The flow and heat transfer model has been examined with the effect of linear thermal radiation and the internal heat source or sink in the flow regime. The Rosseland approximation is utilized for the optically thick nanofluid. To form the closed-form solutions for the governing partial differential equations of conservation of mass, momentum, and energy, the Lie symmetry analysis is used to get the reductions of governing equations and to find the group invariants. These invariants are then utilized to obtain the exact solution for all three cases, i.e., shear thinning fluid, Newtonian fluid, and shear thickening fluid. In the end, all solutions are plotted for the cu -water nanofluid and discussed briefly for the different emerging flow and heat transfer parameters.

scholarly journals Fluid Flow and Heat Transfer in Power-Law Fluids Across Circular Cylinders: Analytical Study

2005 ◽  
Author(s):  
Waqar A. Khan ◽  
Richard J. Culham ◽  
Milan M. Yovanovich
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Integral Equation ◽  
Power Law ◽  
Circular Cylinders ◽  
Integral Approach ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Power Law Fluids ◽  
Power Law Index

An integral approach of the boundary layer analysis is employed for the modeling of fluid flow around and heat transfer from infinite circular cylinders in power-law fluids. The Von Karman-Pohlhausenmethod is used to solve the momentum integral equation whereas the energy integral equation is solved for both isothermal and isoflux boundary conditions. A fourth-order velocity profile in the hydrodynamic boundary layer and a third-order temperature profile in the thermal boundary layer are used to solve both integral equations. Closed form expressions are obtained for the drag and heat transfer coefficients that can be used for a wide range of the power-law index, and generalized Reynolds and Prandtl numbers. It is found that pseudoplastic fluids offer less skin friction and higher heat transfer coefficients than dilatant fluids. As a result, the drag coefficients decrease and the heat transfer increases with the decrease in power-law index. Comparison of the analytical models with available experimental/numerical data proves the applicability of the integral approach for power-law fluids.

scholarly journals Fluid Flow and Heat Transfer in Power-Law Fluids Across Circular Cylinders: Analytical Study

2006 ◽  
Vol 128 (9) ◽  
pp. 870-878 ◽  
Author(s):  
W. A. Khan ◽  
J. R. Culham ◽  
M. M. Yovanovich
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Integral Equation ◽  
Power Law ◽  
Circular Cylinders ◽  
Integral Approach ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Power Law Fluids ◽  
Power Law Index

An integral approach of the boundary layer analysis is employed for the modeling of fluid flow around and heat transfer from infinite circular cylinders in power-law fluids. The Von Karman-Pohlhausen method is used to solve the momentum integral equation whereas the energy integral equation is solved for both isothermal and isoflux boundary conditions. A fourth-order velocity profile in the hydrodynamic boundary layer and a third-order temperature profile in the thermal boundary layer are used to solve both integral equations. Closed form expressions are obtained for the drag and heat transfer coefficients that can be used for a wide range of the power-law index, and generalized Reynolds and Prandtl numbers. It is found that pseudoplastic fluids offer less skin friction and higher heat transfer coefficients than dilatant fluids. As a result, the drag coefficients decrease and the heat transfer increases with the decrease in power-law index. Comparison of the analytical models with available experimental/numerical data proves the applicability of the integral approach for power-law fluids.

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