Laminar Boundary Layer Heat Transfer to Power Law Fluids: An Approximate Analytical Solution.

1999 ◽  
Vol 32 (6) ◽  
pp. 812-816 ◽  
Author(s):  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Analytical Solution ◽  
Laminar Boundary Layer ◽  
Power Law ◽  
Approximate Analytical Solution ◽  
Power Law Fluids

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 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.

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

2016 ◽  
Vol 9 (3) ◽  
pp. 315-336 ◽  
Author(s):  
Botong Li ◽  
Liancun Zheng ◽  
Ping Lin ◽  
Zhaohui Wang ◽  
Mingjie Liao
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Method ◽  
Power Law ◽  
Infinite Plate ◽  
Temperature Fields ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Power Law Function

AbstractThis paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudosimilarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.

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