Coupling Effects of Viscous Sheet and Ambient Fluid on Boundary Layer Flow and Heat Transfer in Power-Law Fluids

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Xiaochuan Liu ◽  
Liancun Zheng ◽  
Goong Chen ◽  
Lianxi Ma
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Similarity Solutions ◽  
Temperature Fields ◽  
Ambient Fluid ◽  
Local Skin ◽  
Flow And Heat Transfer ◽  
Power Law Fluids

This paper investigates the flow and heat transfer of power-law fluids over a stretching sheet where the coupling dynamics influence of viscous sheet and ambient fluid is taken into account via the stress balance. A modified Fourier's law is introduced in which the effects of viscous dissipation are taken into account by assuming that the thermal conductivity is to be shear-dependent on the velocity gradient. The conditions for both velocity and thermal boundary layers admitting similarity solutions are found, and numerical solutions are computed by a Bvp4c program. The results show that the viscous sheet and rheological properties of ambient fluids have significantly influences on both velocity and temperature fields characteristics. The formation of sheet varies with the viscosity of fluid and draw ratio, which then strongly affects the relations of the local skin friction coefficient, the local Nusselt number, and the generalized Reynolds number. Moreover, for specified parameters, the flow and heat transfer behaviors are discussed in detail.

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Yanhai Lin ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Marangoni Convection ◽  
Convection Heat Transfer ◽  
Temperature Fields ◽  
Convection Heat ◽  
Power Law Fluids

This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

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.

Flow and heat transfer of non-Newtonian power-law fluids over a stretching surface with variable thermal conductivity

2019 ◽  
Vol 15 (4) ◽  
pp. 686-698 ◽  
Author(s):  
Meng Yang ◽  
Yanhai Lin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Field ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Physical Parameters ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Power Law Fluids

Purpose The purpose of this paper is to investigate the flow and heat transfer of power-law fluids over a non-linearly stretching sheet with non-Newtonian power-law stretching features. Design/methodology/approach The governing non-linear partial differential equations are reduced to a series of ordinary differential equations by suitable similarity transformations and the numerical solutions are obtained by the shooting method. Findings As the temperature power-law index or the power-law number of the fluids increases, the dimensionless stream function, dimensionless velocity and dimensionless temperature decrease, while the velocity boundary layer and temperature boundary layer become thinner for other fixed physical parameters. The thermal diffusivity varying as a function of the temperature gradient can be used to present the characteristics of flow and heat transfer of non-Newtonian power-law fluids. Originality/value Unlike classical works, the effect of power-law viscosity on the temperature field is considered by assuming that the temperature field is similar to the velocity field with modified Fourier’s law heat conduction for power-law fluid media.

scholarly journals Magnetohydrodynamic thin film and heat transfer of power law fluids over an unsteady stretching sheet with variable thermal conductivity

2016 ◽  
Vol 20 (6) ◽  
pp. 1791-1800 ◽  
Author(s):  
Yanhai Lin ◽  
Liancun Zheng ◽  
Botong Li ◽  
Xinxin Zhang
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Temperature Field ◽  
Power Law ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Temperature Fields ◽  
Thin Film Flow ◽  
Unsteady Stretching Sheet ◽  
Power Law Fluids

This paper presents an investigation on the MHD thin film flow and heat transfer of a power law fluid over an unsteady stretching sheet. The effects of power law viscosity on a temperature field are taken into account with a modified Fourier?s law Proposed by Zheng by assuming that the temperature field is similar to the velocity field. The governing equations are reduced to a system of nonlinear ordinary differential equations. The numerical solutions are obtained by using the shooting method coupled with the Runge-Kutta method. The influence of the Hartmann number, the power law exponent, the unsteadiness parameter, the thickness parameter and the generalized Prandtl number on the velocity and temperature fields are presented graphically and analyzed. Moreover, the critical formula for parameters are derived which indicated that the magnetic field has no effect on the critical value.

Mixed Electroosmotic Pressure Driven Flow and Heat Transfer of Power Law Fluid in a Hydrophobic Microchannel

2017 ◽  
Author(s):  
Ainul Haque ◽  
Ameeya Kumar Nayak
Keyword(s):  
Heat Transfer ◽  
Power Law ◽  
Joule Heating ◽  
Scientific Data ◽  
Channel Height ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Hydrophobic Microchannel ◽  
Pressure Driven Flow ◽  
Pressure Driven

In this paper, a mathematical model has been developed to analyze the combined electroosmotic and pressure driven flow of power law fluids in a micro channel in the presence of Joule heating effects. The effects of Navier slip boundary condition and thermal radiation is examined for effective heat transfer in a hydrophobic microchannel. The analytical treatment has been performed for fluid flow and heat transfer effects in terms of flow governing parameters. This study highlights the effect of channel height to the electric double layer thickness and observed the flow variation due to heat transfer effect with the available scientific data. For a pure EOF, velocity slip have more significant role to get a maximum flow rate as expected. For both pseudo-plastic and dilatent fluids Nusselt number is decreased with the increment of the hydrophobic parameter and dimensionless pressure gradient where as increment in Joule heating effect enhance the heat transfer rate.

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.

Sign in / Sign up

Export Citation Format

Share Document