Similarity Solution for Unsteady Free Convection From a Vertical Plate at Constant Temperature to Power Law Fluids

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
J. Abolfazli Esfahani ◽  
B. Bagherian
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Free Convection ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Theoretic Approach ◽  
Local Skin ◽  
Power Law Fluids

The transformation group theoretic approach is applied to perform an analysis of unsteady free convection flow over a vertical flat plate immersed in a power law fluid. The thermal boundary layer induced within a vertical semi-infinite layer of Boussinseq fluid. The system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions via two-parameter group theory. The obtained ordinary differential equations are solved numerically for velocity and temperature using the fourth order Runge-Kutta and shooting method. The effect of Prandtl number and viscosity index (n) on the thermal boundary-layer, velocity boundary-layer, local Nusselt number, and local skin-friction were studied.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

scholarly journals Effect of Radiation on Free Convection Flow of Non-Newtonian Power-Law Fluids Along a Power-Law Stretching Sheet

2013 ◽  
Vol 61 (1) ◽  
pp. 97-104
Author(s):  
MA Samad ◽  
MR Hossain ◽  
D Kumar
Keyword(s):  
Differential Equations ◽  
Free Convection ◽  
Power Law ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Convection Heat Transfer ◽  
Simultaneous Action ◽  
Integration Scheme ◽  
Convection Flow ◽  
Power Law Fluids

An analysis is carried out to investigate the effects of MHD free convection heat transfer of power-law non-Newtonian fluids along a stretching sheet. This has been done under the simultaneous action of suction, thermal radiation and uniform transverse magnetic field. The stretching sheet is assumed to continuously moving with a power-law velocity and maintaining a uniform surface heat flux. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The resulting non-linear equations are solved numerically using Nachtsheim-Swigert shooting iterative technique along with sixth order Runge-Kutta integration scheme. Numerical results for the non-dimensional velocity and temperature profiles are shown graphically and discussed. The effects of skin-friction coefficient and the local Nusselt number which are of physical and engineering interest are studied and presented in the form of tables for the variation of different physically important parameters. A comparison of the present study is also performed with the previously published work and found excellent agreement. Dhaka Univ. J. Sci. 61(1): 97-104, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15104

scholarly journals Combined Effects of Soret and Dufour on MHD Flow of a Power-Law Fluid Over Flat Plate in Slip Flow Rigime

2018 ◽  
Vol 23 (3) ◽  
pp. 689-705
Author(s):  
K. Saritha ◽  
M.N. Rajasekhar ◽  
B.S. Reddy
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Flat Plate ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Physical Parameters ◽  
Power Law Fluid ◽  
Soret And Dufour Effects ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract A numerical model is developed to study the Soret and Dufour effects on MHD boundary layer flow of a power-law fluid over a flat plate with velocity, thermal and solutal slip boundary conditions. The governing equations for momentum, energy and mass are transformed to a set of non-linear coupled ordinary differential equations by using similarity transformations. These non-linear ordinary differential equations are first linearized using a quasi-linearization technique and then solved numerically based on the implicit finite difference scheme over the entire range of physical parameters with appropriate boundary conditions. The influence of various governing parameters along with velocity, thermal and mass slip parameters on velocity, temperature and concentration fields are examined graphically. Also, the effects of slip parameters, the Soret and Dufour number on the skin friction, Nusselt number and Sherwood number are studied. Results show that the increase in the Soret number leads to a decrease in the temperature distribution and to an increase in concentration fields.

Natural Convection to Power-Law Fluids From a Heated Vertical Plate Under Mixed Thermal Boundary Conditions

1999 ◽  
Author(s):  
Elif Büyük ◽  
Mehmet C. Ece
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Power Law ◽  
Vertical Plate ◽  
Flow Behavior ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Thermal Boundary Conditions ◽  
Power Law Fluids ◽  
Mixed Thermal Boundary Conditions

Abstract Steady free convection laminar boundary-layer flow subject to mixed thermal boundary conditions along a heated vertical plate immersed in a quiescent power-law fluid is investigated. Similarity solutions are obtained numerically for the boundary-layer velocity and temperature profiles. The effects of flow behavior index and the generalized Prandtl number on the surface shear stress and heat flux are determined.

scholarly journals Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1323-1334 ◽  
Author(s):  
Alireza Bahmani ◽  
Hadi Kargarsharifabad
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Skin Friction ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Hartmann Number ◽  
Viscosity Index ◽  
Thermal Boundary Layer Thickness ◽  
Power Law Fluids

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

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.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

scholarly journals A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

2021 ◽  
Vol 11 (11) ◽  
pp. 4798
Author(s):  
Hari Mohan Srivastava ◽  
Sotiris K. Ntouyas ◽  
Mona Alsulami ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Coupled System ◽  
Contraction Mapping Principle ◽  
Arbitrary Domain ◽  
Banach Contraction ◽  
Coupled Boundary Conditions ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

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