scholarly journals On local fractional Volterra integro-differential equations in fractal steady heat transfer

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 789-793 ◽  
Author(s):  
Ai-Min Yang ◽  
Yang Han ◽  
Yu-Zhu Zhang ◽  
Li-Ting Wang ◽  
Di Zhang ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Inverse Problems ◽  
Differential Equations ◽  
Non Linear ◽  
Steady Heat

In this paper we address the inverse problems for the fractal steady heat transfer described by the local fractional linear and non-linear Volterra integro-differential equations. The Volterra integro-differential equations are presented for investigating the fractal heat-transfer.

scholarly journals Numerical study of heat transfer of a micropolar fluid through a porous medium with radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 557-565 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Collocation Method ◽  
Micropolar Fluid ◽  
Legendre Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Shifted Legendre Polynomials ◽  
Non Linear

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an approximate solution for this system of non-linear differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 559-568 ◽  
Author(s):  
G. C. Shit ◽  
R. Haldar ◽  
A. Sinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Layer Flow

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

scholarly journals A mathematical model on MHD slip flow and heat transfer over a nonlinear stretching sheet

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 475-488 ◽  
Author(s):  
Kalidas Das
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Slip Flow ◽  
Inverse Function ◽  
Partial Slip ◽  
Physical Parameters ◽  
Fluid Viscosity ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Non Linear

Some analyses have been carried out to study the influence of suction/blowing, thermal radiation and temperature dependent fluid properties on the hydro-magnetic incompressible electrically conducting fluid flow and heat transfer over a permeable stretching surface with partial slip boundary conditions. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The effects of various physical parameters on the flow and heat transfer characteristics as well as the skin friction coefficient and Nusselt number are illustrated graphically. The physical aspects of the problem are highlighted and discussed.

scholarly journals MHD Effects on Non-Newtonian Power-Law Fluid Past a Continuously Moving Porous Flat Plate with Heat Flux and Viscous Dissipation

2013 ◽  
Vol 18 (2) ◽  
pp. 425-445 ◽  
Author(s):  
N. Kishan ◽  
B. Shashidar Reddy
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Power Law ◽  
Porous Plate ◽  
Power Law Fluid ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
Non Linear

The problem of a magneto-hydro dynamic flow and heat transfer to a non-Newtonian power-law fluid flow past a continuously moving flat porous plate in the presence of sucion/injection with heat flux by taking into consideration the viscous dissipation is analysed. The non-linear partial differential equations governing the flow and heat transfer are transformed into non-linear ordinary differential equations using appropriate transformations and then solved numerically by an implicit finite difference scheme. The solution is found to be dependent on various governing parameters including the magnetic field parameter M, power-law index n, suction/injection parameter ƒw, Prandtl number Pr and Eckert number Ec. A systematical study is carried out to illustrate the effects of these major parameters on the velocity profiles, temperature profile, skin friction coefficient and rate of heat transfer and the local Nusslet number.

Melting heat transfer analysis of non-Newtonian Casson fluid due to moving plate

2018 ◽  
Vol 35 (3) ◽  
pp. 1301-1313 ◽  
Author(s):  
Mahantesh M. Nandeppanavar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Casson Fluid ◽  
Heat Transfer Analysis ◽  
Moving Plate ◽  
Content Type ◽  
Melting Heat ◽  
Linear Ordinary Differential Equations ◽  
Melting Heat Transfer ◽  
Non Linear

Purpose This paper aims to investigate laminar boundary layer flow and heat transfer from a warm laminar Casson liquid to a melting sheet moving parallel to a melting stream. The governing equations, i.e. continuity, momentum and heat transfer, are coupled non-linear partial differential equations. These equations are reduced to non-linear ordinary differential equations by means of similarity transformations, converted into first-order differential equations, and are solved numerically using the Runge–Kutta–Felhberg method with an efficient shooting technique. The velocity and temperature profiles are plotted for various values of the governing parameters, such as the moving parameter, Prandlt number, melting parameter and Casson parameter. It is found that the problem admits multiple solutions. The results of this study are validated by comparing them with the earlier published studies’ results. Thus, a good agreement is obtained. Design/methodology/approach This study carries out numerical solution of melting heat transfer analysis. Findings The findings of this study show the analysis of flow and melting heat transfer characteristics. Research limitations/implications In this study, analysis of dual solution is carried out. Originality/value In this paper, the melting heat transfer analysis on Blasius flow of a Casson fluid is taken into consideration. To the best of the author’s knowledge, no investigations have been reported on this topic.

scholarly journals Non-linear radiation influence on oblique stagnation point flow of Maxwell fluid

2018 ◽  
Vol 64 (4) ◽  
pp. 420 ◽  
Author(s):  
Abuzar Ghaffari ◽  
T. Javed ◽  
I. Mustafa
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Maxwell Fluid ◽  
Stagnation Point Flow ◽  
Non Linear ◽  
Linear Radiation

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged through streamlines graphs. It is also observed that oblique stagnation point flow behaves like orthogonal stagnation point flow, when free stream velocity is very large as compared to stretching velocity.

MHD Boundary Layer Slip Flow and Heat Transfer of Nanofluid Past a Vertical Stretching Sheet with Non-Uniform Heat Generation/Absorption

2014 ◽  
Vol 13 (03) ◽  
pp. 1450019 ◽  
Author(s):  
S. Das ◽  
R. N. Jana ◽  
O. D. Makinde
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Slip Flow ◽  
Uniform Heat ◽  
Mhd Boundary Layer ◽  
Non Linear

An investigation of the magnetohydrodynamics (MHD) boundary layer slip flow over a vertical stretching sheet in nanofluid with non-uniform heat generation/absorbtion in the presence of a uniform transverse magnetic field has been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the surface of the sheet. The results show that there are significant effects of various pertinent parameters on velocity and temperature profiles.

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