scholarly journals Modelling laminar transport phenomena in a Casson rheological fluid from an isothermal sphere with partial slip in a non-Darcy porous medium

2013 ◽  
Vol 40 (4) ◽  
pp. 469-510 ◽  
Author(s):  
Ramachandra Prasad ◽  
Subba Rao ◽  
Bhaskar Reddy ◽  
Anwar Bég
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Flow And Heat Transfer ◽  
Fluid Parameter

The flow and heat transfer of Casson fluid from a permeable isothermal sphere in the presence of slip condition in a non-Darcy porous medium is analyzed. The sphere surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. Increasing the velocity slip parameter is found to decrease the velocity and boundary layer thickness and increases the temperature and the boundary layer thickness. The velocity decreases with the increase the non-Darcy parameter and is found to increase the temperature. The velocity increases with the increase the Casson fluid parameter and is found to decrease the temperature. The Skin-friction coefficient and the local Nusselt number is found to decrease with the increase in velocity and thermal slip parameters respectively.

Flow and heat transfer to Sisko fluid with partial slip

2016 ◽  
Vol 94 (8) ◽  
pp. 724-730 ◽  
Author(s):  
Masood Khan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Layer Thickness ◽  
Analytical Solutions ◽  
Boundary Layer Thickness ◽  
Velocity Slip ◽  
Partial Slip ◽  
Exact Analytical Solutions ◽  
Flow And Heat Transfer

In this paper we study the partial slip effects on the flow and heat transfer of an incompressible non-Newtonian fluid over a nonlinear stretching sheet. The velocity slip boundary condition based on the Sisko constitutive fluid model is introduced. Suitable dimensionless variables are used to convert the governing partial differential equations into ordinary differential equations. Numerical solutions of these equations are obtained by the Runge–Kutta Fehlberg method. Additionally, the exact analytical solutions are presented in some special cases. The computational results for the velocity, temperature, skin-friction coefficient, and Nusselt number are presented in graphical and tabular forms. To validate the numerical results obtained, a comparison is made with the exact analytical solutions. The analysis of the results obtained shows that enhancement in the velocity slip parameter reduces the velocity as well as the momentum boundary layer thickness. However, quite the opposite is true with the temperature and corresponding thermal boundary layer thickness.

scholarly journals Hydromagnetic flow and heat transfer over a bidirectional stretching surface in a porous medium

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 205-220 ◽  
Author(s):  
Iftikhar Ahmad ◽  
Manzoor Ahmed ◽  
Zaheer Abbas ◽  
Muhammad Sajid
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Porous Medium ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Mhd Flow ◽  
Heat Transfer Analysis ◽  
Flow And Heat Transfer ◽  
Bidirectional Stretching

In this study, we present a steady three-dimensional magnetohydrodynamic (MHD) flow and heat transfer characteristics of a viscous fluid due to a bidirectional stretching sheet in a porous medium. The heat transfer analysis has been carried out for two heating processes namely (i) the prescribed surface temperature (PST) and (ii) prescribed surface heat flux (PHF). In addition the heat transfer rate varies along the surface. The similarity solution of the governing boundary layer partial differential equations is developed by employing homotopy analysis method (HAM). The quantities of interest are velocity, temperature, skin-friction and wall heat flux. The results obtained are presented through graphs and tabular data. It is observed that both velocity and boundary layer thickness decreases by increasing the porosity and magnetic field. This shows that application of magnetic and porous medium cause a control on the boundary layer thickness. Moreover, the results are also compared with the existing values in the literature and found in excellent agreement.

MHD Flow of Carreau Liquid with Partial Slip and Newtonian Heating

2018 ◽  
Vol 7 (4.10) ◽  
pp. 637
Author(s):  
S. Eswaramoorthi ◽  
K. Loganathan ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari ◽  
S. Rajan
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Partial Slip ◽  
Newtonian Heating ◽  
Linear Ordinary Differential Equations

This work deliberates the MHD flow of Carreau liquid past a stretching plate with thermal radiation, viscous dissipation and Joule heating. Additionally, partial velocity slip and Newtonian heating effects are included in our study. The similarity transformations are used to convert the governing dimensional partial differential equations into dimensionless ordinary differential equations. Homotopy analysis method (HAM) is employed to find the convergent series solutions of the governed non-linear ordinary differential equations. It is found that the magnetic field parameter slowdown the liquid motion and rises the liquid temperature. In addition, heat generation parameter enhances the thermal boundary layer thickness and chemical reaction parameter suppresses the solutal boundary layer thickness.  

scholarly journals Partial Slip Flow and Heat Transfer over a Stretching Sheet in a Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rajesh Sharma ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Flow And Heat Transfer

The boundary layer flow and heat transfer of a nanofluid over a stretching sheet are numerically studied. Velocity slip is considered instead of no-slip condition at the boundary as is usually appears in the literature. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. Numerical solutions of these equations are obtained using finite element method (FEM). The variations of velocity and temperature inside the boundary layer as well as the skin friction coefficient and the heat transfer rate at the surface for some values of the governing parameters, namely, the nanoparticle volume fraction and the slip parameter are presented graphically and discussed. Comparison with published results for the regular fluid is presented and it is found to be in excellent agreement.

scholarly journals Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Swirling Flow ◽  
Velocity Profiles ◽  
Partial Slip ◽  
Injection Velocity ◽  
Slip Boundary Conditions ◽  
Slip Boundary

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

scholarly journals Analysis of Non-Darcy MHD Flow of a Casson Fluid over a Non-linearly Stretching Sheet with Partial Slip in a Porous Medium

2019 ◽  
pp. 1-15
Author(s):  
Bhim Sen Kala
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Boundary Layer Thickness ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Momentum Equation ◽  
Partial Slip ◽  
Nonlinearly Stretching Sheet ◽  
The Mathematical Model

In this paper, we have analysed the non-Darcy MHD flow of a Casson fluid over a nonlinearly stretching sheet in a porous medium. In the mathematical model, using similarity variables, the momentum equation is transformed to non-dimensional ordinary differential equation. And then it is solved numerically using bvp4c method, a Matlab in- built bvp4c-programm. A discussion for the effects of the parameters involved on the boundary layer thickness and the magnitude of the velocity and skin friction has been done graphically and numerically using figures and tables.

scholarly journals MHD Stagnation-Point Flow of Casson Fluid and Heat Transfer over a Stretching Sheet with Thermal Radiation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Krishnendu Bhattacharyya
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Velocity Ratio ◽  
Casson Fluid ◽  
Velocity Boundary Layer

The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If velocity ratio parameter (B) and magnetic parameter (M) increase, then the velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson parameter (β). The velocity ratio parameter, Casson parameter, and magnetic parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of velocity ratio parameter. The rate of heat transfer is enhanced with increasing magnetic parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.

Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink

2015 ◽  
Vol 25 (4) ◽  
pp. 762-781 ◽  
Author(s):  
Tasawar Hayat ◽  
Taseer Muhammad ◽  
Sabir Ali Shehzad ◽  
A. Alsaedi
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Three Dimensional ◽  
Stretching Surface ◽  
Three Dimensional Flow ◽  
Soret And Dufour Effects ◽  
Content Type ◽  
Dimensional Flow

Purpose – The purpose of this paper is to study the Soret and Dufour effects in three-dimensional flow induced by an exponential stretching surface in a porous medium. Design/methodology/approach – Series solutions are developed. Findings – The authors observed that the temperature profile and thermal boundary layer thickness are enhanced when the authors increase the values of Dufour number. It is also examined that the concentration field and its associated boundary layer thickness are higher for the larger values of Soret number. Originality/value – Such investigation is not available in the literature.

scholarly journals MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions

2020 ◽  
Vol 9 (1) ◽  
pp. 457-469
Author(s):  
Bidyut Mandal ◽  
Krishnendu Bhattacharyya ◽  
Astick Banerjee ◽  
Ajeet Kumar Verma ◽  
Anil Kumar Gautam
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Soret Effect ◽  
Lewis Number ◽  
Continuous Group ◽  
Governing Equations ◽  
Soret Number ◽  
Stretching Plate

AbstractThis work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number.

Scrutinization of Chemical Reaction Effect on Flow and Mass Transfer of Prandtl Liquid over a Riga Plate in the Presence of Solutal Slip Effect

2018 ◽  
Vol 16 (8) ◽  
Author(s):  
B.J. Gireesha ◽  
K. Ganesh Kumar ◽  
B.C. Prasannakumar
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Layer Thickness ◽  
Chemical Reaction ◽  
Boundary Layer Thickness ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Riga Plate

AbstractIn the present paper focused on flow and mass transfer of Prandtl fluid over a Riga plate. The effects of chemical reaction and solutal slip are taken into the account. The governing partial differential equations are reduced into a set of coupled non linear ordinary differential equations using suitable similarity transformations. These equations are then solved using Runge-Kutta-Fehlberg-45 method. Behaviour of emerging parameters are presented graphically and discussed for velocity and concentration distribution. Numerical values of reduced skin friction coefficient and Sherwood number are shown in table and are discussed. From the plotted results it can be observed that the solutal boundary layer thickness decreases for larger values of chemical reaction parameter and Schmidt number. Also, momentum boundary layer thickness rise with stronger modified Hartman number.

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