scholarly journals Analytical Solution of MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet with Partial Slip

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Samir Kumar Nandy
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Thermal Slip ◽  
Slip Parameter ◽  
Flow And Heat Transfer

This paper investigates the hydromagnetic boundary layer flow and heat transfer of a non-Newtonian Casson fluid in the neighborhood of a stagnation point over a stretching surface in the presence of velocity and thermal slips at the boundary. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformations. The analytic solutions are developed by a homotopy analysis method (HAM). The results pertaining to the present study indicate that the flow and temperature fields are significantly influenced by Casson parameter (), the magnetic parameter , the velocity slip parameter , and the thermal slip parameter . An increase in the velocity slip parameter causes decrease in the flow velocity, while an increase in the value of the thermal slip parameter causes increase in the temperature of the fluid. It is also observed that the velocity at a point decreases with increase in .

Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Tapas Ray Mahapatra ◽  
Samir Kumar Nandy ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Fluid Velocity ◽  
Velocity Slip ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Shrinking Sheet ◽  
Slip Parameter ◽  
Similarity Transformations ◽  
Flow And Heat Transfer

In this paper, the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet is investigated in the presence of velocity and thermal slips. With the help of similarity transformations, the governing Navier–Stokes and the energy equations are reduced to ordinary differential equations, which are then solved numerically using a shooting technique. Interesting solution behavior is observed for the similarity equations with multiple solution branches for certain parameter domain. Fluid velocity increases due to the increasing value of the velocity slip parameter resulting in a decrease in the temperature field. Temperature at a point increases with increase in the thermal slip parameter. The effects of the slips, stretching/shrinking, and the magnetic parameters on the skin friction or the wall shear stress, heat flux from the surface of the sheet, velocity, and temperature profiles are computed and discussed.

scholarly journals Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation

2020 ◽  
Vol 21 (1) ◽  
pp. 41-51
Author(s):  
Nur Syamila Yusof ◽  
Siti Khuzaimah Soid ◽  
Mohd Rijal Illias ◽  
Ahmad Sukri Abd Aziz ◽  
Nor Ain Azeany Mohd Nasir
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Velocity Slip ◽  
Casson Fluid ◽  
Numerical Results ◽  
Thermal Slip ◽  
Slip Parameter ◽  
Riga Plate

This study is aimed to analyze the steady of stagnation point flow and radiative heat transfer of a non-Newtonian fluid which is Casson fluid passing over an exponentially permeable slippery Riga plate in presence of thermal radiation, magnetic field, velocity slip, thermal slip, and viscous dissipation effects. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation then solved numerically by boundary value problem solver (BVP4C) in MATLAB software package. The numerical results are evaluated with previous researches to reach an agreement with the parameters of the current study. This study is discussing the behavior of the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number for various physical parameters such as magnetic field, radiation, suction, thermal slip, velocity slip, Prandtl number, Eckert number and modified Hartmann number. Numerical results are shown graphically for each parameter with different values. It is found that the momentum boundary layer thickness increases with increasing the values of Casson parameter. The temperature decreases when the velocity slip parameter and thermal slip parameter are increased.

scholarly journals MHD Partial Slip Flow and Heat Transfer of Nanofluids through a Porous Medium Over a Stretching Sheet with Convective Boundary Condition

2020 ◽  
Vol 12 (1) ◽  
pp. 39-59
Author(s):  
Yohannes Yirga
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Partial Slip ◽  
Slip Parameter ◽  
Convective Boundary ◽  
Porosity Parameter ◽  
Flow And Heat Transfer ◽  
Convective Parameter

This paper investigates the boundary layer analysis for magnetohydrodynamic partial slip flow and heat transfer of nanofluids through porous media over a stretching sheet with convective boundary condition. Four types of nanoparticles, namely copper, alumina, copper oxide and titanium oxide in the ethylene glycol (50%, i.e., Pr = 29.86) and water (i.e., Pr = 6.58) based fluids are studied. The governing highly nonlinear and coupled partial differential equations are solved numerically using fourth order Runge-Kutta method with shooting techniques. The velocity and temperature profiles are obtained and utilized to compute the skin friction coefficient and local Nusselt number for different values of the governing parameters viz. nanoparticle volume fraction parameter, magnetic field parameter, porosity parameter, velocity slip parameter and convective parameter. It is found that the velocity distribution of the nanofluids is a decreasing function of the magnetic parameter, porosity parameter, and velocity slip parameter. However, temperature of the nanofluids is an increasing function of magnetic field parameter, nanoparticle volume fraction parameter, porosity parameter, velocity slip parameter and convective parameter. The flow and heat transfer characteristics of the four nanofluids are compared. Moreover, comparison of the numerical results is made with previously published works for special cases and an excellent agreement is found.  Keywords: Magnetohydrodynamics, Partial Slip, Porous medium, Convective boundary, Nanofluid.

Hall effect on MHD flow and heat transfer of nanofluids over a stretching wedge in the presence of velocity slip and Joule heating

Open Physics ◽  
2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Xiaohong Su ◽  
Liancun Zheng
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Hall Effect ◽  
Joule Heating ◽  
Volume Fraction ◽  
Wedge Angle ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Temperature Fields ◽  
Flow And Heat Transfer

AbstractThis paper deals with the boundary layer flow and heat transfer of nanofluids over a stretching wedge with velocity-slip boundary conditions. In this analysis, Hall effect and Joule heating are taken into consideration. Four different types of water-base nanofluids containing copper (Cu), silver (Ag), alumina (Al2O3), and titania (TiO2) nanoparticles are analyzed. The partial differential equations governing the flow and temperature fields are converted into a system of nonlinear ordinary differential equations using a similarity transformation. The resulting similarity equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The effects of types of nanoparticles, the volume fraction of nanoparticles, the magnetic parameter, the Hall parameter, the wedge angle parameter, and the velocityslip parameter on the velocity and temperature fields are discussed and presented graphically, respectively.

Stagnation-Point Flow and Heat Transfer of a Casson Fluid towards a Stretching Sheet

2012 ◽  
Vol 67 (1-2) ◽  
pp. 70-76 ◽  
Author(s):  
Meraj Mustafa ◽  
Tasawar Hayat ◽  
Pop Ioan ◽  
Awatif Hendi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Analytic Solutions ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Stream Velocity ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

This article reports the flow of a Casson fluid in the region of stagnation-point towards a stretching sheet. The characteristics of heat transfer with viscous dissipation are also analyzed. The partial differential equations representing the flow and heat transfer of the Casson fluid are reduced to ordinary differential equations through suitable transformations. The flow is therefore governed by the Casson fluid parameter β, the ratio of the free stream velocity to the velocity of the stretching sheet a=c, the Prandtl number Pr, and the Eckert number Ec. The analytic solutions in the whole spatial domain have been computed by the homotopy analysis method (HAM). The dimensionless expressions for the skin friction coefficient and the local Nusselt number have been calculated and discussed.

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.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

Unsteady separated stagnation-point flow and heat transfer past a stretching/shrinking sheet in a copper-water nanofluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2588-2605 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stagnation Point ◽  
Design Methodology ◽  
Similarity Transformation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das. Design/methodology/approach A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Findings It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case. Originality/value The authors believe that all numerical results are new and original, and have not been published elsewhere.

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.

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

2015 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Stream Velocity ◽  
Slip Parameter ◽  
Mhd Boundary Layer

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

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