Finite difference approach in porous media transport modeling for magnetohydrodynamic unsteady flow over a vertical plate

2014 ◽  
Vol 24 (5) ◽  
pp. 1204-1223 ◽  
Author(s):  
Sahin Ahmed ◽  
Abdul Batin ◽  
Ali J. Chamkha
Keyword(s):  
Nusselt Number ◽  
Finite Difference ◽  
Thermal Radiation ◽  
Drag Force ◽  
Local Nusselt Number ◽  
Vertical Plate ◽  
Two Dimensional ◽  
Local Skin ◽  
Content Type ◽  
Electrically Conducting

Purpose – The purpose of this paper is to examine the effects of Darcian drag force and radiation-conduction on unsteady two-dimensional magnetohydrodynamic flow of viscous, electrically conducting and Newtonian fluid over a vertical plate adjacent to a Darcian regime in presence of thermal radiation and transversal magnetic field. A well-tested, numerically stable Crank-Nicolson finite-difference procedure is employed for the conservation equations. Excellent agreement is obtained for numerical solutions with previously published work. Design/methodology/approach – In this investigation, an efficient, accurate, extensively validated and unconditionally stable finite-difference scheme based on the Crank-Nicolson model is developed to solve the governing coupled, non-linear partial differential equations. The accuracy and effectiveness of the method are demonstrated. Findings – Different numerical results are obtained and presented graphically to explain the effect of various physical parameters on the velocity and temperature profiles, local, as well as average, skin friction and Nusselt number. It is found that, with a rise in Darcian drag force, flow velocity and temperature are reduced, but increased for all times. Both average and local skin frictions are reduced considerably with an increase in Darcian drag force, but reversed behavior is observed for the local Nusselt number. Increasing the thermal radiation effects accelerated the flow velocity as well as the fluid temperature and wall local skin friction in a saturated porous medium, but effectively reduced the local Nusselt number and average Nusselt number at the wall. Comparison with previously published works in the limits shows excellent agreement. Research limitations/implications – The analysis is valid for unsteady, two-dimensional laminar flow of an optically thick no-gray gas, electrically conducting, and Newtonian fluid past an isothermal vertical surface adjacent to the Darcian regime with variable surface temperature. An extension to three-dimensional flow case is left for future work. Practical implications – Practical interest of such study includes applications in electromagnetic lubrication, boundary cooling, bio-physical systems and in many branches of engineering and science. It is well known that the effect of thermal radiation is important in space technology and high temperature processes. Thermal radiation also plays an important role in controlling heat transfer process in polymer processing industry.

Effects of chemical reaction and thermal radiation on unsteady double diffusive convection

2014 ◽  
Vol 24 (5) ◽  
pp. 1124-1140 ◽  
Author(s):  
A.M. Rashad ◽  
Sameh Elsayed Ahmed ◽  
Mohamed Ahmed Mansour
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Local Nusselt Number ◽  
Darcy Number ◽  
Content Type ◽  
Various Boundary Conditions ◽  
Chemical Reaction Parameter ◽  
Local Sherwood Number ◽  
Buoyancy Ratio

Purpose – The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects. Design/methodology/approach – In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled. Findings – Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase. Originality/value – The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.

Hartmann Newtonian radiating MHD flow for a rotating vertical porous channel immersed in a Darcian Porous Regime

2014 ◽  
Vol 24 (7) ◽  
pp. 1454-1470 ◽  
Author(s):  
Sahin Ahmed ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Thermal Radiation ◽  
Exact Solutions ◽  
Drag Force ◽  
Body Force ◽  
Porous Channel ◽  
Content Type ◽  
Electrically Conducting ◽  
Variable Surface

Purpose – The purpose of this paper is to develop and correct the problem studied by Makinde and Mhone (2005) to a rotating vertical porous channel immersed in a Darcian porous regime in presence of a strong transverse magnetic filled and with the application of thermal radiation. In this investigation, the fluid is considered to be of viscous, electrically conducting, Newtonian and radiating and is optically thin with a relatively low density. Excellent agreement is obtained for exact solutions with those of previously published works. Design/methodology/approach – In this investigation, a closed form analytical method based on the complex notations for the velocity, temperature and the pressure is developed to solve the governing coupled, non-linear partial differential equations. The accuracy and effectiveness of the method are demonstrated. Findings – Interestingly observed that, the Lorentizian body force is not act as a drag force as in conventional MHD flows, but as an aiding body force and this will serve to accelerate the flow and boost the primary velocities. Due to the large rotation of the channel, the primary velocities are become flattered and shift towards the walls of the channel. With a rise in Darcian drag force, flow velocity and shear stress are found to reduce. Moreover, increasing thermal radiation and rotation of the channel strongly depress the shear stress, and maximum flow reversal, i.e. back flow is observed due to large Darcian resistance, thermal radiation and rotation. Research limitations/implications – The analysis is valid for unsteady, two-dimensional laminar flow of an optically thick no-gray gas, electrically conducting, and Newtonian fluid past an isothermal vertical surface adjacent to the Darcian regime with variable surface temperature. An extension to three-dimensional flow case is left for future work. Practical implications – Practical interest of such study includes applications in magnetic control of molten iron flow in the steel industry, liquid metal cooling in nuclear reactors, magnetic suppression of molten semi-conducting materials and meteorology and in many branches of engineering and science. It is well known that the effect of thermal radiation is important in space technology and high-temperature processes. Thermal radiation also plays an important role in controlling heat transfer process in polymer processing industry. Originality/value – The paper presents useful conclusions with the help of graphical results obtained from studying exact solutions based on complex notations for Darcian drag force, rotation of the channel and conduction-radiation heat transfer interaction by unsteady rotational flow in a vertical porous channel embedded in a Darcian porous regime under the application hydromagnetic force. The results of this study may be of interest to engineers for heat transfer augmentation and drag reduction in heat exchangers as well as MHD boundary layer control of re-entry vehicles, etc.

Radiative hybrid nanofluid flow past a rotating permeable stretching/shrinking sheet

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Stability Analysis ◽  
Differential Equations ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Current Work ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin ◽  
Content Type

Purpose This paper aims to discuss a stability analysis on Cu-Al2O3/water nanofluid having a radiation and suction impacts over a rotating stretching/shrinking sheet. Design/methodology/approach The partial differential equations are converted into nonlinear ordinary differential equations using similarity transformation and then being solved numerically using built in function in Matlab software (bvp4c). The effects of pertinent parameters on the temperature and velocity profiles together with local Nusselt number and skin friction are reported. Findings Compared to previously published studies, the current work is noticed to be in good deal. The analysis further shows that the non-unique solutions exist for certain shrinking parameter values. Hence, a stability analysis is executed using a linear temporal stability analysis and concluded that the second solution is unstable, while the first solution is stable. The effect of suction parameter is observed to be significant in obtaining the solutions. The improvement of the local skin friction and the decrease of the local Nusselt number on the shrinking surface are observed with the increment of the copper nanoparticle volume fractions. Originality/value The originality of current work is the numerical solutions and stability analysis of hybrid nanofluid in rotating flow. This work has also resulted in producing the non-unique solutions for the shrinking sheet, and a stability analysis has also been executed for this flow showing that the second solution is unstable, while the first solution is stable. This paper is therefore valuable for engineers and scientist to get acquainted with the properties of the flow, its behavior and the way to predict it. The authors admit that all the findings are original and were not published anywhere else.

Hydromagnetic-oscillatory flow of a nanofluid with Hall effect and thermal radiation past vertical plate in a rotating porous medium

2018 ◽  
Vol 14 (2) ◽  
pp. 360-386 ◽  
Author(s):  
Sreedevi Gandluru ◽  
Prasada Rao D.R.V. ◽  
O.D. Makinde
Keyword(s):  
Porous Medium ◽  
Thermal Radiation ◽  
Hall Effect ◽  
Oscillatory Flow ◽  
Vertical Plate ◽  
Hall Current ◽  
Local Skin ◽  
Content Type ◽  
Special Cases ◽  
The Impact

Purpose The purpose of this paper is to investigate the impact of thermal radiation interaction with Hall current, buoyancy force, and oscillatory surface temperature on hydromagnetic-mixed convective heat exchange stream of an electrically conducting nanofluid past a moving permeable plate in a porous medium within a rotating system. Design/methodology/approach Analytical closed-form solutions are obtained for both the momentum and the energy equations using the perturbation method. Findings The effects of various important parameters on velocity and temperature fields within the boundary layer are discussed for three different water-based nanofluids containing copper (Cu), aluminum oxide (Al2O3), and titanium dioxide (TiO2) as nanoparticles. Local skin friction and Nusselt number are illustrated graphically and discussed quantitatively. The results show that Hall current significantly affects the flow system. Results for some special cases of the present analysis are in good agreement with the existing literature. Originality/value The problem is relatively original to study the hydromagnetic-oscillatory flow of a nanofluid with Hall effect and thermal radiation past a vertical plate in a rotating porous medium.

Chemical Reaction and Thermal Radiation Effects on MHD Mixed Convection over a Vertical Plate with Variable Fluid Properties

2018 ◽  
Vol 387 ◽  
pp. 332-342
Author(s):  
R. Suresh Babu ◽  
B. Rushi Kumar ◽  
Oluwole Daniel Makinde
Keyword(s):  
Thermal Radiation ◽  
Chemical Reaction ◽  
Radiation Effects ◽  
Vertical Plate ◽  
Numerical Comparison ◽  
Electrically Conducting ◽  
Fluid Properties ◽  
Integral Scheme ◽  
Dimensional Parameters ◽  
Homogeneous Chemical

This article investigates the magnetohydrodynamic mixed convective heat, and mass transfer flow of an incompressible, viscous, Boussinesq, electrically conducting fluid from a vertical plate in a sparsely packed porous medium in the presence of thermal radiation and an nth order homogeneous chemical reaction between the fluid and the diffusing species numerically. In this investigation, the fluid and porous properties like thermal and solutal diffusivity, permeability and porosity are all considered to be vary. The governing non-linear PDE's for the fluid flow are derived and transformed into a system of ODE's using an appropriate similarity transformation. The resultant equations are solved numerically using shooting technique and Runge-Kutta integral scheme with the help of Newton-Raphson algorithm in order to know the characteristics of the fluid for various non-dimensional parameters which are controlling the physical system graphically. The results of the numerical scheme are validated and a numerical comparison has been made with the available literature in the absence of some parameters and found that in good agreement. Nomenclature

Nanofluid flow past an impulsively started vertical plate with variable surface temperature

2016 ◽  
Vol 26 (1) ◽  
pp. 328-347 ◽  
Author(s):  
Rajesh Vemula ◽  
A J Chamkha ◽  
Mallesh M. P.
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Aluminium Oxide ◽  
Skin Friction Coefficient ◽  
Viscous Drag ◽  
Content Type ◽  
Variable Surface ◽  
Variable Surface Temperature

Purpose – The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature. Design/methodology/approach – The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations. Findings – The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m. Research limitations/implications – The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. Practical implications – The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods). Originality/value – This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

Heat transfer analysis of ethylene glycol-based Casson nanofluid around a horizontal circular cylinder with MHD effect

2020 ◽  
Vol 234 (13) ◽  
pp. 2569-2580 ◽  
Author(s):  
Firas A Alwawi ◽  
Hamzeh T Alkasasbeh ◽  
AM Rashad ◽  
Ruwaidiah Idris
Keyword(s):  
Nusselt Number ◽  
Circular Cylinder ◽  
Ethylene Glycol ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Heat Transfer Analysis ◽  
Constant Wall Temperature ◽  
Local Skin ◽  
Casson Nanofluid ◽  
Horizontal Circular Cylinder

In this work, efforts were taken to investigate the free convection of ethylene glycol-based Casson nanofluid and it is affected by a magnetic field about a horizontal circular cylinder. Three different types of oxide nanoparticles were used along with constant wall temperature. Tiwari and Das's nanofluid model was used to investigate the MHD free convective flow of Casson nanofluid. The transformed governing PDEs were solved via the Keller box method. Numerical and graphical findings were acquired by using MATLAB software, in addition to studying and analyzing the influence of related parameters, on the velocity, temperature, local skin friction coefficient, and local Nusselt number. The results demonstrate that copper oxide ethylene glycol-based Casson nanofluid has the lowest local Nusselt number, velocity and, it has the highest temperature. Also, our results were in excellent agreement with prior published results.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

Computational Study of Three-Dimensional Stagnation Point Nanofluid Bioconvection Flow on a Moving Surface With Anisotropic Slip and Thermal Jump Effect

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
M. J. Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail ◽  
O. Anwar Bég
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Stagnation Point ◽  
Local Nusselt Number ◽  
Local Density ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Slip Parameter ◽  
Moving Surface ◽  
Local Skin

The effects of anisotropic slip and thermal jump on the three-dimensional stagnation point flow of nanofluid containing microorganisms from a moving surface have been investigated numerically. Anisotropic slip takes place on geometrically striated surfaces and superhydrophobic strips. Zero mass flux of nanoparticles at the surface is applied to achieve practically applicable results. Using appropriate similarity transformations, the transport equations are reduced to a system of nonlinear ordinary differential equations with coupled boundary conditions. Numerical solutions are reported by means of very efficient numerical method provided by the symbolic code Maple. The influences of the emerging parameters on the dimensionless velocity, temperature, nanoparticle volumetric fraction, density of motile microorganism profiles, as well as the local skin friction coefficient, the local Nusselt number, and the local density of the motile microorganisms are displayed graphically and illustrated in detail. The computations demonstrate that the skin friction along the x-axis is enhanced with the velocity slip parameter along the y-axis. The converse response is observed for the dimensionless skin friction along the y-axis. The heat transfer rate is increased with greater velocity slip effects but depressed with the thermal slip parameter. The local Nusselt number is increased with Prandtl number and decreased with the thermophoresis parameter. The local density for motile microorganisms is enhanced with velocity slip parameters and depressed with the bioconvection Lewis number, thermophoresis, and Péclet number. Numerical results are validated where possible with published results and excellent correlation is achieved.

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