Non-uniform mass transfer in MHD mixed convection flow of water over a sphere with variable viscosity and Prandtl number

2016 ◽  
Vol 26 (7) ◽  
pp. 2235-2251 ◽  
Author(s):  
J. Rajakumar ◽  
P. Saikrishnan ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Slot Suction

Purpose The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field. Design/methodology/approach The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme. Findings The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0. Originality/value The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

scholarly journals MHD Nonlinear Mixed Convection Flow of Micropolar Nanofluid over Nonisothermal Sphere

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Wubshet Ibrahim ◽  
Chaluma Zemedu
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Mathematical Formulation ◽  
Magnetic Field Effect ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Nonlinear Boundary Value Problems ◽  
Micropolar Nanofluid ◽  
Nonlinear Mixed Convection

In this paper, two-dimensional steady laminar boundary layer flow of a nonlinear mixed convection flow of micropolar nanofluid with Soret and magnetic field effect over a nonisothermal sphere is evaluated. The mathematical formulation for the flow problem has been made with appropriate similarity transformation and dimensionless variables, and the main nonlinear boundary value problems were reduced into mixed high-order nonlinear ordinary differential equations. Solution for velocity, microrotation, temperature, and concentration has been obtained numerically. The equations were calculated using method bvp4c from Matlab software for various quantities of main parameters. The effects of various parameters on skin friction coefficient f″0, wall duo stress coefficient -G′0, and convection mass transfer coefficient -Φ′0 are analysed and presented through the graphs and tables. The convergence test has been maintained. For the number of points greater than the suitable mesh number of points, the precision is not influenced but the set time is increased. Moreover, a comparison with a previous paper, obtainable in the literature, has been presented and an excellent agreement is obtained. The findings indicate that an increase in the values of nonisothermal parameters (m, P), magnetic Ma, thermal and solutal nonlinear convection (λ, s) parameter, and Soret number is to enhance the temperature difference between the boundary layer and ambient fluid to diffuse which increases the velocity profile f′ζ and their boundary layer thicknesses near the surface of the sphere.

Unsteady mixed convection flow at a three-dimensional stagnation point

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Unsteady Mixed Convection

Purpose This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function. Findings The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

Boundary layer flow near stagnation-points on a vertical surface with slip in the presence of transverse magnetic field

2014 ◽  
Vol 24 (3) ◽  
pp. 643-653 ◽  
Author(s):  
Ibrahim Yakubu Seini ◽  
Daniel Oluwole Makinde
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Stagnation Point ◽  
Vertical Surface ◽  
Skin Friction Coefficient ◽  
Content Type ◽  
Layer Flow

Purpose – The purpose of this paper is to investigate the MHD boundary layer flow of viscous, incompressible and electrically conducting fluid near a stagnation-point on a vertical surface with slip. Design/methodology/approach – In the study, the temperature of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing differential equations are transformed into systems of ordinary differential equations and solved numerically by a shooting method. Findings – The effects of various parameters on the heat transfer characteristics are discussed. Graphical results are presented for the velocity and temperature profiles whilst the skin-friction coefficient and the rate of heat transfers near the surface are presented. It is observed that the presence of the magnetic field increases the skin-friction coefficient and the rate of heat transfer near the surface towards the stagnation-point. Originality/value – The presence of magnetic field increases the skin-friction coefficient and the rate of heat transfer near the surface towards the stagnation-point.

scholarly journals Effect of Temperature-Dependent Variable Viscosity on Magnetohydrodynamic Natural Convection Flow along a Vertical Wavy Surface

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Nazma Parveen ◽  
Md. Abdul Alim
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Effect Of Temperature ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Natural Convection Flow

The effect of temperature dependent variable viscosity on magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a nondimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms are shown graphically for a selection of parameters set consisting of viscosity parameter (), magnetic parameter (), and Prandtl number (Pr). Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are also presented in tabular form.

Numerical study of laminar mixed convection flow in a lid-driven square cavity filled with porous media

2018 ◽  
Vol 28 (4) ◽  
pp. 857-877 ◽  
Author(s):  
Najib Hdhiri ◽  
Brahim Ben Beya
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Mixed Convection ◽  
Transfer Rate ◽  
Richardson Number ◽  
Convection Flow ◽  
Brinkman Model ◽  
Mixed Convection Flow ◽  
Content Type

Purpose The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure. Design/methodology/approach The authors used the finite volume method. Findings The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium. Originality/value A comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

scholarly journals MHD Heat and Mass Transfer Steady Flow of a Convective Fluid Through a Porous Plate in The Presence of Multiple Parameters

2021 ◽  
Vol 89 (2) ◽  
pp. 56-75
Author(s):  
Obulesu Mopuri ◽  
Charankumar Ganteda ◽  
Bhagyashree Mahanta ◽  
Giulio Lorenzini
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mass Transfer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Perturbation Technique ◽  
Fluid Velocity ◽  
Convection Flow ◽  
Concentration Profiles ◽  
Mixed Convection Flow

The main aim of this investigation is to study thermo diffusion, heat source/sink, Joule and chemical effects on heat transfer in MHD mixed convection flow and mass transfer past an infinite vertical plate with ohmic heating and viscous dissipation have been studied. We consider the mixed convection flow of an incompressible and electrically conducting viscous fluid such that x* -axis is taken along the plate in upward direction and y* -axis is normal to it. A transverse constant magnetic field is applied i.e., in the direction of y*-axis. Approximate solutions have been derived for velocity, temperature, concentration profiles, skin friction, rate of heat transfer and rate of mass transfer using perturbation technique. The obtained results are discussed with the help of graphs to observe the effect of various parameters like Grashof number (Gr), the modified Grashof number (Gm), magnetic parameter (M), Permeability parameter(K), Prandtl number (Pr), Heat Sink(Q), Radiation Parameter (F), Soret parameter (S0), Eckert number (E),Schmidt number(Sc) and Chemical reaction parameter(K0) taking two cases viz. Fluid velocity, temperature and concentration profiles are comparison with Pr=0.71(Air) and Pr =7 (Water) various parameters in cooled and heated plates. Case I: when Gr > 0 (flow on cooled plate), and Case II: Gr < 0, (flow on heated plate). Both the fluid velocity and concentration rising with the increment values of Soret parameter in the fluids Air and Water and also discussed skin friction, Nusselt number and Sherwood number in the fluid’s mercury, electrolytic solution, air and water. The novelty of this study is the consideration of simultaneous occurrence of radiation, heat absorption as well as thermo- diffusion in the magnetic field. It varies in several aspects such as non-dimensional parameters, analytical solutions, and graphical solutions, the analytic solution using the Perturbation technique, and numerical solution using Matlab software for the profile.

scholarly journals G-jitter induced mixed convection flow of a second grade fluid past an inclined stretching sheet

2018 ◽  
Vol 189 ◽  
pp. 01006
Author(s):  
Rawi Noraihan Afiqah ◽  
Ilias Mohd Rijal ◽  
Rahimah Mahat ◽  
Isa Zaiton Mat ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Modulation Frequency ◽  
Second Grade ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Second Grade Fluid ◽  
Grade Fluid

An analysis was carried out to study the mixed convection flow of a non-Newtonian second grade fluid past an inclined stretching sheet in the presence of a g-jitter effect. The transformed governing equation, consisting of coupled non-linear partial differential equations, was solved numerically using an implicit finite-difference scheme known as the Keller-box method. The flow and heat transfer characteristics in terms of velocity and temperature profiles as well as the skin friction and heat transfer coefficients influenced by the amplitude of modulation, frequency of oscillation, inclination angle and second grade parameters were presented graphically and analysed in detail. The findings revealed that the heat transfer coefficient is enhanced with an increase in the second grade parameter, whereas the opposite trend is observed for the skin friction coefficient.

Viscous dissipation effect on mixed convection flow of a micropolar fluid over an exponentially stretching sheet

2009 ◽  
Vol 87 (4) ◽  
pp. 359-368 ◽  
Author(s):  
Mohamed Abd El-Aziz
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mixed Convection ◽  
Viscous Dissipation ◽  
Convective Transport ◽  
Convection Flow ◽  
Local Similarity ◽  
Mixed Convection Flow ◽  
Local Skin ◽  
Exponential Stretching

Micropolar boundary-layer flow and heat transfer characteristics associated with a heated exponential stretching continuous sheet being cooled by a mixed convection flow are examined. The relevant heat transfer mechanisms are of interest in a wide variety of practical applications such as hot rolling, continuous casting, extrusion, and drawing. The wall temperature and stretching velocity are assumed to vary according to specific exponential forms. The contributions of buoyancy along with viscous dissipation on the convective transport in the boundary-layer region is analyzed in the opposing and assisting flow situations. Local similarity solutions are obtained for the boundary-layer equations governing the problem. A parametric study of the mixed convection parameter ξ, the micropolar parameter Δ, the Eckert number Ec, the parameter of temperature distribution n, and Prandtl number Pr is conducted and a representative set of numerical results for the velocity, angular velocity, temperature profiles, local skin friction coefficient, wall couple stress parameter, and local Nusselt number are illustrated graphically to show typical trends of the solutions.

MHD-mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall

2017 ◽  
Vol 27 (6) ◽  
pp. 1231-1248 ◽  
Author(s):  
T. Javed ◽  
Z. Mehmood ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Bottom Wall ◽  
Local Thermal Equilibrium ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Left And Right

Purpose The purpose of this paper is to analyze numerical results for heat transfer through mixed convection in an incompressible steady lid-driven fluid flow inside a trapezoidal cavity in the presence of a uniform magnetic field. Design/methodology/approach In this study, the authors have considered three different cases, in which left and right walls of the cavity are tilted at different angles of 0, 30 and 45 degrees, respectively. Both left and right side walls of the cavity are taken cold and the upper wall is insulated and assumed moving with constant speed, whereas the bottom wall is considered to be heated uniformly/non-uniformly. To eliminate pressure term, penalty method is applied to governing Navier–Stokes’ equations. The reduced equations are solved by Galerkin weighted residual technique of finite element method. Grid-independent results are obtained and shown in terms of plots for streamlines, isotherms, Nusselt number and average Nusselt number for a wide range of flow parameters, including Rayleigh numbers Ra, Prandtl number Pr and Hartman number Ha. Findings It has been observed that the effects of moving lid become negligible for Ra = 100,000, whereas increasing Rayleigh number results in stronger streamline circulation and convection dominant effects inside the enclosure. Local Nusselt number Nu along the bottom wall is observed to be maximum at edges and it reduces while moving toward the center from edges, and attains minimum value at the center of the bottom wall. Research limitations/implications The problem is modeled for laminar and incompressible flow, induced magnetic field has been considered negligibly small and local thermal equilibrium has been assumed. Originality/value In this investigation, the authors have presented new and original results for mixed convection flow inside a lid-driven trapezoidal cavity under the influence of a magnetic field. Hence, this study would be important for the researchers working in the area of heat transfer in cavity flows involving magnetic effects to become familiar with the flow behavior and properties.

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