Magnetohydrodynamic Time-Dependent Bio-Nanofluid Flow in a Porous Medium with Variable Thermophysical Properties

In this work, a theoretical model with a numerical solution is brought forward for a bio-nanofluid with varying fluid features over a slippery sheet. The partial differential equations (PDEs) involving temperature-dependent quantities have been translated into ordinary differential equations (ODEs) by using similarity variables. Numerical verifications have been done in three different methods: finite difference method, shooting method, and bvp4c. To figure out the influence of parameters on the flows, the graphs are plotted for the velocity, temperature, concentration, and microorganism curves. The boundary layer thickness of the microorganism profile reduces with the Schmidt number and Peclet number. In addition to adding radiative heat flux, we added heat generation, rate of chemical reaction, and first-order slip. Adding these parameters brought new aspects to the underlying profiles. Moreover, the obtained data of the skin friction coefficient, the local Nusselt number, the local Sherwood number, and the local density of motile microorganisms are tabulated against various parameters for the physical parameters. From the results, it is apparent that the local Nusselt number decreases with the Brownian and thermophoretic parameters. The data obtained for physical parameters have a close agreement with the published data. Finally, the graphs for slip conditions are significantly different when the comparison is drawn with no-slip condition.

Download Full-text

Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms

Journal of Heat Transfer ◽

10.1115/1.4026011 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 30

Author(s):

Khairy Zaimi ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Stagnation Point ◽

Sherwood Number ◽

Local Nusselt Number ◽

Local Density ◽

Skin Friction Coefficient ◽

Shrinking Sheet ◽

Gyrotactic Microorganisms ◽

Local Sherwood Number

The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Péclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

Download Full-text

MHD flow, under the kinetic postulate, of fluids that are initially liquid under thermal radiation effects

Canadian Journal of Physics ◽

10.1139/cjp-2018-0102 ◽

2019 ◽

Vol 97 (6) ◽

pp. 579-587

Author(s):

Azad Hussain ◽

Zainia Muneer ◽

M.Y. Malik ◽

Saadia Ghafoor

Keyword(s):

Nusselt Number ◽

Differential Equations ◽

Thermal Radiation ◽

Skin Friction ◽

Radiation Effects ◽

Shooting Method ◽

Porous Plate ◽

Mhd Flow ◽

Physical Parameters ◽

Runge Kutta Method

The present study focuses on the non-Newtonian magnetohydrodynamic flow, under the kinetic postulate, of fluids that are initially liquid past a porous plate in the appearance of thermal radiation effects. Resemblance transfigurations are used to metamorphose the governing equations for temperature and velocity into a system of ordinary differential equations. We then solved these differential equations subject to convenient boundary conditions by using the shooting method along with the Runge–Kutta method. Heat transfer and characteristic flow results are acquired for different compositions of physical parameters. These results are extended graphically to demonstrate interesting attributes of the physics of the problem. Nusselt number and skin friction coefficients are also discussed via graphs and tables for different values of dimensionless parameters. Decline occurs in velocity profile due to escalating values of M. Temperature profile depicts growing behavior due to acceleration in the values of λ and M. Nusselt number and skin friction curves represent rising behavior according to their parameters.

Download Full-text

Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽

10.3390/math8071175 ◽

2020 ◽

Vol 8 (7) ◽

pp. 1175

Author(s):

Nor Ain Azeany Mohd Nasir ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Differential Equations ◽

Prandtl Number ◽

Heat Generation ◽

Local Nusselt Number ◽

Magnetic Parameter ◽

Skin Friction Coefficient ◽

Shrinking Sheet ◽

Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

Download Full-text

Viscous Dissipation and Joule Heating Effects on MHD Bioconvection Flow of a Nanofluid Containing Gyrotactic Microorganisms Over a Vertical Isothermal Cone

Journal of Nanofluids ◽

10.1166/jon.2020.1744 ◽

2020 ◽

Vol 9 (3) ◽

pp. 242-255

Author(s):

Hossam A. Nabwey ◽

S. M. M. El-Kabeir ◽

A. M. Rashad ◽

M. M. M. Abdou

Keyword(s):

Magnetic Field ◽

Nusselt Number ◽

Friction Coefficient ◽

Sherwood Number ◽

Local Density ◽

Skin Friction Coefficient ◽

Local Skin ◽

Gyrotactic Microorganisms ◽

Local Skin Friction ◽

Local Sherwood Number

The main objective of the present study is to explore the flow of a nanofluid containing gyrotactic microorganisms over a vertical isothermal cone surface in the presence of viscous dissipation and Joule heating. The combined effects of a transverse magnetic field and Navier slip in the flow are considered. Using appropriate transforms the set of partial differential equations governing the flow are converted to a set of ordinary differential equations. Influence of the parameters governing the flow is shown for velocity, temperature, concentration and motilemicroorganisms as well as local skin Friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number. An increasing in the value of Eckert number rises the velocity of the fluid and reduce the temperature, concentration and density of motile microorganisms profiles, while buoyancy ratio Nr and magnetic field parameters increase local skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number decrease as a result of the presence of Lorentz force which resist the motion of the flow. On the other hand, the motile microorganisms boundary layer thickness decreases with an increasing on the bioconvection Lewis number.

Download Full-text

Non-similar characteristics of mixed convective slip flow over a wedge with temperature-dependent thermo-physical properties

Modern Physics Letters B ◽

10.1142/s0217984919504554 ◽

2019 ◽

Vol 33 (36) ◽

pp. 1950455

Author(s):

Nepal Chandra Roy ◽

Sudharonjon Roy ◽

Naved Azum ◽

Anish Khan ◽

Abdullah M. Asiri ◽

...

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Skin Friction ◽

Sherwood Number ◽

Local Nusselt Number ◽

Slip Flow ◽

Skin Friction Coefficient ◽

Local Skin ◽

Local Skin Friction ◽

Local Sherwood Number

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

Download Full-text

Effects of Non-Uniform Heat Generation/Absorption and Radiation on Hydromagnetic Dissipative Flow over a Porous Nonlinear Stretching Surface with Heat and Mass Fluxes

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2019-0048 ◽

2019 ◽

Vol 24 (4) ◽

pp. 36-52

Author(s):

S.P. Anjali Devi ◽

M. Agneeshwari

Keyword(s):

Differential Equations ◽

Heat Generation ◽

Nonlinear Partial Differential Equations ◽

Skin Friction Coefficient ◽

Iteration Scheme ◽

Published Data ◽

Physical Parameters ◽

Similarity Transformations ◽

Uniform Heat ◽

Nonlinear Stretching

Abstract Forced convective heat and mass transfer flow of hydromagnetic, radiating and dissipative fluid over a porous nonlinear stretching sheet in the presence of non-uniform heat generation/absorption is investigated numerically. The system of nonlinear partial differential equations governing the physical problem is reduced to nonlinear ordinary differential equations by means of suitable similarity transformations and are solved numerically using Nachtsheim Swigert shooting iteration scheme together with fourth order Runge Kutta method. The effects of various physical parameters on velocity, temperature and concentration distributions are depicted graphically. The important findings of this study exhibited that the effect of non-uniform heat generation/absorption parameter and radiation parameter have significant role in controlling thermal boundary layer thickness and temperature. Numerical values of the skin friction coefficient, temperature and concentration at the wall are shown in a tabular form. A comparison is made with previously published data which results in good agreement.

Download Full-text

The Magnetohydrodynamic Boundary Layer Flow of a Nanofluid past a Stretching/Shrinking Sheet with Slip Boundary Conditions

Journal of Applied Mathematics ◽

10.1155/2014/907152 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 7

Author(s):

Syahira Mansur ◽

Anuar Ishak

Keyword(s):

Nusselt Number ◽

Local Nusselt Number ◽

Magnetic Parameter ◽

Velocity Slip ◽

Skin Friction Coefficient ◽

Shrinking Sheet ◽

Slip Parameter ◽

Slip Boundary ◽

Layer Flow ◽

Local Sherwood Number

The magnetohydrodynamic (MHD) boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.

Download Full-text

MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical Reaction

Advances in Mathematical Physics ◽

10.1155/2021/9950993 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

J. Bouslimi ◽

M. Omri ◽

R. A. Mohamed ◽

K. H. Mahmoud ◽

S. M. Abo-Dahab ◽

...

Keyword(s):

Porous Medium ◽

Nusselt Number ◽

Friction Coefficient ◽

Thermal Radiation ◽

Skin Friction ◽

Heat Generation ◽

Joule Heating ◽

Local Nusselt Number ◽

Skin Friction Coefficient ◽

Physical Parameters

In this article, the effect of electromagnetic force with the effect of thermal radiation on the Williamson nanofluid on a stretching surface through a porous medium was studied considering the effect of both heat generation/absorption and Joule heating. On the other hand, the effect of Brownian motion and thermophoresis coefficients was considered. The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. Moreover, the effect of the resulting physical parameters on the distributions of velocity, temperature, and concentration of nanoparticles has been studied by using graphical forms with an interest in providing physical meanings to each parameter. Finally, special diagrams were made to explain the study of the effect of some physical parameters on the skin friction coefficient and the local Nusselt number; these results led to reinforcement in the values of the skin friction coefficient for the increased values of the magnetic field and the Darcy number while the effect on the local Nusselt number by thermal radiation as well as the heat generation/absorption coefficients became negative.

Download Full-text

Hall Effects on Unsteady Magnetohydrodynamic Flow of a Nanofluid Past an Oscillatory Vertical Rotating Flat Plate Embedded in Porous Media

Journal of Nanofluids ◽

10.1166/jon.2021.1776 ◽

2021 ◽

Vol 10 (2) ◽

pp. 259-269

Author(s):

M. Veera Krishna ◽

N. Ameer Ahamad ◽

Ali J. Chamkha

Keyword(s):

Heat Transfer ◽

Porous Media ◽

Nusselt Number ◽

Friction Coefficient ◽

Local Nusselt Number ◽

Hall Current ◽

Skin Friction Coefficient ◽

Engineering Industry ◽

Hall Effects ◽

The Impact

In the current investigative paper, the impact of Hall current on an unsteady magnetohydrodynamic liberated convection revolving flow of a nanofluid restricted with a uniform absorbent medium over an oscillatory moving vertical smooth plate with convective as well as diffusive frontier conditions has been reviewed. The non-dimensionalized governing differential equations by the appropriate frontier conditions are resolved by the perturbations technique. The impacts of the physical constants on the flow as well as the heat transfer features are displayed graphically and analyzed for Cu as well as Al2O3 nanoparticles. For the engineering industry, the skin friction coefficient, local Nusselt number, along with the Sherwood’s number are examined numerically in detail.

Download Full-text

A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

Mathematics ◽

10.3390/math7121199 ◽

2019 ◽

Vol 7 (12) ◽

pp. 1199 ◽

Cited By ~ 2

Author(s):

Jing Zhu ◽

Yaxin Xu ◽

Xiang Han

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Temperature Jump ◽

Thin Sheet ◽

Velocity Slip ◽

Skin Friction Coefficient ◽

Slip Condition ◽

Physical Parameters ◽

Nanofluid Flow ◽

Flow And Heat Transfer

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

Download Full-text