scholarly journals Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates

2019 ◽  
Vol 24 (3) ◽  
pp. 75 ◽  
Author(s):  
Musawenkhosi Mkhatshwa ◽  
Sandile Motsa ◽  
Precious Sibanda
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Thermal Radiation ◽  
Surface Temperature ◽  
Skin Friction ◽  
Spectral Method ◽  
Heat Generation ◽  
Volume Fraction ◽  
Nanoparticle Volume Fraction ◽  
Flat Plates

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag–water nanofluid has higher skin friction and surface temperature than the Cu–water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

Impact of heat generation/absorption on the unsteady magnetohydrodynamic stagnation point flow and heat transfer of nanofluids

2019 ◽  
Vol 30 (2) ◽  
pp. 557-574 ◽  
Author(s):  
Rahimah Jusoh ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Shear Stress ◽  
Stability Analysis ◽  
Unsteady Flow ◽  
Heat Generation ◽  
Volume Fraction ◽  
Nanoparticle Volume Fraction ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this study is to describe the unsteady three-dimensional magnetohydrodynamic stagnation point flow of nanofluids with heat generation/absorption. Design/methodology/approach The comprehensive numerical simulations in this study accommodate a physical insight into the heat transfer and flow problem. The use of finite difference method through the bvp4c function in Matlab provides the numerical results and graphical illustrations for the heat transfer rate and shear stress. Findings Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first solution complies the stability behavior. Silver nanoparticles dominate the highest thermal conductivity. Accretion of the rate of heat transfer is obtained with an increment in the magnitude of heat absorption, suction parameter and nanoparticle volume fraction. A stronger magnetic field and larger unsteadiness parameter contribute to the increase of the surface shear stress. Practical implications Many practical fluid mechanics problems involve the time-dependent element. Practically, an unsteady flow of nanofluid can be implemented in the micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors. Originality/value In spite of numerous studies on the unsteady flow, none of the researchers combined the effect of heat generation/absorption and magnetic field in the nanofluid model. The behavior of the flow and heat transfer have been analyzed thoroughly with the variations in the unsteadiness parameter, heat source/sink and nanoparticle volume fraction. Moreover, the discovery of dual solutions in this model strengthens the novelty of this study. Subsequently, the implementation of stability analysis leads to a remarkable revelation where the first solution is found to be stable.

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

2015 ◽  
Vol 93 (5) ◽  
pp. 532-541 ◽  
Author(s):  
M. Modather M. Abdou ◽  
E. Roshdy EL-Zahar ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Heat Transfer Characteristics

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

scholarly journals Mixed Convection of a Radiating Magnetic Nanofluid past a Heated Permeable Stretching/Shrinking Sheet in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Feleke Buta Tadesse ◽  
Oluwole Daniel Makinde ◽  
Lemi Guta Enyadene
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Volume Fraction ◽  
Flow Stability ◽  
Collective Effects ◽  
Shrinking Sheet ◽  
Convective Heating

This paper analyzes the collective effects of buoyancy force, thermal radiation, convective heating, and magnetic field on stagnation point flow of an electrically conducting nanofluid past a permeable stretching/shrinking sheet in a porous medium. Similarity transformations are used on the resulting nonlinear partial differential equations to transfer into a system of coupled nonlinear ordinary differential equations. The fourth-fifth-order Runge–Kutta–Fehlberg method with shooting technique is applied to solve numerically. Results are obtained for dimensionless velocity, temperature, and nanoparticle volume fraction as well as the skin friction and local Nusselt and Sherwood numbers. The results indicate the existence of two real solutions for the shrinking sheet in the range of λ c < λ < 0 . The fluid flow stability is maintained by increasing the magnetic field effect, whereas the porous medium parameter inflates the flow stability. It is also noted that both the skin friction coefficient and the local Sherwood number approximately decline with the intensification of thermal radiation within the range from 9.83% to 14% and the range from 48.86% to 78.66%, respectively. It is also evident in the present work that the local Nusselt number upsurges with the porous and suction/injection parameters.

A Study on Hydromagnetic Pulsating Flow of a Nanofluid in a Porous Channel With Thermal Radiation

2016 ◽  
Vol 33 (2) ◽  
pp. 213-224 ◽  
Author(s):  
A. Vijayalakshmi ◽  
S. Srinivas
Keyword(s):  
Heat Transfer ◽  
Titanium Dioxide ◽  
Thermal Radiation ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Porous Channel ◽  
Nanoparticle Volume Fraction ◽  
Governing Equations ◽  
Nanofluid Flow

AbstractThe present study investigates the hydromagnetic pulsating nanofluid flow in a porous channel with thermal radiation. In this work, we considered water as the base fluid and silver (Ag), copper (Cu), alumina (Al2O3) and titanium dioxide (TiO2) as nanoparticles. The Maxwell-Garnetts and Brinkman models are used to evaluate the effective thermal conductivity and viscosity of the nanofluid. The governing equations are solved analytically and the influence of various parameters on velocity, temperature and heat transfer rate has been discussed through graphical results. From the results, it is found that the rate of heat transfer enhances with an increase of nanoparticle volume fraction. Further, the heat transfer rate is higher for silver nanoparticles as compared with copper, alumina and titanium dioxide.

scholarly journals Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Krishnendu Bhattacharyya ◽  
G. C. Layek
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Volume Fraction ◽  
Lewis Number ◽  
Nanoparticle Volume Fraction ◽  
Layer Flow ◽  
Wall Mass

A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.

scholarly journals MHD mixed convection of hybrid nanofluid in a wavy porous cavity employing local thermal non-equilibrium condition

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zehba Raizah ◽  
Abdelraheem M. Aly ◽  
Noura Alsedais ◽  
Mohamed Ahmed Mansour
Keyword(s):  
Heat Transfer ◽  
Absorption Coefficient ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Equilibrium Condition ◽  
Volume Fraction ◽  
Hybrid Nanofluid ◽  
Radiation Parameter ◽  
Non Equilibrium

AbstractThe current study treats the magnetic field impacts on the mixed convection flow within an undulating cavity filled by hybrid nanofluids and porous media. The local thermal non-equilibrium condition below the implications of heat generation and thermal radiation is conducted. The corrugated vertical walls of an involved cavity have $${T}_{c}$$ T c and the plane walls are adiabatic. The heated part is put in the bottom wall and the left-top walls have lid velocities. The controlling dimensionless equations are numerically solved by the finite volume method through the SIMPLE technique. The varied parameters are scaled as a partial heat length (B: 0.2 to 0.8), heat generation/absorption coefficient (Q: − 2 to 2), thermal radiation parameter (Rd: 0–5), Hartmann number (Ha: 0–50), the porosity parameter (ε: 0.4–0.9), inter-phase heat transfer coefficient (H*: 0–5000), the volume fraction of a hybrid nanofluid (ϕ: 0–0.1), modified conductivity ratio (kr: 0.01–100), Darcy parameter $$\left(Da: 1{0}^{-1}\,\mathrm{ to }\,1{0}^{-5}\right)$$ D a : 1 0 - 1 to 1 0 - 5 , and the position of a heat source (D: 0.3–0.7). The major findings reveal that the length and position of the heater are effective in improving the nanofluid movements and heat transfer within a wavy cavity. The isotherms of a solid part are significantly altered by the variations on $$Q$$ Q , $${R}_{d}$$ R d , $${H}^{*}$$ H ∗ and $${k}_{r}$$ k r . Increasing the heat generation/absorption coefficient and thermal radiation parameter is improving the isotherms of a solid phase. Expanding in the porous parameter $$\varepsilon$$ ε enhances the heat transfer of the fluid/solid phases.

scholarly journals The effect of thermal radiation, heat generation and suction/injection on the mechanical properties of unsteady continuous moving cylinder in a nanofluid

2015 ◽  
Vol 19 (5) ◽  
pp. 1591-1601 ◽  
Author(s):  
El-Sayed El-Bashbeshy ◽  
Tarek Emam ◽  
Mohamed Abdel-Wahed
Keyword(s):  
Mechanical Properties ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Volume Fraction ◽  
Nanoparticle Volume Fraction ◽  
Radiation Heat ◽  
Cooling Medium ◽  
Moving Cylinder ◽  
Radiation Heat Generation

The effect of thermal radiation, heat generation, suction/injection, nanoparticles type, and nanoparticle volume fraction on heat transfer characteristics and the mechanical properties of unsteady moving cylinder embedded into cooling medium consist of water with Cu; Ag or Al2O3 particles are studied. The governing time dependent boundary layer equations are transformed to ordinary differential equations containing unsteadiness parameter, thermal radiation parameter, heat source parameter, suction/injection parameter, curvature parameter, nanoparticle volume fraction and Prandlt number. These equations are solved numerically. The velocity and Temperature profiles within the boundary layer are plotted and discussed in details for various values of the different parameters. Also the effects of the cooling medium and the external thermal forces on the mechanical properties of the cylinder are investigated.

scholarly journals Conjugate Heat and Mass Transfer on Fluctuating Mixed Convection Flow along a Vertical Wedge with Thermal Radiation

2017 ◽  
Vol 22 (3) ◽  
pp. 539-565
Author(s):  
M.N. Firoza ◽  
N.C. Roy ◽  
Md. A. Hossain
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Thermal Radiation ◽  
Surface Temperature ◽  
Skin Friction ◽  
Heat And Mass Transfer ◽  
Numerical Solutions ◽  
Asymptotic Series ◽  
Frequency Range ◽  
Vertical Wedge

AbstractWe study the boundary layer characteristics of heat and mass transfer flow past a vertical wedge in the presence of thermal radiation. The surface temperature and the species concentration are assumed to be oscillating in the magnitude but not in the direction of oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the series solution for the low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions have been presented in terms of the amplitudes and phase angles of the skin friction, the rate of heat transfer and the mass transfer with the variations of Richardson’s number, the Prandtl number, the conduction–radiation parameter, the surface temperature parameter and the Schmidt number. Furthermore, the effects of these parameters are examined in terms of the transient skin friction, heat transfer and mass transfer.

Heat transfer of water–graphene oxide nanofluid magnetohydrodynamic flow through a channel in the presence of the induced magnetic field

2020 ◽  
pp. 095440622094890
Author(s):  
Nematollah Askari ◽  
Hossein Salmani ◽  
Mohammad Hasan Taheri ◽  
Mojtaba Masoumnezhad ◽  
Mohammad Ali Kazemi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Nanoparticle Volume Fraction ◽  
Induced Current ◽  
Induced Magnetic Field ◽  
Magnetic Prandtl Number ◽  
Injection Parameter ◽  
Flow Through

In the present study, the heat transfer of nanofluid magnetohydrodynamic (MHD) fluid flow through a channel with radiation and viscous dissipation effect is considered. Also, the induced magnetic field is considered. The main aim of the study is to obtain the impact of the induced magnetic field, nanoparticle volume fraction, non-electrically conducting, and conducting walls on the MHD nanofluid flow and heat transfer. Hence, the governing equations include momentum, energy, and induced magnetic field equations that are transformed into non-dimensional forms. The analytical least square method (LSM) and numerical finite element method (FEM) effectively conducted for solving the problem. The results of LSM and FEM are compared, and it is observed that there is an excellent agreement. The effect of several parameters such as Hartmann number, suction/injection parameter, magnetic Prandtl number, radiation parameter, Eckert number, and nanoparticle volume fraction are demonstrated and discussed. It can be concluded that the augmentation of the Hartmann number reduces the value of velocity by up to 50%, and the magnetic Prandtl number augmentation reduces the non-dimensional velocity value of about 10% but increases the induced current density value more than twice. Moreover, the increase of radiation parameter, Eckert number, and nanoparticle volume fraction enhance the heat transfer by 20–50%. Besides, the absolute value of the induced magnetic field increases when the Hartmann number rises. Further, the injection parameter decreases the value of velocity and induced magnetic field by 40–50%; whereas, the value of temperature increases by about 40%, and the induced current density increases by 5–7 times. The suction parameter has the contrary effect.

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