M.M. El‐Refaee, M.M. Elsayed, N.M. Al‐Najem and I.E. Megahid
A fast false implicit transient scheme FITS is developed to predict thetwo‐dimensional steady‐state solutions ofbuoyancy‐assisted laminar internal flows. This new scheme uses…
Abstract
A fast false implicit transient scheme FITS is developed to predict the two‐dimensional steady‐state solutions of buoyancy‐assisted laminar internal flows. This new scheme uses the control volume based on power law technique in conjugation with the alternating direction implicit (ADI) and the successive grid refinement (SGR) procedures to solve the transient vorticity and energy transport equations. The ADI procedure allows the power law, which gives an excellent approximation to the exact 1‐D solution, to be applied locally in one‐dimensional sense for each sweep in the co‐ordinates’ directions. This in turn increased the solution accuracy and hence permits the use of a larger time increment. As a result a remarkable increase in the convergence rate to steady‐state is achieved. The final solution is obtained by successively refining the grid as the solution advances in time. The efficiency of FITS is verified by comparing the present predictions with three steady‐state benchmark solutions: natural convection of a heat generating fluid in a rectangular enclosure, natural convection inside a cavity with two isothermal walls, and a vertical buoyancy‐assisted laminar backward‐facing step flow.
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N.M. Al‐Najem, K.M. Khanafer and M.M. El‐Refaee
This paper numerically investigates the effect of the transverse magnetic field on flow field patterns and heat transfer processes in a tilted square cavity. The horizontal walls…
Abstract
This paper numerically investigates the effect of the transverse magnetic field on flow field patterns and heat transfer processes in a tilted square cavity. The horizontal walls of the enclosure are assumed to be insulated while the vertical walls are kept isothermal. The power law control volume approach is developed to solve the conservation equations at Prandtl number of 0.71. Validation tests with existing data demonstrate the ability of the present scheme to produce accurate results. The effects of Grashof number, enclosure inclination angle, and Hartmann number are also investigated. The study covers the range of the Hartmann number from 0 to 100, the enclosure inclination angle from 0° to ‐90° with Grashof number of 104 and 106. The effect of the magnetic field is found to suppress the convection currents and heat transfer inside the cavity. This effect is significant for low inclination angles and high Grashof numbers. Additionally, it is noted that there is no variation of average Nusselt number with respect to inclination angle for high Hartmann number.
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Alin V. Roşca, Natalia C. Roşca, Ioan Pop and Mikhail A. Sheremet
This paper aims to study numerically the steady natural convective heat transfer of a hybrid nanosuspension (Ag-MgO/H2O) within a partially heated/cooled trapezoidal region with…
Abstract
Purpose
This paper aims to study numerically the steady natural convective heat transfer of a hybrid nanosuspension (Ag-MgO/H2O) within a partially heated/cooled trapezoidal region with linear temperature profiles at inclined walls under an effect of uniform Lorentz force. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates.
Design/methodology/approach
The governing equations formulated using the Oberbeck–Boussinesq approach and single-phase nanoliquid model are transformed to a non-dimensional form by using non-dimensional variables. The obtained equations with appropriate boundary conditions are resolved by the finite difference technique. The developed code has been validated comprehensively. Analysis has been performed for a wide range of governing parameters, including Rayleigh number (Ra = 105), Prandtl number (Pr = 6.82), Hartmann number (Ha = 0–100), magnetic field inclination angle (φ = 0–?/2) and nanoparticles volume fraction (φhnf = 0 and 2%).
Findings
It has been shown that inclined magnetic field can be used to manage the energy transport performance. An inclusion of nanoparticles without Lorentz force influence allows forming more stable convective regime with descending heat plume in the central zone, while such a regime was performed for clear fluid only for moderate and high Hartmann numbers. Moreover, the average overall entropy generation can be decreased with a growth of the Hartmann number, while an addition of hybrid nanoparticles allows reducing this parameter for Ha = 30 and 50. The average Nusselt number can be increased with a growth of the nanoparticles concentration for low values of the magnetic field intensity.
Originality/value
Governing equations written using the conservation laws and dimensionless non-primitive variables have been resolved by the finite difference approach. The created numerical code has been verified by applying the grid independence test and computational outcomes of other researchers. The comprehensive analysis for various key parameters has been performed.
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Mohammad Ghalambaz, Mahmoud Sabour, Ioan Pop and Dongsheng Wen
The present study aims to address the flow and heat transfer of MgO-MWCNTs/EG hybrid nanofluid in a complex shape enclosure filled with a porous medium. The enclosure is subject…
Abstract
Purpose
The present study aims to address the flow and heat transfer of MgO-MWCNTs/EG hybrid nanofluid in a complex shape enclosure filled with a porous medium. The enclosure is subject to a uniform inclined magnetic field and radiation effects. The effect of the presence of a variable magnetic field on the natural convection heat transfer of hybrid nanofluids in a complex shape cavity is studied for the first time. The geometry of the cavity is an annular space with an isothermal wavy outer cold wall. Two types of the porous medium, glass ball and aluminum metal foam, are adopted for the porous space. The governing equations for mass, momentum and heat transfer of the hybrid nanofluid are introduced and transformed into non-dimensional form. The actual available thermal conductivity and dynamic viscosity data for the hybrid nanofluid are directly used for thermophysical properties of the hybrid nanofluid.
Design/methodology/approach
The governing equations for mass, momentum and heat transfer of hybrid nanofluid are introduced and transformed into non-dimensional form. The thermal conductivity and dynamic viscosity of the nanofluid are directly used from the experimental results available in the literature. The finite element method is used to solve the governing equations. Grid check procedure and validations were performed.
Findings
The effect of Hartmann number, Rayleigh number, Darcy number, the shape of the cavity and the type of porous medium on the thermal performance of the cavity are studied. The outcomes show that using the composite nanoparticles boosts the convective heat transfer. However, the rise of the volume fraction of nanoparticles would reduce the overall enhancement. Considering a convective dominant regime of natural convection flow with Rayleigh number of 107, the maximum enhancement ratio (Nusselt number ratio compared to the pure fluid) for the case of glass ball is about 1.17 and for the case of aluminum metal foam is about 1.15 when the volume fraction of hybrid nanoparticles is minimum as 0.2 per cent.
Originality/value
The effect of the presence of a variable magnetic field on the natural convection heat transfer of a new type of hybrid nanofluids, MgO-MWCNTs/EG, in a complex shape cavity is studied for the first time. The results of this paper are new and original with many practical applications of hybrid nanofluids in the modern industry.
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Surabhi Nishad, Sapna Jain and Rama Bhargava
This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach.
Abstract
Purpose
This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach.
Design/methodology/approach
The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B0 has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid.
Findings
The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease.
Originality/value
The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.
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Nepal Chandra Roy and Sherajum Monira
The purpose of this study is to investigate the natural convection characteristics of a reacting hybrid nanofluid in an open porous cavity bounded by vertical wavy walls subject…
Abstract
Purpose
The purpose of this study is to investigate the natural convection characteristics of a reacting hybrid nanofluid in an open porous cavity bounded by vertical wavy walls subject to an inclined magnetic field.
Design/methodology/approach
The physical domain of the problem is constructed using coordinate transformations, and the equations are transformed accordingly. The resulting equations are then solved using finite difference method. Numerical results for the streamlines, isotherms and isoconcentration are illustrated with varying relevant parameters.
Findings
Whatever the values of parameters, streamlines have two counter-rotating cells, and their intensities are the highest near the open end. Moreover, the maximum temperature and the minimum concentration are obtained in close proximity to the open end. The strength of streamlines is increased with increasing Rayleigh number, Frank-Kamenetskii number and Darcy number, whereas it is decreased with the increment of volume fractions of nanoparticles.
Research limitations/implications
The limitations of this study are that the model is suitable for thermal equilibrium cases and constant thermo-physical properties, while the results can predict two-dimensional flow behaviors.
Originality/value
To the best of the authors’ knowledge, there is no study on the natural convection induced by a chemical reaction in an open cavity bounded by vertical wavy walls. The findings might be used to gather knowledge about the flow, energy and reactant distributions in an open space containing a chemical reaction.
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N.S. Bondareva, M. A. Sheremet and I. Pop
Unsteady natural convection of water-based nanofluid within a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical…
Abstract
Purpose
Unsteady natural convection of water-based nanofluid within a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno is presented. The paper aims to discuss these issues.
Design/methodology/approach
The left vertical and right inclined walls of the enclosure are kept at constant but different temperatures whereas the top and bottom horizontal walls are adiabatic. All boundaries are assumed to be impermeable to the base fluid and to nanoparticles. In order to study the behavior of the nanofluid, a non-homogeneous Buongiorno’s mathematical model is taken into account. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite difference scheme the dimensionless governing equations are numerically solved.
Findings
The governing parameters are the Rayleigh, Hartmann and Lewis numbers along with the inclination angle of the magnetic field relative to the gravity vector, the aspect ratio and the dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall, as well as on the developments of streamlines, isotherms and isoconcentrations are analyzed. The results show that key parameters have substantial effects on the flow, heat and mass transfer characteristics.
Originality/value
The present results are new and original for the heat transfer and fluid flow in a right-angle trapezoidal cavity under the influence of a uniform inclined magnetic field using the mathematical nanofluid model proposed by Buongiorno. The results would benefit scientists and engineers to become familiar with the flow behavior of such nanofluids, and the way to predict the properties of this flow for possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.
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The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique…
Abstract
Purpose
The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique magnetic field. The momentum equations include the magnetic effect, and the induced magnetic field due to the motion of the electrically conducting fluid is neglected. Quadratic triangular elements are used to ensure accurate approximation for second order derivatives of stream function appearing in the vorticity equation.
Design/methodology/approach
Governing equations in terms of stream function and vorticity are solved by FEM using quadratic triangular elements. Vorticity boundary conditions are obtained through Taylor series expansion of stream function equation by using more interior stream function values to improve the accuracy. Isothermally heated or cooled and/or adiabatic conditions for the temperature are imposed. Results are obtained for Rayleigh number values and Hartmann number values up to 1000000 and 100, respectively.
Findings
It is observed that streamlines form a thin boundary layer close to the heated walls as Ha increases. The same effect is seen in the vorticity contours, and isotherms are not affected much. As Ra increases streamlines are deformed moving from the heated walls through cooled walls. Vorticity starts to develop boundary layers close to heated and adjacent walls. Isotherms are pushed towards the sinusoidally heated wall whereas in the case of linearly heated left and bottom walls they expand towards cooled part of the cavity as Ra increases.
Originality/value
The application of FEM with quadratic elements for solving natural convection flow problem under the effect of a magnetic field is new in the sense that the results are obtained for large values of Rayleigh and Hartmann numbers.
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Majid Ashouri, Mohammad Behshad Shafii and Hossein Rajabi Kokande
The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also…
Abstract
Purpose
The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks.
Design/methodology/approach
The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works.
Findings
The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks.
Originality/value
No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.
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Sofen K. Jena, Swarup K. Mahapatra and Amitava Sarkar
The current study aims to address the interaction between participating media radiation with thermo-gravitational convection of an electrically conducting fluid enclosed within a…
Abstract
Purpose
The current study aims to address the interaction between participating media radiation with thermo-gravitational convection of an electrically conducting fluid enclosed within a tilted enclosure under an externally imposed time-independent uniform magnetic field.
Design/methodology/approach
The differentially heated boundaries of the tilted enclosure are considered to be diffuse, gray and the enclosed fluid is assumed to be absorbing, emitting and isotropically scattering. The Navier-Stokes equations, meant for magneto convection are solved using modified MAC method. Gradient dependent consistent hybrid upwind scheme of second order is used for discretization of the convective terms. Discrete ordinate method, with S8 approximation, is used to model radiative transport equation in the presence of radiatively active medium.
Findings
Effect of uniform magnetic field with different magnitudes and orientations of cavity has been numerically simulated. The effect of participating media radiation has been investigated for different optical thicknesses, emissivities, scattering albedos and Planks number. The results are provided in both graphical and tabular forms. The flow lines, isotherms bring clarity in the understanding of flow behaviour and heat transfer characteristics.
Originality/value
Despite the idealized nature, the present study is quite essential to understand the cumbersome physics of realistic problem.