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Journal ArticleDOI

Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls

TL;DR: In this paper, a comprehensive numerical investigation of the natural convection in a hydro-dynamically as well as thermally anisotropic porous enclosure with insulated side walls is presented.
Abstract: In this article, a comprehensive numerical investigation of the natural convection in a hydro-dynamically as well as thermally anisotropic porous enclosure with insulated side walls is presented. T...
Citations
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Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Journal ArticleDOI
TL;DR: In this paper, the thermal efficacy of half-sinusoidal non-uniform heating at different spatial frequencies for a porous natural convection system using Cu-Al2O3/water hybrid nanofluid and magnetic field was examined.
Abstract: The present work aims to examine the thermal efficacy of half-sinusoidal nonuniform heating at different spatial frequencies for a porous natural convection system using Cu–Al2O3/water hybrid nanofluid and magnetic field. The system is presented utilizing a classical square enclosure heated nonuniformly at the bottom wall, and the sidewalls are allowed to exchange heat with the surroundings. The Brinkman–Forchheimer–Darcy model is adopted catering other additional terms for buoyant force and magnetic field. The governing equations are transformed into nondimensional forms and then solved numerically using a finite volume-based computing code. The importance and fundamental flow physics are explored in terms of the pertinent parameters such as the amplitude (I) and spatial frequency (f) of half-sinusoidal heating, Darcy–Rayleigh number (Ram), volume fraction of hybrid nanoparticles ( $$ \phi $$ ), and Hartmann number (Ha). The flow structure and heat transfer characteristics are analyzed and presented utilizing heatlines, streamlines and isotherms and average Nusselt number. The results show that the use of half-sinusoidal nonuniform heating along with hybrid nanofluid can be a viable method for enhancement and control of the overall thermal performance. The study indicates that half-sinusoidal heating could be a promising technique for better heat transfer even in the presence of flow dampening effects like porous media and magnetic fields.

83 citations

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate an approach for augmenting heat transfer through porous media subjected to nonuniform heating during the magnetohydrodynamic flow of a hybrid nanofluid of Cu-Al2O3/water.
Abstract: The intent of this study is to demonstrate an approach for augmenting heat transfer through porous media subjected to nonuniform heating during the magnetohydrodynamic flow of a hybrid nanofluid of Cu–Al2O3/water. The efficacy of such a heating technique is examined utilizing a classical flow geometry consisting of a square cavity. The heating is made at the bottom following a half-sinusoidal function of different frequencies, along with the presence of a uniform magnetic field. The thermal conditions of the cavity, particularly at the bottom wall, drive thermo-hydrodynamics and associated heat transfer. Furthermore, the addition of different types of nanoparticles to the base liquid in order to boost the thermal performance of conventional fluids and mono-nanofluids is a current technique. The coupled nonlinear governing equations are solved numerically in dimensionless forms adapting the finite volume approach, the Brinkman–Forchheimer–Darcy model, local thermal equilibrium and single-phase model. The study is conducted for wide ranges of parametric impacts to analyze global heat transfer performance. The results of this study reveal that the multi-frequency spatial heating during hybrid nanofluid flow can be utilized as a powerful means to improve the thermal performance of a system operating under different ranges of parameters, even with the presence of porous media and magnetic fields. In addition to different heating frequencies, the variations in amplitude (I) and superposed uniform temperature ( $$\theta_{\text{os}}$$ ) to half-sinusoidal heating are also examined thoughtfully in the analysis for different concentrations of Cu–Al2O3 nanoparticles. Compared to the base liquid, the hybrid nanofluid can contribute toward higher heat transfer.

70 citations

Journal ArticleDOI
TL;DR: In this paper, the Brinkman model has been employed for porous medium and the governing equations written using non-dimensional parameters have been worked out by the finite difference technique for natural convective circulation in a rotating porous chamber with an element of variable volumetric heat generation.

19 citations

Journal ArticleDOI
TL;DR: In this paper, numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting is presented.
Abstract: Purpose This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting. Design/methodology/approach The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed. Findings The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained. Practical implications The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities. Originality/value The authors believe that the presented results are original and have not been published elsewhere.

8 citations

References
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Book ChapterDOI

[...]

01 Jan 2012

139,059 citations


"Natural convection in a square cavi..." refers background or methods in this paper

  • ...[12] while studying the effect of MHD flow on the local Nusselt number (Nux)....

    [...]

  • ...Following [1,10,12] the expression for the Nux is evaluated as follows....

    [...]

Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations


"Natural convection in a square cavi..." refers background in this paper

  • ...[21] have studied the impact of the solid wall thickness on the heat transfer rate....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium and numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers.

275 citations

Journal ArticleDOI
TL;DR: In this article, the effect of the electric field on nanofluid viscosity is taken into account and the numerical results show that the voltage used can change the flow shape.
Abstract: Natural convection heat transfer of a nanofluid in the presence of an electric field is investigated. The control volume finite element method (CVFEM) is utilized to simulate this problem. A Fe3O4–ethylene glycol nanofluid is used as the working fluid. The effect of the electric field on nanofluid viscosity is taken into account. Numerical investigation is conducted for several values of Rayleigh number, nanoparticle volume fraction, and the voltage supplied. The numerical results show that the voltage used can change the flow shape. The Coulomb force causes the isotherms to become denser near the bottom wall. Heat transfer rises with increase in the voltage supplied and Rayleigh number. The effect of electric field on heat transfer is more pronounced at low Rayleigh numbers due to the predomination of the conduction mechanism.

181 citations

Journal ArticleDOI
TL;DR: In this article, a two-dimensional, rectangular enclosure with sinusoidal temperature profile on the upper wall and adiabatic conditions on the bottom and sidewalls is numerically investigated.
Abstract: Natural convection in a two-dimensional, rectangular enclosure with sinusoidal temperature profile on the upper wall and adiabatic conditions on the bottom and sidewalls is numerically investigated. The applied sinusoidal temperature is symmetric with respect to the midplane of the enclosure. Numerical calculations are produced for Rayleigh numbers in the range 10 2 to 10 8 , and results are presented in the form of streamlines, isotherm contours, and distributions of local Nusselt number. The circulation patterns are shown to increase in intensity, and their centers to move toward the upper wall corners with increasing Rayleigh number. As a result, the thermal boundary layer is confined near the upper wall regions. The values of the maximum and the minimum local Nusselt number at the upper wall are shown to increase with increasing Rayleigh number. Finally, an increase in the enclosure aspect ratio produces an analogous increase of the fluid circulation intensity.

154 citations