Natural Convection in an Anisotropic Porous Enclosure Due to Nonuniform Heating From the Bottom Wall

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Ashok Kumar ◽  
P. Bera
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Principal Direction ◽  
Orientation Angle ◽  
Bottom Wall ◽  
Nonuniform Heating ◽  
Material Derivative ◽  
Porous Enclosure

A comprehensive numerical investigation on the natural convection in a hydrodynamically anisotropic porous enclosure is presented. The flow is due to nonuniformly heated bottom wall and maintenance of constant temperature at cold vertical walls along with adiabatic top wall. Brinkman-extended non-Darcy model, including material derivative, is considered. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been adopted to solve numerically the governing conservative equations of mass, momentum, and energy by using a stream-function vorticity formulation. Special attention is given to understand the effect of anisotropic parameters on the heat transfer rate as well as flow configurations. The numerical experiments show that in the case of isotropic porous enclosure, the maximum rates of bottom as well as side heat transfers (Nub and Nus) take place at the aspect ratio, A, of the enclosure equal to 1, which is, in general, not true in the case of anisotropic porous enclosures. The flow in the enclosure is governed by two different types of convective cells: rotating (i) clockwise and (ii) anticlockwise. Based on the value of media permeability as well as orientation angle, in the anisotropic case, one of the cells will dominate the other. In contrast to isotropic porous media, enhancement of flow convection in the anisotropic porous enclosure does not mean increasing the side heat transfer rate always. Furthermore, the results show that anisotropy causes significant changes in the bottom as well as side average Nusselt numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow dynamics and temperature profile and consequently on the heat transfer rates.

scholarly journals Numerical study of natural convection nanofluids flow in tilted cavities with a partially thermally heat source

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110606
Author(s):  
Djamila Benyoucef ◽  
Samira Noui ◽  
Afaf Djaraoui
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Tilt Angle ◽  
Transfer Rate ◽  
Base Fluid ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Bottom Wall

Numerically, natural convection heat transfer of nanofluids in a two-dimensional tilt square enclosure was investigated, with a partial heat source embedded on the bottom wall subject to a fixed heat flux. The remaining portions of the horizontal bottom wall are assumed to be adiabatic, while the upper horizontal wall and the vertical ones are supposed to be at a relatively low temperature. Using the finite volume method and the SIMPLER algorithm, the governing equations have been discretized and solved. Simulations have been carried out for more than one nanoparticle and base fluid, a range of Rayleigh numbers ([Formula: see text] Ra [Formula: see text]), various values of heat source length and location (0.2 [Formula: see text]  B [Formula: see text] 0.8 and 0.2 [Formula: see text]  D [Formula: see text] 0.5, respectively), solid volume fraction ([Formula: see text]) as well as tilt angle ([Formula: see text]). The results indicate that the heat transfer performance increases by adding nanoparticles into the base fluid. An optimum solid volume fraction raises and reduces the heat transfer rate and maximum temperature of the surface heat source. respectively. Moreover, the results show a significant impact of the tilt angle on the flow, temperature patterns, and the heat transfer rate with a specific tilt angle depending to the pertinent parameters.

Influence of Non-Uniform Sinusoidal Periodic Bottom Boundary Condition on Natural Convection in an Isotropic Porous Enclosure

2011 ◽  
Vol 110-116 ◽  
pp. 1576-1581 ◽  
Author(s):  
Manish Kr. Khandelwal ◽  
P. Bera
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Fluid Flow ◽  
Natural Convection ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Bottom Wall ◽  
Isotropic Case ◽  
Material Derivative ◽  
Porous Enclosure

A comprehensive numerical investigation on the natural convection in an isotropic porous enclosure is presented. All the walls of the enclosure are adiabatic except the bottom wall which is partially heated and cooled by sinusoidal temperature profile. The governing equations were written under assumption of Brinkman-extended non-Darcy model, including material derivative, and then solved by numerically using spectral element method (SEM). The heat transfer and fluid flow mechanisms in isotropic case are governed by periodicity parameter (N) Rayleigh Number (Ra), Darcy number (Da), aspect ratio (A), Prandtl number (Pr) and media permeability (K). The main emphasize is given on effect of N on local heat transfer as well as mechanism of heat transfer and fluid flow in enclosure. The results shows that, as the periodicity is decreased on increasing N the absolute value of Nux at the bottom left corner point increases. For odd values of N, the local heat transfer profile is symmetric about the line x=0.5, which is consequence of symmetric boundary condition at the bottom wall of the enclosure. The entire flow is governed by two type convective cells: (i) rotating clockwise (ii) rotating anticlockwise. Furthermore for even values of N cells rotating anticlockwise are dominated and covered the entire domain. In particular the present analysis shows that, different periodicity of temperature boundary condition has the significant effect on the flow mechanism and consequently on the heat transfer rate.

Conjugate Natural Convection in Porous Medium With a Thick Square-Wave Partition

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Jayesh Subhash Chordiya ◽  
Ram Vinoy Sharma
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Convection Heat Transfer ◽  
Thermal Conductivity Ratio ◽  
Convection Heat ◽  
Square Wave ◽  
Porous Enclosure

Abstract Natural convection within a differentially heated porous enclosure is substantially affected by the presence of partition, fins, or baffles within it. However, not much is known about the effect of partition shape and size. Thus, a solid thick partition in a square-wave shape embedded within a differentially heated porous enclosure has been investigated in this numerical analysis. Through this study, it is sought to contemplate the reduction in the convection heat transfer rate that could be achieved across a differentially heated porous enclosure. The influence of partition thickness, partition amplitude, thermal conductivity ratio, and partition position has been studied. Darcy’s flow model has been solved using the successive accelerated replacement scheme by the finite difference method. One of the findings of this study suggests that lower thermal conductivity of partition, lower partition amplitude, and higher thickness results in a greater reduction in the convection heat transfer rate.

scholarly journals Natural convection of Nanoliquid from a Cylinder in Square Porous Enclosure using Buongiorno’s Two-phase Model

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Abeer Alhashash
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Heated Surface ◽  
Active Surface ◽  
Darcy Number ◽  
Cylinder Surface ◽  
Two Phase ◽  
Porous Enclosure

AbstractNatural convection of nanoliquid in a square porous enclosure has been studied using non homogeneous two-phase Buongiorno’s model. The outer of enclosure has cold temperature and a circular cylinder is put at the center. A finite heated segment is located on the top cylinder surface which is otherwise insulated. The momentum in the porous layer is modeled applying the Brinkman-Forchheimer equations. The analysis are conducted in the following interval of the associated groups: the portion of heated surface (5% ≤ H ≤ 100%), the concentration (0.0 ≤ ϕ ≤ 0.04), the Darcy number, 10−5 ≤ Da ≤ 10−2 and the cylinder size, (0.15 ≤ R ≤ 0.25). The minimum heat transfer rate of the active surface were obtained at location ξ = 90°. In general, the ratio of the heat transfer per unit area of the heat source decreases as the length of the heated surface increases. The heat transfer rate is intensified for the half thermally active surface and high value of Darcy number at higher nanoparticles concentration.

scholarly journals A RANS K-? SIMULATION OF 2D TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH HEATING SOURCES

2019 ◽  
Vol 20 (1) ◽  
pp. 229-244
Author(s):  
Mehdi Ahmadi ◽  
Seyed Ali Agha Mirjalily ◽  
Seyed Amir Abbas Oloomi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Turbulent Natural Convection ◽  
Cold Source ◽  
Thermal Sources

ABSTRACT: This study is conducted to investigate turbulent natural convection flow in an enclosure with thermal sources using the low-Reynolds number (LRN) k-? model. This enclosure has a cold source with temperature Tc and a hot source with temperature Th as thermal sources, other walls of the enclosure are adiabatic. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources, and thermal sources aspect ratio on the flow field, temperature, and rate of heat transfer. To achieve this aim, the equations of continuity, momentum, energy, turbulent kinetic energy, and kinetic energy dissipation are employed in the case of 2D turbulence with constant thermo-physical properties except the density in the buoyancy term (Boussinesq approximation). To numerically solve these equations, the finite volume method and SIMPLE algorithm are used. According to the modeling results, the most optimal temperature distribution in the enclosure is seen when the hot source is below the cold source. With decreasing distance between hot and cold sources, heat transfer rate increases. The maximal heat transfer rate is derived via study of the heating sources aspect ratio. In constant positions of cold and hot sources on a wall, the heat transfer rate increases with increasing Rayleigh number (Ra=109-1011). ABSTAK: Kajian ini dijalankan bagi mengkaji perubahan semula jadi aliran perolakan dalam tempat tertutup dengan sumber haba menggunakan model k-? nombor Reynolds-rendah (LRN). Bekas tertutup ini mempunyai dua sumber haba iaitu sumber sejuk dengan suhu Tc dan sumber panas dengan suhu Th, manakala dinding lain bekas ini adalah adiabatik. Tujuan kajian ini adalah bagi mengesan perubahan nombor Rayleigh, mengubah sumber sejuk dan panas dan nisbah sumber haba kepada kawasan aliran, suhu dan halaju perubahan haba. Bagi mencapai tujuan tersebut, persamaan sambungan, momentum, tenaga, tenaga kinetik perolakan, dan pengurangan tenaga kinetik telah dilaksanakan dalam kes perolakan 2D dengan sifat fizikal-haba berterusan (malar) kecuali isipadu terma keapungan (anggaran Boussinesq). Bagi menyelesaikan persamaan ini secara berangka, kaedah isipadu terhad dan algorithma MUDAH telah digunakan. Berdasarkan keputusan model, suhu distribusi optimal dalam bekas tertutup dilihat apabila sumber panas adalah kurang daripada sumber sejuk. Dengan pengurangan jarak antara sumber panas dan sejuk, kadar pertukaran haba meningkat. Kadar pertukaran haba maksima telah diperoleh melalui kajian nisbah  aspek sumber pemanasan. Kadar pertukaran haba bertambah dengan bertambahnya nombor Rayleigh  (Ra=109-1011), pada posisi tetap sumber sejuk dan panas pada dinding bekas.

Effect of a Magnetic Field on the Heat Transfer Rate on Free Convection in a Rectangular Cavity

2005 ◽  
Author(s):  
Gustavo Gutierrez ◽  
Ezequiel Medici
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Stokes Equations ◽  
Rectangular Cavity ◽  
Convection Flow ◽  
Interesting Phenomenon ◽  
The Magnetic Field

The interaction between magnetic fields and convection is an interesting phenomenon because of its many important engineering applications. Due to natural convection motion the electric conductive fluid in a magnetic field experiences a Lorenz force and its effect is usually to reduce the flow velocities. A magnetic field can be used to control the flow field and increase or reduce the heat transfer rate. In this paper, the effect of a magnetic field in a natural convection flow of an electrically conducting fluid in a rectangular cavity is studied numerically. The two side walls of the cavity are maintained at two different constant temperatures while the upper wall and the lower wall are completely insulated. The coupling of the Navier-Stokes equations with the Maxwell equations is discussed with the assumptions and main simplifications assumed in typical problems of magnetohydrodynamics. The nonlinear Lorenz force generates a rich variety of flow patterns depending on the values of the Grashof and Hartmann numbers. Numerical simulations are carried out for different Grashof and Hartmann numbers. The effect of the magnetic field on the Nusselt number is discussed as well as how convection can be suppressed for certain values of the Hartmann number under appropriate direction of the magnetic field.

Investigation of the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three dimensional lattice Boltzmann flux solver

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mahyar Ashouri ◽  
Mohammad Mehdi Zarei ◽  
Ali Moosavi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Lattice Boltzmann ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Maximum Heat ◽  
Content Type ◽  
Dimensional Lattice ◽  
Fin Spacing

Purpose The purpose of this paper is to investigate the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three-dimensional lattice Boltzmann flux solver. Design/methodology/approach Three-dimensional lattice Boltzmann flux solver is used in the present study for simulating conjugate heat transfer within an annulus. D3Q15 and D3Q7 models are used to solve the fluid flow and temperature field, respectively. The finite volume method is used to discretize mass, momentum and energy equations. The Chapman–Enskog expansion analysis is used to establish the connection between the lattice Boltzmann equation local solution and macroscopic fluxes. To improve the accuracy of the lattice Boltzmann method for curved boundaries, lattice Boltzmann equation local solution at each cell interface is considered to be independent of each other. Findings It is found that the maximum heat transfer rate occurs at low fin spacing especially by increasing the fin height and decreasing the internal-cylindrical distance. The effect of inner cylinder eccentricity is not much considerable (up to 5.2% enhancement) while the impact of fin eccentricity is more remarkable. Negative fin eccentricity further enhances the heat transfer rate compared to a positive fin eccentricity and the maximum heat transfer enhancement of 91.7% is obtained. The influence of using perforated fins is more considerable at low fin spacing although some heat transfer enhancements are observed at higher fin spacing. Originality/value The originality of this paper is to study three-dimensional natural convection in a finned-horizontal annulus using three-dimensional lattice Boltzmann flux solver, as well as to apply symmetry and periodic boundary conditions and to analyze the effect of eccentric annular fins (for the first time for air) and perforated annular fins (for the first time so far) on the heat transfer rate.

scholarly journals Natural convection in a Square Enclosure with Partially Active Vertical Wall

2020 ◽  
Vol 330 ◽  
pp. 01004
Author(s):  
Abdennacer Belazizia ◽  
Smail Benissaad ◽  
Said Abboudi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Vertical Wall ◽  
Left Wall ◽  
Convection And Heat Transfer ◽  
Square Enclosure ◽  
Active Location

Steady, laminar, natural convection flow in a square enclosure with partially active vertical wall is considered. The enclosure is filled with air and subjected to horizontal temperature gradient. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on three parameters: Rayleigh number (Ra =103-106), Prandtl number (Pr=0.71), and the aspect ratio of the enclosure (A=1). The active location takes two positions in the left wall: top (T) and middle (M). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat transfer rate. The results including the streamlines, isotherm patterns, flow velocity and the average Nusselt number for different values of Ra. The obtained results show that the increase of Ra leads to enhance heat transfer rate. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also by moving the active location from the top to the middle on the left vertical wall, convection and heat transfer rate are more important in case (M). Furthermore for high Rayleigh number (Ra=106), Convection mechanism in (T) case is principally in the top of the enclosure, whereas in the remaining case it covers the entire enclosure.

Natural Convection Inside a Square Cavity Heated From Below and Symmetrically Cooled at Both Sides: Effects of Various Dirichlet Boundary Conditions at the Bottom Wall

2005 ◽  
Author(s):  
Satyajit Roy ◽  
Tanmay Basak
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Transfer Rate ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Bottom Wall ◽  
Uniform Heating ◽  
Square Cavity ◽  
Rayleigh Numbers

A numerical study is performed to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over the range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 105 and Prandtl number Pr, 0.7 ≤ Pr ≤ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained.

scholarly journals Numerical Analysis Natural Convection Heat Transfer from Vertical Cylinder Annular Fins with The Addition of Slits

2021 ◽  
Vol 9 (4) ◽  
pp. 405-409
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Convection Heat Transfer ◽  
Vertical Cylinder ◽  
Simulation Method ◽  
Cylinder Length ◽  
Annular Fin ◽  
Annular Fins

One method of increasing the heat transfer rate of the fins is by adding slits to the fins. The purpose of this study was to analyze the heat transfer rate by adding slits in the annular fins with a vertical cylinder under natural convection conditions. The vertical cylinder length, cylinder diameter, fin diameter, and distance between the fins are 313 mm, 25 mm, 125 mm, and 7 mm, respectively. The number of slits varied from 2 slits and 4 slits and the spacing of the slits was kept constant by 5 mm. This research was conducted with a simulation method using Autodesk CFD 2019 software. As a result, fins with slits and fins without slits were compared. The value of the heat transfer rate that occurs and the heat transfer coefficient in the annular fin with slits is better than the fin without slits. The highest heat transfer rates were 142.928 W and 2.6022 W/m 2K for an annular fin with 2 slits

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