Natural Convection in a Horizontal Porous Medium Subjected to an End-to-End Temperature Difference

1978 ◽  
Vol 100 (2) ◽  
pp. 191-198 ◽  
Author(s):  
A. Bejan ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Temperature Difference ◽  
Transfer Rate ◽  
Horizontal Cylinder ◽  
Horizontal Layer ◽  
Parallel Plates ◽  
End To End

Natural convection in a porous medium filling a slender horizontal space with an end-to-end temperature difference is studied analytically. The end-to-end temperature difference gives rise to a horizontal counterflow pattern augmenting the heat transfer rate through the porous medium. Two basic geometries are considered: horizontal layer confined between two adiabatic and impermeable parallel plates, and horizontal cylinder surrounded by an adiabatic and impermeable cylindrical surface. Nusselt number relations are derived in terms of the Rayleigh number and the cavity aspect ratio. The end-wall permeability is shown to affect the heat transfer rate through the medium.

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.

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.

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.

Mixed Convective Heat Transfer From a Heated Horizontal Plate in a Porous Medium Near an Impermeable Surface

1988 ◽  
Vol 110 (2) ◽  
pp. 390-394 ◽  
Author(s):  
P. H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Saturated Porous Medium ◽  
Forced Flow ◽  
Horizontal Plate ◽  
Flowing Fluid ◽  
Buoyancy Forces ◽  
Two Dimensional Flow

Two-dimensional flow over a horizontal plate in a saturated porous medium mounted near an impervious adiabatic horizontal surface and subjected to a horizontal forced flow has been numerically investigated. The plate is heated to a uniform temperature that is higher than the temperature of the flowing fluid. The conditions considered are such that the buoyancy forces have an effect on the flow and, therefore, on the heat transfer rate from the plate. The full governing equations, written in dimensionless form, have been solved for a range of values of the governing parameters using the finite element method. The heat transfer rate from the plate is influenced both by the dimensionless depth of the plate below the surface and the importance of the buoyancy forces, the latter having been characterized by a parameter which is equal to the ratio of the Darcy–Rayleigh number to Peclet number. The conditions under which these parameters have a negligible effect on the heat transfer rate are discussed.

Design and Analysis of a Heat Exchanger Network

2012 ◽  
Vol 9 (1) ◽  
pp. 85-91
Author(s):  
Mohammad Azim Aijaz ◽  
T. S. Ravikumar
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Heat Transfer Rate ◽  
Temperature Difference ◽  
Transfer Rate ◽  
Outlet Temperature ◽  
Optimal Temperature ◽  
Heat Exchanger Network ◽  
Cold Fluid ◽  
Temperature Heat

the hot fluid outlet temperature, cold fluid outlet temperature, heat transfer rate and effectiveness at varying hot and cold fluid inlet temperatures using, log mean temperature difference (LMTD) and effectiveness-number of transfer units (ε-NTU) method. The obtained result illustrates how heat transfer rate and effectiveness increases or decreases at varying hot and cold fluid inlet temperatures. The result obtained from both LMTD and å-NTU method gives statistically significant values. The objective of this paper is to find out the optimal temperature at which heat transfer rate and effectiveness are maximum.

scholarly journals Maximum Heat Transfer Rate Density in Two-Dimensional Minichannels and Microchannels

2003 ◽  
Author(s):  
M. Favre-Marinet ◽  
S. Le Person ◽  
A. Bejan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Transition To Turbulence ◽  
Experimental Investigations ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Optimal Spacing

Experimental investigations of the flow and the associated heat transfer were conducted in two-dimensional microchannels in order to test possible size effects on the laws of hydrodynamics and heat transfer and to infer optimal conditions of use from the measurements. The test section was designed to modify easily the channel height e between 1 mm and 0.1 mm. Measurements of the overall friction factor and local Nusselt numbers show that the classical laws of hydrodynamics and heat transfer are verified for e > 0.4 mm. For lower values of e, a significant decrease of the Nusselt number is observed, whereas the Poiseuille number continues to have the conventional value of laminar developed flow. The transition to turbulence is not affected by the channel size. For fixed pressure drop across the channel, a maximum of heat transfer rate density is found for a particular value of e. The corresponding dimensionless optimal spacing and heat transfer rate density are in very good agreement with the predictions of Bejan and Sciubba (1992). This paper is the first time that the optimal spacing between parallel plates is determined experimentally.

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