Analysis of Melting in the Presence of Natural Convection in the Melt Region

1977 ◽  
Vol 99 (4) ◽  
pp. 520-526 ◽  
Author(s):  
E. M. Sparrow ◽  
S. V. Patankar ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Tube Wall ◽  
Vertical Tube ◽  
Fusion Temperature ◽  
Conduction Model ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference

An analysis of multidimensional melting is performed which takes account of natural convection induced by temperature differences in the liquid melt. Consideration is given to the melt region created by a heated vertical tube embedded in a solid which is at its fusion temperature. Solutions were obtained by an implicit finite-difference scheme tailored to take account of the movement of the liquid-solid interface as melting progresses. The results differed decisively from those corresponding to a conventional pure-conduction model of the melting problem. The calculated heat transfer rate at the tube wall decreased at early times and attained a minimum, then increased and achieved a maximum, and subsequently decreased. This is in contrast to the pure conduction solution whereby the heat transfer rate decreases monotonically with time. The thickness of the melt region was found to vary along the length of the tube, with the greatest thickness near the top. This contrasts with the uniform thickness predicted by the conduction solution. These findings indicate that natural convection effects, although unaccounted for in most phase change analyses, are of importance and have to be considered.

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.

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

scholarly journals Experimental Study for Counter to Cross Flow Air Cooled Heat Exchanger in Concentric Tube using Rectangular Copper Fins Spacing with Internal Spiral Grooving

2021 ◽  
pp. 203-208
Author(s):  
Rakesh Kumar Tiwari ◽  
Ajay Singh ◽  
Parag Mishra
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Natural Convection ◽  
Heat Exchanger ◽  
Forced Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Cross Flow ◽  
Variable Number ◽  
Air Cooled Heat Exchanger

In this manuscript we have presented eight variation of Air-Cooled Heat Exchanger (ACHE) design with internal spiral grooving, all of them are having variable number of rectangular copper fins with different distances between the fins. In the proposed design we get the value of heat transfer rate of a counter to cross flow ACHE is 7833.77 watt, 4068.13 watt, 2736.95 watt, 2161.49 watt, 1802.89 watt, 1546.44 watt, 1336.51 watt and 1165.74 watt in natural convection (without fan) for 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, 2.5 cm, 3.0 cm, 3.5 cm and 4.0 cm respectively. Then again, value of rate of heat transfer in forced convection (with fan) are 8007.46 watt, 4084.81 watt, 2754.69 watt, 2205.98 watt, 1809.24 watt, 1555.39 watt, 1352.88 watt and 1172.78 watt for 0.5 cm, 1.0 cm, 1.5cm, 2.0 cm, 2.5 cm, 3.0 cm, 3.5 cm and 4.0 cm respectively.

scholarly journals Effect of Fin Number and Position on Non-linear Characteristics of Natural Convection Heat Transfer in Internally Finned Horizontal Annulus

2021 ◽  
Vol 9 ◽  
Author(s):  
Kun Zhang ◽  
Yu Zhang ◽  
Xiaoyu Wang ◽  
Liangbi Wang
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Stokes Equations ◽  
Convection Heat Transfer ◽  
The Self ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Simpler Algorithm

Detailed numerical calculations are performed for investigating the effect of fin number and position on unsteady natural convection heat transfer in internally finned horizontal annulus. The SIMPLER algorithm with Quick scheme is applied for solving the Navier Stokes equations of flow and heat transfer. The results show that the heat transfer rate in annulus with fins increases with the increasing numbers of fin and Rayleigh numbers. For Ra = 2 × 105, the effect of numbers of fins and fins position at the bottom part on the unsteady solutions can be neglected, because the self-oscillation phenomenon is mainly affected by natural convection at the upper part of annulus. Although the fin positions cannot increase heat transfer rate significantly in the case of four fins, the self-oscillated solutions can be suppressed by altering fins position.

Enhanced Heat Transfer Rate Measured for Natural Convection in Liquid Gallium in a Cubical Enclosure Under a Static Magnetic Field

1998 ◽  
Vol 120 (4) ◽  
pp. 1027-1032 ◽  
Author(s):  
Toshio Tagawa ◽  
Hiroyuki Ozoe
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Heated Wall ◽  
Electric Heater ◽  
Liquid Gallium ◽  
Cubical Enclosure ◽  
Moderate Magnetic Field

The heat transfer rate of natural convection in liquid gallium in a cubical enclosure was measured experimentally under an external magnetic field applied horizontally and parallel to the vertical heated wall and the opposing cooled wall and the opposing cooled wall of the enclosure. One vertical wall was heated with an electric heater and the opposing wall was cooled isothermally with running water. Experiments were conducted in the range of modified Rayleigh number from 1.85 × 106 to 4.76 × 106 and of Hartmann number from 0 to 573. The average Nusselt number was measured and found to increase when a moderate magnetic field was applied, but to decrease under a stronger magnetic field. This result means that the heat transfer rate has a maximum value at a certain moderate magnetic field, which supports our previous numerical analyses.

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