Effet du maximum de densité sur la convection libre de l'eau dans une cavité fermée

1979 ◽  
Vol 6 (4) ◽  
pp. 481-493 ◽  
Author(s):  
L. Robillard ◽  
P. Vasseur
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Wall Temperature ◽  
Transient Flow ◽  
Coupled System ◽  
Flow Patterns ◽  
Maximum Density ◽  
Temperature Fields ◽  
Constant Wall Temperature ◽  
Square Enclosure

One of the most important factors affecting the rate of heat transfer by natural convection is the temperature–density relationship of the convecting fluid. The importance of this factor is greatly amplified when the heat is being transferred to a medium that has a maximum density at a given temperature. Water at low temperatures offers such a behavior, its density attaining a maximum value near 3.98 °C. thereafter decreasing with decreasing temperature. This phenomenon is responsible for unusual flow patterns in areas of water exposed to near freezing temperatures.This investigation is a theoretical analysis of the transient natural convection of water contained in a square enclosure with constant wall temperature. Initially the water is assumed to be at a uniform temperature above 0 °C, the wall temperature being suddenly applied.An alternating direction implicit finite-difference schema was used to solve the coupled system of partial differential equations. The transient flow and temperature fields, and local and overall heat transfer are greatly affected by the inversion of flow patterns caused by the maximum density. Their respective values for different flow situations are presented in this study.

A Pseudospectral Analysis of Laminar Natural Convection Flow and Heat Transfer Between Two Inclined Parallel Plates

2006 ◽  
Author(s):  
Serkan Kasapoglu ◽  
Ilker Tari
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Convection Flow ◽  
Parallel Plates ◽  
Natural Convection Flow ◽  
Constant Wall Temperature ◽  
Laminar Natural Convection

Three dimensional laminar natural convection flow of and heat transfer in incompressible air between two inclined parallel plates are analyzed with the Boussinesq approximation by using spectral methods. The plates are assumed to be infinitely long in streamwise (x) and spanwise (z) directions. For these directions, periodic boundary conditions are used and for the normal direction (y), constant wall temperature and no slip boundary conditions are used. Unsteady Navier-Stokes and energy equations are solved using a pseudospectral approach in order to obtain velocity and temperature fields inside the channel. Fourier series are used to expand the variables in × and z directions, while Chebyshev polynomials are used to expand the variables in y direction. By using the temperature distribution between the plates, local and average Nusselt numbers (Nu) are calculated. Nu values are correlated with φ, which is the inclination angle, and with Ra·cosφ to compare the results with the literature.

Analysis of the Time-Dependent Heating on the Natural Convection from a Vertical Open Ended Porous Cylinder

2008 ◽  
Vol 273-276 ◽  
pp. 28-33 ◽  
Author(s):  
Djamel Eddine Ameziani ◽  
K. Bouhadef ◽  
Rachid Bennacer
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Wall Temperature ◽  
Flow Model ◽  
Convection Heat Transfer ◽  
Lateral Wall ◽  
Natural Convection Heat Transfer ◽  
Porous Cylinder ◽  
Constant Wall Temperature ◽  
Unsteady Natural Convection

The problem of unsteady natural convection heat transfer in a vertical opened porous cylinder submitted to a sinusoidal time variation temperature on the lateral wall has been investigated numerically. The widely used Darcy flow model without flow establishment at the cylinder exit has been used. In the case of constant wall temperature, two types of flows were obtained, with and without fluid recirculation, depending on the filtration Rayleigh number (Ra), the aspect ratio (A) and the Biot number (Bi) have been obtained. The obtained heat transfer, in case of low dimensionless oscillations amplitude (XA<0.5), shows a non significant enhancement (less than 5%) in comparison to the constant wall temperature case.

Pseudo-Steady-State Natural Convection Heat Transfer Inside a Vertical Cylinder

1986 ◽  
Vol 108 (2) ◽  
pp. 310-316 ◽  
Author(s):  
Y. S. Lin ◽  
R. G. Akins
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Wall Temperature ◽  
Convection Heat Transfer ◽  
Vertical Cylinder ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Constant Wall Temperature ◽  
Stream Functions

The SIMPLER numerical method was used to calculate the pseudo-steady-state natural convection heat transfer to a fluid inside a closed vertical cylinder for which the boundary temperature was spatially uniform and the temperatures throughout the entire system were increasing at the same rate. (Pseudo-steady state is comparable to the steady-state problem for a fluid with uniform heat generation and constant wall temperature.) Stream functions, temperature contours, axial velocities, and temperature profiles are presented. The range of calculation was 0.25 < H/D < 2, Ra < 107, and Pr = 7. This range includes conduction to weak turbulence. A characteristic length defined as 6 × (volume)/(surface area) was used since it seemed to produce good regression results. The overall heat transfer for the convection-dominated range was found to be correlated by Nu = 0.519 Ra0.255, where the temperature difference for both the Nusselt and Rayleigh numbers was the center temperature minus the wall temperature. Correlations using other temperature differences are also presented for estimating the volumetric mean and minimum temperatures.

scholarly journals Control temperature fluctuations in two-phase CuO-water nanofluid by transfiguration of the enclosures

2020 ◽  
pp. 334-334
Author(s):  
Hadi Pourziaei Araban ◽  
Javad Alinejad ◽  
Ganji Domiri
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Wall Temperature ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Temperature Fields ◽  
Two Phase ◽  
Flux Boundary Condition

The innovation of this paper is to simulate two-phase nanofluid natural convection inside the transformable enclosure to control the heat transfer rate under different heat flux. Heat transfer of a two-phase CuO-water nanofluid in an enclosure under different heat flux has many industrial applications including energy storage systems, thermal control of electronic devices and cooling of radioactive waste containers. The Lattice Boltzmann Method based on the D2Q9 method has been utilized for modeling velocity and temperature fields. Streamlines, isotherms and nanoparticle volume fraction, have been investigated for control the heat transfer rate for several cases. The purpose of this feasibility study is to achieve uniform temperature profiles and Tmax < 50?C under different heat flux. Natural convection heat transfer in the rectangular and parallelogram enclosures with positive and negative angular adiabatic walls were simulated. The average wall temperature under heat flux boundary condition has been studied to predict optimal levels of effective factors to control the maximum wall temperature. The results illustrated parallelogram enclosures with positive angle of case 1 and case 3 and 4 with rectangular enclosures were best cases for considering physical conditions. Average of temperature for these cases were 37.9, 29.7 and 38.2, respectively.

New benchmark solutions for transient natural convection in partially porous annuli

2016 ◽  
Vol 26 (3/4) ◽  
pp. 1187-1225 ◽  
Author(s):  
Nicola Massarotti ◽  
Michela Ciccolella ◽  
Gino Cortellessa ◽  
Alessandro Mauro
Keyword(s):  
Natural Convection ◽  
Free Convection ◽  
Transient Flow ◽  
Flow Behavior ◽  
Outer Radius ◽  
Temperature Fields ◽  
Content Type ◽  
Transient Natural Convection ◽  
Velocity And Temperature Fields ◽  
Benchmark Solutions

Purpose – The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro-ri. Moreover, several Darcy numbers have been considered. Design/methodology/approach – A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement. Findings – For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number. Research limitations/implications – A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems. Practical implications – The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility. Originality/value – This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

Natural Convection in a Horizontal Layer of Water Cooled From Above to Near Freezing

1975 ◽  
Vol 97 (1) ◽  
pp. 47-53 ◽  
Author(s):  
R. E. Forbes ◽  
J. W. Cooper
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Natural Convection ◽  
Hydrodynamic Instability ◽  
Convective Heat Transfer Coefficient ◽  
Free Water ◽  
Ambient Air ◽  
Maximum Density ◽  
Surface Boundary ◽  
Initial Water

Natural convection in horizontal layers of water cooled from above to near freezing was studied analytically. The water was confined laterally and underneath by rigid insulators, and the upper horizontal surface was subjected to: (1) a constant 0C temperature, rigid conducting boundary, and (2) a free, water to air convection boundary condition, in which the convective heat transfer coefficient was held constant at values of 5.68 W/m2 · K and 284 W/m2 · K (1.0 and 50.0 Btu/hr ft2F) and the temperature of the ambient air was maintained at 0C. The ratios of the width to the depth of the rectangular water layers under consideration were W/D = 1, 3, and 6. Initially the water is assumed to be at a uniform temperature of either 4C or 8C, and then the upper surface boundary condition was suddenly applied. It was observed in all cases for which the initial water temperature was 4C, that the water remained stagnant and became thermally stratified. Heat transfer application of either of the surface boundary conditions to water initially at 8C produced large convective eddies extending from the bottom to the top of the layer of water. As the liquid layer cooled further, two distinct horizontal regions appeared, the 4C isothermal line separating the two. This produces a region of hydrodynamic instability in the fluid since the maximum density fluid (4C) is physically located above the less dense fluid in the lower portion of the cavity. The large eddies which appeared initially were confined to the hydrodynamically unstable region bounded by the 4C isotherm and the bottom of the cavity. The action of viscous shearing forces upon the stable water above the 4C isotherm produced a second “layer” of eddies. An alternating direction implicit finite difference method was used to solve the coupled system of partial differential equations. The paper presents transient isotherms and streamlines and a discussion of the effect of maximum density on the flow patterns.

Numerical Simulation of Heat Transfer in Laminar Natural Convection of Mixed Newtonian-Non-Newtonian and Pure Non-Newtonian Nanofluids in a Square Enclosure

2021 ◽  
pp. 1-44
Author(s):  
Ajay Vallabh ◽  
P.S. Ghoshdastidar
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Base Fluid ◽  
Volume Fraction ◽  
Numerical Study ◽  
Transfer Model ◽  
Nanoparticle Concentration ◽  
Left Wall ◽  
Square Enclosure ◽  
First Case

Abstract This paper presents a steady-state heat transfer model for the natural convection of mixed Newtonian-Non-Newtonian (Alumina-Water) and pure Non-Newtonian (Alumina-0.5 wt% Carboxymethyl Cellulose (CMC)/Water) nanofluids in a square enclosure with adiabatic horizontal walls and isothermal vertical walls, the left wall being hot and the right wall cold. In the first case the nanofluid changes its Newtonian character to Non-Newtonian past 2.78% volume fraction of the nanoparticles. In the second case the base fluid itself is Non-Newtonian and the nanofluid behaves as a pure Non-Newtonian fluid. The power-law viscosity model has been adopted for the non-Newtonian nanofluids. A finite-difference based numerical study with the Stream function-Vorticity-Temperature formulation has been carried out. The homogeneous flow model has been used for modelling the nanofluids. The present results have been extensively validated with earlier works. In Case I the results indicate that Alumina-Water nanofluid shows 4% enhancement in heat transfer at 2.78% nanoparticle concentration. Following that there is a sharp decline in heat transfer with respect to that in base fluid for nanoparticle volume fractions equal to and greater than 3%. In Case II Alumina-CMC/Water nanofluid shows 17% deterioration in heat transfer with respect to that in base fluid at 1.5% nanoparticle concentration. An enhancement in heat transfer is observed for increase in hot wall temperature at a fixed volume fraction of nanoparticles, for both types of nanofluid.

2D Natural Convection and Radiation Heat Transfer Simulations of a PWR Fuel Assembly Within a Constant Temperature Support Structure

2006 ◽  
Author(s):  
Pablo E. Araya Go´mez ◽  
Miles Greiner
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fuel Assembly ◽  
Heat Generation ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Fuel Rods ◽  
Water Reactor

Two-dimensional simulations of steady natural convection and radiation heat transfer for a 14×14 pressurized water reactor (PWR) spent nuclear fuel assembly within a square basket tube of a typical transport package were conducted using a commercial computational fluid dynamics package. The assembly is composed of 176 heat generating fuel rods and 5 larger guide tubes. The maximum cladding temperature was determined for a range of assembly heat generation rates and uniform basket wall temperatures, with both helium and nitrogen backfill gases. The results are compared with those from earlier simulations of a 7×7 boiling water reactor (BWR). Natural convection/radiation simulations exhibited measurably lower cladding temperatures only when nitrogen is the backfill gas and the wall temperature is below 100°C. The reduction in temperature is larger for the PWR assembly than it was for the BWR. For nitrogen backfill, a ten percent increase in the cladding emissivity (whose value is not well characterized) causes a 4.7% reduction in the maximum cladding to wall temperature difference in the PWR, compared to 4.3% in the BWR at a basket wall temperature of 400°C. Helium backfill exhibits reductions of 2.8% and 3.1% for PWR and BWR respectively. Simulations were performed in which each guide tube was replaced with four heat generating fuel rods, to give a homogeneous array. They show that the maximum cladding to wall temperature difference versus total heat generation within the assembly is not sensitive to this geometric variation.

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