Numerical simulation of turbulent natural convection combined with surface thermal radiation in a square cavity

2015 ◽  
Vol 25 (7) ◽  
pp. 1600-1618 ◽  
Author(s):  
Igor V Miroshnichenko ◽  
M A Sheremet
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Turbulent Flow ◽  
Stream Function ◽  
Computational Time ◽  
Content Type ◽  
Turbulent Natural Convection ◽  
Algebraic Transformation ◽  
Primitive Variables

Purpose – The purpose of this paper is to present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity. Design/methodology/approach – The governing equations formulated in dimensionless variables “stream function, vorticity and temperature,” within the Boussinesq approach taking into account the standard two equation k-ε turbulence model with physical boundary conditions have been solved using an iterative implicit finite-difference method. Findings – It has been found that using of the presented algebraic transformation of the mesh allows to effectively conduct numerical analysis of turbulent natural convection with thermal surface radiation. It has been shown that the average convective Nusselt number increases with the Rayleigh number and decreases with the surface emissivity, while the average radiative Nusselt number is an increasing function of these key parameters. It has been shown that a presence of surface thermal radiation effect leads to an expansion of the eddy viscosity zones close to the walls. Originality/value – It should be noted that for the first time in this paper we used stream function and vorticity variables with very effective algebraic transformation of the mesh in order to create a non-uniform mesh for an analysis of turbulent flow. Such method allows to reduce the computational time essentially in comparison with using of the primitive variables. The considered method has been successfully validated on the basis of the experimental and numerical data of other authors in case of turbulent natural convection without thermal radiation. The used numerical method would benefit scientists and engineers to become familiar with the analysis of turbulent convective heat and mass transfer, and the way to predict the properties of the turbulent flow in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

Turbulent natural convection combined with surface thermal radiation in a square cavity with local heater

2018 ◽  
Vol 28 (7) ◽  
pp. 1698-1715 ◽  
Author(s):  
Igor Miroshnichenko ◽  
Mikhail Sheremet ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Thermal Radiation ◽  
Thermal Plume ◽  
Square Cavity ◽  
Content Type ◽  
Turbulent Natural Convection ◽  
Industrial Sectors ◽  
Bottom Cavity

Purpose The purpose of this paper is to conduct a numerical analysis of transient turbulent natural convection combined with surface thermal radiation in a square cavity with a local heater. Design/methodology/approach The domain of interest includes the air-filled cavity with cold vertical walls, adiabatic horizontal walls and isothermal heater located on the bottom cavity wall. It is assumed in the analysis that the thermophysical properties of the fluid are independent of temperature and the flow is turbulent. Surface thermal radiation is considered for more accurate analysis of the complex heat transfer inside the cavity. The governing equations have been discretized using the finite difference method with the non-uniform grid on the basis of the special algebraic transformation. Turbulence was modeled using the k–ε model. Simulations have been carried out for different values of the Rayleigh number, surface emissivity and location of the heater. Findings It has been found that the presence of surface radiation leads to both an increase in the average total Nusselt number and intensive cooling of such type of system. A significant intensification of convective flow was also observed owing to an increase in the Rayleigh number. It should be noted that a displacement of the heater from central part of the bottom wall leads to significant modification of the thermal plume and flow pattern inside the cavity. Originality/value An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady turbulent natural convection combined with surface thermal radiation in a square air-filled cavity in the presence of a local isothermal heater. The results would benefit scientists and engineers to become familiar with the analysis of turbulent convective–radiative heat transfer in enclosures with local heaters, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Effect of Periodicity of Non-Uniform Sinusoidal Side Heating on Natural Convection in an Anisotropic Porous-Enclosure

2011 ◽  
Vol 110-116 ◽  
pp. 1613-1618 ◽  
Author(s):  
S. Kapoor ◽  
P. Bera
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Stream Function ◽  
Numerical Study ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Porous Enclosure

A comprehensive numerical study on the natural convection in a hydrodynamically anisotropic as well as isotropic porous enclosure is presented, flow is induced by non uniform sinusoidal heating of the right wall of the enclosure. The principal directions of the permeability tensor has been taken oblique to the gravity vector. The spectral Element method has been adopted to solve numerically the governing differential equations by using the vorticity-stream-function approach. The results are presented in terms of stream function, temperature profile and Nusselt number. The result show that the maximum heat transfer takes place at y = 1.5 when N is odd.. Also, increasing media permeability, by changing K* = 1 to K* = 0.2, increases heat transfer rate at below and above right corner of the enclosure. Furthermore, for the all values of N, profiles of local Nusselt number (Nuy) in isotropic as well as anisotropic media are similar, but for even values of N differ slightly at N = 2.. In particular the present analysis shows that, different periodicity (N) of temperature boundary condition has the significant effect on the flow pattern and consequently on the local heat transfer phenomena.

scholarly journals Natural convection of Bingham fluids in rectangular cross-sectional cylindrical annuli with differentially heated vertical walls

2019 ◽  
Vol 29 (1) ◽  
pp. 43-77 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Natural Convection ◽  
Yield Stress ◽  
Thermal Transport ◽  
Second Order ◽  
Bingham Fluids ◽  
Cross Sectional ◽  
Content Type ◽  
The Mean

PurposeThis paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (ri/L1/8 to 16, whereLis the difference between outer and inner radii); aspect ratio (AR=H/Lfrom 1/8 to 8 whereHis the enclosure height); and nominal Rayleigh number (Rafrom 103to 106) for a single representative value of Prandtl number (Pris 500).Design/methodology/approachThe Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.FindingsIt is found that the mean Nusselt number based on the inner peripheryNu¯iincreases (decreases) with an increase inRa(Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasingri/Lfor both Newtonian (i.e.Bn= 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt numberNu¯inormalised by the corresponding Nusselt number due to pure conductive transport (i.e.Nu¯i/(Nu¯i)cond) shows a non-monotonic trend with increasingARin the CWT configuration for a given set of values ofRa,Pr,Lifor both Newtonian (i.e.Bn= 0) and Bingham fluids, whereasNu¯i/(Nu¯i)condincreases monotonically with increasingARin the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasingAR, and these competing effects are responsible for the non-monotonicNu¯i/(Nu¯i)condvariation withARin the CWT configuration.Originality/valueDetailed scaling analysis is utilised to explain the observed influences ofRa,BN,ri/LandAR, which along with the simulation data has been used to propose correlations forNu¯i.

scholarly journals Numerical study of the turbulent natural convection of nanofluids in a partially heated cubic cavity

2021 ◽  
pp. 57-57
Author(s):  
Zakaria Lafdaili ◽  
Sakina El-Hamdani ◽  
Abdelaziz Bendou ◽  
Karim Limam ◽  
Bara El-Hafad
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Heat Exchange ◽  
Metallic Nanoparticles ◽  
Volume Fraction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Stability Characteristic ◽  
Horizontal Strip ◽  
Turbulent Natural Convection

In this work we study numerically the three-dimensional turbulent natural convection in a partially heated cubic cavity filled with water containing metallic nanoparticles, metallic oxides and others based on carbon.The objective is to study and compare the effect of the addition of nanoparticles studied in water and also the effect of the position of the heated partition on the heat exchange by turbulent natural convection in this type of geometry, which can significantly improve the design of heat exchange systems for better space optimization. For this we have treated numerically for different volume fractions the turbulent natural convection in the two cases where the cavity is heated respectively by a vertical and horizontal strip in the middle of one of the vertical walls. To take into account the effects of turbulence, we used the standard turbulence model ? - ?. The governing equations are discretized by the finite volume method using the power law scheme which offers a good stability characteristic in this type of flow. The results are presented in the form of isothermal lines and current lines. The variation of the mean Nusselt number is calculated for the two positions of the heated partition as a function of the volume fraction of the nanoparticles studied in water for different Rayleigh numbers.The results show that carbon-based nanoparticles intensify heat exchange by convection better and that the position of the heated partition significantly influences heat exchange by natural convection. In fact, an improvement in the average Nusselt number of more than 20% is observed for the case where the heated partition is horizontal.

Natural convection in differentially heated enclosures subjected to variable temperature boundaries

2019 ◽  
Vol 29 (11) ◽  
pp. 4130-4141 ◽  
Author(s):  
Abdulmajeed Mohamad ◽  
Mikhail A. Sheremet ◽  
Jan Taler ◽  
Paweł Ocłoń
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Uniform Heating ◽  
Content Type ◽  
Left Hand ◽  
Heating And Cooling ◽  
Right Hand ◽  
The Right

Purpose Natural convection in differentially heated enclosures has been extensively investigated due to its importance in many industrial applications and has been used as a benchmark solution for testing numerical schemes. However, most of the published works considered uniform heating and cooling of the vertical boundaries. This paper aims to examine non-uniform heating and cooling of the mentioned boundaries. The mentioned case is very common in many electronic cooling devices, thermal storage systems, energy managements in buildings, material processing, etc. Design/methodology/approach Four cases are considered, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature is kept at a constant, cold temperature. In the second case, the left-hand wall’s temperature linearly increases along the wall, while the right-hand wall’s temperature is kept a constant, cold temperature. The third case, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature linearly increases along the wall. In the fourth case, the left-hand and the right-hand walls’ temperatures decrease along the wall, symmetry condition. Hence, four scenarios of natural convection in enclosures were covered. Findings It has been found that the average Nusselt number of the mentioned cases is less than the average Nusselt number of the uniformly heated and cooled enclosure, which reflects the physics of the problem. The work quantifies the deficiency in the rate of the heat transfer. Interestingly one of the mentioned cases showed two counter-rotating horizontal circulations. Such a flow structure can be considered for passively, highly controlled mechanism for species mixing processes application. Originality/value Previous works assumed that the vertical boundary is subjected to a constant temperature or to a sinusoidal varying temperature. The subject of the work is to examine the effect of non-uniformly heating and/or cooling vertical boundaries on the rate of heat transfer and flow structure for natural convection in a square enclosure. The temperature either linearly increases or decreases along the vertical coordinate at the boundary. Four scenarios are explored.

Natural convection flow in a vertical micro-annulus with time-periodic thermal boundary conditions

2018 ◽  
Vol 14 (5) ◽  
pp. 1064-1081
Author(s):  
Basant Kumar Jha ◽  
Michael O. Oni
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Content Type ◽  
Thermal Boundary Conditions ◽  
The Impact ◽  
Time Periodic

PurposeThe purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.Design/methodology/approachAnalytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.FindingsIt is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.Research limitations/implicationsNo laboratory practical or experiment was conducted.Practical implicationsCooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.Originality/valueIn view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

Effects of chemical reaction and thermal radiation on unsteady double diffusive convection

2014 ◽  
Vol 24 (5) ◽  
pp. 1124-1140 ◽  
Author(s):  
A.M. Rashad ◽  
Sameh Elsayed Ahmed ◽  
Mohamed Ahmed Mansour
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Local Nusselt Number ◽  
Darcy Number ◽  
Content Type ◽  
Various Boundary Conditions ◽  
Chemical Reaction Parameter ◽  
Local Sherwood Number ◽  
Buoyancy Ratio

Purpose – The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects. Design/methodology/approach – In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled. Findings – Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase. Originality/value – The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.

scholarly journals Lattice Boltzmann simulation of turbulent natural convection in tall enclosures

2015 ◽  
Vol 19 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Hasan Sajjadi ◽  
Reza Kefayati
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Lattice Boltzmann ◽  
Average Nusselt Number ◽  
Large Eddy Simulations ◽  
Turbulent Natural Convection ◽  
Aspect Ratios ◽  
Lattice Boltzmann Simulation ◽  
Large Eddy ◽  
Rayleigh Numbers

In this paper Lattice Boltzmann simulation of turbulent natural convection with large-eddy simulations (LES) in tall enclosures which is filled by air with Pr=0.71 has been studied. Calculations were performed for high Rayleigh numbers (Ra=107-109) and aspect ratios change between 0.5 to 2 (0.5<AR<2). The present results are validated by finds of an experimental research at Ra=1.58x109. Effects of the aspect ratios in different Rayleigh numbers are displayed on streamlines, isotherm counters, vertical velocity and temperature at the middle of the cavity, local Nusselt number and average Nusselt number. The average Nusselt number increases with the augmentation of Rayleigh numbers. The increment of the aspect ratio causes heat transfer to decline in different Rayleigh numbers.

Turbulent Natural Convection in Partitioned Square Cavities with Different Lengths and Positions

2018 ◽  
Vol 877 ◽  
pp. 313-319
Author(s):  
A. Nouri-Borujerdi ◽  
F. Sepahi
Keyword(s):  
Natural Convection ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Bottom Wall ◽  
Staggered Grid ◽  
Viscous Effects ◽  
Left Wall ◽  
Turbulent Natural Convection ◽  
Upwind Schemes

The effect of partition on turbulent natural convection has been investigated numerically with different lengths and positions in an air filled square cavity. The top wall of the cavity is assumed to be cold and the other three walls are hot. Two-dimensional governing equations based on Reynolds-averaged Navier-Stokes equations are solved numerically by control volume method in a staggered grid manner. The iterative SIMPLE algorithm is also used to solve the discretized momentum equations to compute the intermediate velocity and pressure fields linked through the momentum equations. The hybrid differencing scheme which is based on a combination of central and upwind schemes is employed to discretize the convective and diffusion terms of the equations respectively. To describe the structure of turbulent flow which is changed due to the increasing importance of viscous effects, wall function was applied to simulate the turbulent flow. The results show that when the partition is placed on the top or bottom wall, the heat transfer rate through the bottom wall increases by increasing the partition length. The number of vortices established in the cavity depends on the partition length. Furthermore, when the partition is mounted on the left or right wall, only a small part of the top wall has a direct interaction with the left wall and the rest of that has an indirect interaction with the bottom wall.

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