Correction for semi-infinite assumption in the theories of natural convection and determination of average Nusselt number for finite inclined plates

A numerical study has been carried out for laminar natural convection heat transfer within a two-dimensional modified square enclosure having a triangular roof. The vertical sidewalls are differentially heated considering a constant flux heat source strip is flush mounted with the left wall. The opposite wall is considered isothermal having a temperature of the surrounding fluid. The rest of the walls are adiabatic. Air is considered as the fluid inside the enclosure. The solution has been carried out on the basis of finite element analysis by a non-linear parametric solver to examine the heat transfer and fluid flow characteristics. Different heights of the triangular roof have been considered for the present analysis. Fluid flow fields and isotherm patterns and the average Nusselt number are presented for the Rayleigh numbers ranging from 103 to 106 in order to show the effects of these governing parameters. The average Nusselt number computed for the case of isoflux heating is also compared with the case of isothermal heating as available in the literature. The outcome of the present investigation shows that the convective phenomenon is greatly influenced by the inclined roof height. Keywords: Natural convection, triangular roof, Rayleigh number, isoflux heating. Doi:10.3329/jme.v39i1.1826 Journal of Mechanical Engineering, vol. ME39, No. 1, June 2008 1-7

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Modeling of natural convection of a concentrated solar power receiver absorber tube in interaction with neighbouring absorbers

EUREKA Physics and Engineering ◽

10.21303/2461-4262.2021.001871 ◽

2021 ◽

pp. 53-61

Author(s):

Olanrewaju Miracle Oyewola ◽

Niyi Ezekiel Olukayode ◽

Olusegun Olufemi Ajide

Keyword(s):

Nusselt Number ◽

Natural Convection ◽

Average Nusselt Number ◽

Solar Power ◽

Renewable Energy Sources ◽

Navier Stokes ◽

Element Formulation ◽

Concentrated Solar Power ◽

Set Up ◽

Energy Equations

Concentrated Solar Power (CSP) technology stands out among other renewable energy sources not only because of its ability to address current energy security and environmental challenges but because its energy can be stored for future use. To ensure optimum performance in this system, the heat losses need to be evaluated for better design. This work studies the natural convection in the receiver absorber tube of a CSP plant taking into consideration the influence of neighboring absorbers. A 2-Dimensional model was adopted in this study. Initially, a single absorber tube was considered, it was subjected to heat flux at the top wall, the bottom wall was insulated and a temperature differential was set up at the lateral walls. The dimensionless forms of Navier-Stokes and energy equations were solved using the finite element formulation of COMSOL Multiphysics software. The result obtained for a single absorber tube showed good agreement with existing research works. This validated model was then extended to multiple absorber tubes (two to six absorber tubes). On the basis of the study, there is an observed increase in the intensity and dominance of convective heat transfer with an increase in the number of absorber tubes. This is occasioned by an increase in the average surface temperature as well as average Nusselt number. For the Rayleigh number of 104, 105 and 106, the average Nusselt number increases with the number of absorber tubes by 13.87 %, 6.26 %, and 1.55 %, respectively. This increment suggests effect of thermal interactions among the neighboring absorber tubes

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Natural convection in differentially heated enclosures subjected to variable temperature boundaries

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-02-2019-0137 ◽

2019 ◽

Vol 29 (11) ◽

pp. 4130-4141 ◽

Cited By ~ 3

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.

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Thermal Behavior of Silicon Heat Spreader Coated With Diamond Film

Electronic and Photonic Packaging, Electrical Systems Design and Photonics, and Nanotechnology ◽

10.1115/imece2004-59485 ◽

2004 ◽

Author(s):

T. W. Lin ◽

M. C. Wu ◽

C. H. Peng ◽

P. L. Chen ◽

Y. H. Hung

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Natural Convection ◽

Silicon Wafer ◽

Diamond Film ◽

Silicon Surface ◽

Average Nusselt Number ◽

Diamond Surface ◽

Heat Spreader ◽

Heat Spreaders

In the present study, an experimental setup with stringent measurement methods for performing the natural convection from a horizontal heated chip mounted with a silicon heat spreader coated with diamond film has been successfully established. The parametric studies on the local and average effective heat transfer characteristics for natural convection from a horizontal smooth silicon wafer, rough silicon wafer or silicon wafer coated with diamond film spreader have been explored. The influencing parameters and conditions include Grashof number and spreader material with different surface treatment conditions. From the results, an axisymmetric bowl-shaped Nu profile is achieved, and the highest heat transfer performance occurs at the location near the rim of the heated surfaces for various heat spreaders. The local Nusselt number for a specified convective heat flux decreases along the distance from the disk rim toward the center. The local or average Nusselt number increases with increasing Grashof number for various heat spreaders. As compared with the average Nusselt number for smooth water surface (Ra=5.69nm), the heat transfer enhancements for rough silicon surface (Ra=516.61nm) and rough diamond surface (Ra=319.51nm) are 10.42% and 7.69%, respectively. Furthermore, new correlations for local and average Nusselt numbers for various heat spreaders are presented, respectively. As compared with the smooth silicon surface, the external thermal resistance for rough silicon surface and rough diamond surface are reduced to 91.18% and 90.73%, respectively; and the maximum thermal resistances for rough silicon wafer and silicon wafer coated with diamond film are reduced to 90.43% and 92.61%, respectively.

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Lattice Boltzmann simulation of turbulent natural convection in tall enclosures

Thermal Science ◽

10.2298/tsci120105066s ◽

2015 ◽

Vol 19 (1) ◽

pp. 155-166 ◽

Cited By ~ 13

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.

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Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

Journal of Heat Transfer ◽

10.1115/1.2717241 ◽

2006 ◽

Vol 129 (6) ◽

pp. 717-726 ◽

Cited By ~ 30

Author(s):

Kamil Kahveci

Keyword(s):

Heat Flux ◽

Nusselt Number ◽

Natural Convection ◽

Thermal Resistance ◽

Average Nusselt Number ◽

Numerical Study ◽

Finite Thickness ◽

Vertical Wall ◽

Uniform Heat Flux ◽

Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

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Heat Transfer Due to Natural Convection in a Periodically Heated Slot

Journal of Heat Transfer ◽

10.1115/1.4007420 ◽

2012 ◽

Vol 135 (2) ◽

Cited By ~ 14

Author(s):

M. Z. Hossain ◽

J. M. Floryan

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Temperature Field ◽

Natural Convection ◽

Average Nusselt Number ◽

Horizontal Direction ◽

Wave Number ◽

Lower Wall ◽

Maximum Heat ◽

Maximum Heat Transfer

Heat transfer resulting from the natural convection in a fluid layer contained in an infinite horizontal slot bounded by solid walls and subject to a spatially periodic heating at the lower wall has been investigated. The heating produces sinusoidal temperature variations along one horizontal direction characterized by the wave number α with the amplitude expressed in terms of a suitably defined Rayleigh number Rap. The maximum heat transfer takes place for the heating with the wave numbers α = 0(1) as this leads to the most intense convection. The intensity of convection decreases proportionally to α when α→0, resulting in the temperature field being dominated by periodic conduction with the average Nusselt number decreasing proportionally to α2. When α→∞, the convection is confined to a thin layer adjacent to the lower wall with its intensity decreasing proportionally to α−3. The temperature field above the convection layer looses dependence on the horizontal direction. The bulk of the fluid sees the thin convective layer as a “hot wall.” The heat transfer between the walls becomes dominated by conduction driven by a uniform vertical temperature gradient which decreases proportionally to the intensity of convection resulting in the average Nusselt number decreasing as α−3. It is shown that processes described above occur for Prandtl numbers 0.001 < Pr < 10 considered in this study.

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ISPH simulations of natural convection from heated rotating paddles on a circular cylinder inside a cross-shaped cavity filled with a nanofluid

10.22541/au.160640288.84638521/v1 ◽

2020 ◽

Author(s):

Abdelraheem Mahmoud Aly ◽

Ehab Mahmoud

Keyword(s):

Heat Transfer ◽

Porous Media ◽

Nusselt Number ◽

Fluid Flow ◽

Natural Convection ◽

Circular Cylinder ◽

Average Nusselt Number ◽

Volume Fraction ◽

Heterogeneous Porous Media ◽

Convection Flow

The numerical simulations of the uniform circular rotation of paddles on circular cylinder results natural convection flow of Al2O3-water in a cross-shaped porous cavity were performed by incompressible representation of smoothed particle hydrodynamics entitled ISPH method. The two vertical area of a cross-shaped cavity is saturated with homogeneous porous media and the whole horizontal area of a cross-shaped cavity is saturated with heterogeneous porous media. The inner paddles on the circular cylinder are rotating around their center by a uniform circular velocity. The whole embedded body of paddles on a circular cylinder has temperature Th. The wall-sides of a cross-shaped cavity are positioned at a temperature Tc. The current geometry can be applied in analysis and understanding the thermophysical behaviors of the electronic motors. The angular velocity is taken as ! = 7:15 and consequently the natural convection case is only considered due to the low speed of inner rotating shape. The performed simulations are represented in the graphical for the temperature distributions, velocity fields and tabular forms for average Nusselt number. The results revealed that an augmentation on paddle length rises the heat transfer and speed of fluid flow inside a cross shaped cavity. Also, an incrementation on Rayleigh number augments the heat transfer and speed of the fluid flow inside a cross-shaped cavity. The fluid flow is circulated only around the rotating inner shape when Darcy parameter decreases to Da = 105. Average Nusselt number Nu enhances by an increment on the paddle lengths and nanoparticles volume fraction

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Prediction of Natural Convection Heat Transfer Phenomena of Nanofluids in Corrugated Annulus

10.21203/rs.3.rs-39325/v1 ◽

2020 ◽

Author(s):

Sattar Aljobair ◽

Akeel Abdullah Mohammed ◽

Israa Alesbe

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Natural Convection ◽

Rayleigh Number ◽

Average Nusselt Number ◽

Volume Fraction ◽

Outer Cylinder ◽

Convection Heat Transfer ◽

Natural Convection Heat Transfer ◽

Convection Heat

Abstract The natural convection heat transfer and fluid flow characteristic of water based Al2O3 nano-fluids in a symmetrical and unsymmetrical corrugated annulus enclosure has been studied numerically using CFD. The inner cylinder is heated isothermally while the outer cylinder is kept constant cold temperature. The study includes eight models of corrugated annulus enclosure with constant aspect ratio of 1.5. The governing equations of fluid motion and heat transfer are solved using stream-vorticity formulation in curvilinear coordinates. The range of solid volume fractions of nanoparticles extends from PHI=0 to 0.25, and Rayleigh number varies from 104 to 107. Streamlines, isotherms, local and average Nusselt number of inner and outer cylinder has been investigated in this study. Sixty-four correlations have been deduced for the average Nusselt number for the inner and outer cylinders as a function of Rayleigh number have been deduced for eight models and five values of volume fraction of nano particles with an accuracy range 6-12 %. The results show that, the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. Also, increase the number of undulations in unsymmetrical annuli reduces the heat transfer rates which remain higher than that in symmetrical annuli. There is no remarkable change in isotherms contour with increase of volume fraction of nanofluid.

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Effect of Various Tilted Positions of a Thin Fin on Natural Convection of Laminar Viscous Flow in a Square Cavity

International Journal of Heat and Technology ◽

10.18280/ijht.390527 ◽

2021 ◽

Vol 39 (5) ◽

pp. 1634-1642

Author(s):

Syed Fazuruddin ◽

Seelam Sreekanth ◽

G Sankara Sekhar Raju

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Fluid Flow ◽

Natural Convection ◽

Rayleigh Number ◽

Finite Difference ◽

Average Nusselt Number ◽

Vertical Position ◽

Inclination Angles ◽

Rayleigh Numbers

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

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