A Comparative Numerical Study on Conjugate Natural Convection From Vertical Hollow Cylinder With Finite Thickness Placed on Ground and in Air

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Manoj Kumar Dash ◽  
Sukanta Kumar Dash
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Loss ◽  
Hollow Cylinder ◽  
Average Nusselt Number ◽  
Total Heat ◽  
Outer Diameter ◽  
Thermal Plume ◽  
Total Heat Loss

Abstract The present work reports a comparative analysis of natural convection heat transfer from a thick hollow vertical cylinder either placed on the ground or suspended in the air. The numerical simulations have been performed by varying the cylinder length to its outer diameter (L/Do) in the range of 0.2–20, the thickness ratio (Di/Do) in a range of 0.5–0.9, and Rayleigh number (Ra) from 104 to 108. The flow and heat transfer characteristics have been delineated precisely with the presentation of the thermal plume and flow field in the vicinity of the cylinder. The variation of average Nusselt number (Nu), local Nu, and contribution to total heat loss from different surfaces with the pertinent parameters have been elucidated graphically. The average Nu is always more for the cylinder in the air compared with the case when it is on the ground. However, the difference between the Nu for these two cases diminishes, as the L/Do increases. It has also been found that the contribution to total heat loss from the inner surface of the hollow cylinder suspended in air increases with L/Do, attains a peak, and decreases sharply. Cooling time curves for the cylinder placed in air or on the ground have been described precisely. Finally, a correlation for the average Nusselt number as a function of all the pertinent parameters has been proposed that can be useful for industrial and academic purposes.

Numerical Analysis of Natural Convection Heat Transfer From a Vertical Hollow Cylinder Suspended in Air

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Swastik Acharya ◽  
Sumit Agrawal ◽  
Sukanta K. Dash
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Hollow Cylinder ◽  
Outer Surface ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Natural convection heat transfer from a vertical hollow cylinder suspended in air has been analyzed numerically by varying the Rayleigh number (Ra) in the laminar (104 ≤ Ra ≤ 108) regime. The simulations have been carried out by changing the ratio of length to pipe diameter (L/D) in the range of 0.05 ≤ L/D≤20. Full conservation equations have been solved numerically for a vertical hollow cylinder suspended in air using algebraic multigrid solver of fluent 13.0. The flow and the temperature field around the vertical hollow cylinder have been observed through velocity vectors and temperature contours for small and large L/D. It has been found that the average Nusselt number (Nu) for vertical hollow cylinder suspended in air increases with the increase in Rayleigh number (Ra) and the Nu for both the inner and the outer surface also increases with Ra. However, with the increase in L/D, average Nu for the outer surface increases almost linearly, whereas the average Nu for the inner surface decreases and attains asymptotic value at higher L/D for low Ra. In this study, the effect of parameters like L/D and Ra on Nu is analyzed, and a correlation for average Nusselt number has been developed for the laminar regime. These correlations are accurate to the level of ±6%.

scholarly journals Natural convection in a differentially heated enclosure with triangular roof

1970 ◽  
Vol 39 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Sumon Saha ◽  
Noman Hasan ◽  
Chowdhury Md Feroz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Element Analysis ◽  
Left Wall ◽  
Square Enclosure

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

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.

Thermal Behavior of Silicon Heat Spreader Coated With Diamond Film

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.

Heat Transfer Due to Natural Convection in a Periodically Heated Slot

2012 ◽  
Vol 135 (2) ◽  
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.

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

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

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

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.

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

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.

scholarly journals Effect of radiation on the flow structure and heat transfer in a 2-D gray medium

2019 ◽  
Vol 23 (6 Part A) ◽  
pp. 3603-3614
Author(s):  
Nesrine Rachedi ◽  
Madiha Bouafia ◽  
Messaoud Guellal ◽  
Saber Hamimid
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Radiative Transfer Equation ◽  
Numerical Study ◽  
Discrete Ordinates ◽  
Square Cavity ◽  
Discrete Ordinates Method ◽  
Gray Medium

A numerical study of combined natural convection and radiation in a square cavity filled with a gray non-scattering semi-transparent fluid is conducted. The horizontal walls are adiabatic and the vertical are differentially heated. Convection is treated by the finite volumes approach and the discrete ordinates method is used to solve radiative transfer equation using S6 order of angular quadrature. Representative results illustrating the effects of the Rayleigh number, the optical thickness and the Planck number on the flow and temperature distribution are reported. In addition, the results in terms of the average Nusselt number obtained for various parametric conditions show that radiation modifies significantly the thermal behavior of the fluid within the enclosure.

Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
S. Roy ◽  
Tanmay Basak ◽  
Ch. Thirumalesha ◽  
Ch. Murali Krishna
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nusselt Number ◽  
Natural Convection ◽  
Prandtl Number ◽  
Average Nusselt Number ◽  
Bottom Wall ◽  
Nonuniform Heating ◽  
Triangular Enclosure ◽  
Prandtl Numbers

A penalty finite element analysis with biquadratic elements has been carried out to investigate natural convection flows within an isosceles triangular enclosure with an aspect ratio of 0.5. Two cases of thermal boundary conditions are considered with uniform and nonuniform heating of bottom wall. The numerical solution of the problem is illustrated for Rayleigh numbers (Ra), 103⩽Ra⩽105 and Prandtl numbers (Pr), 0.026⩽Pr⩽1000. In general, the intensity of circulation is found to be larger for nonuniform heating at a specific Pr and Ra. Multiple circulation cells are found to occur at the central and corner regimes of the bottom wall for a small Prandtl number regime (Pr=0.026−0.07). As a result, the oscillatory distribution of the local Nusselt number or heat transfer rate is seen. In contrast, the intensity of primary circulation is found to be stronger, and secondary circulation is completely absent for a high Prandtl number regime (Pr=0.7–1000). Based on overall heat transfer rates, it is found that the average Nusselt number for the bottom wall is 2 times that of the inclined wall, which is well, matched in two cases, verifying the thermal equilibrium of the system. The correlations are proposed for the average Nusselt number in terms of the Rayleigh number for a convection dominant region with higher Prandtl numbers (Pr=0.7 and 10).

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