scholarly journals Effect of Linearly Varying Heating Inside a Square Cavity under Natural Convection

2021 ◽  
Vol 19 (4) ◽  
pp. 336-344
Author(s):  
AJITH KUMAR R ◽  
Kunjunni M
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Free Convection ◽  
Thermal Management ◽  
Heat Transfer Process ◽  
Stream Line ◽  
Square Enclosure ◽  
Temperature Distributions ◽  
Increasing Temperature

Telecommunication devices such as ADSL Modems or Wi-Fi routers are being widely used around the globe. Thermal management of such equipments are of critical importance as the increased power consumptions caused by technological upgrades results in increased heat generation within these systems. The heat transfer process inside such sealed and passively cooled equipments can be simplified as natural convection inside enclosures. Studying actual conditions inside electronic enclosure are necessary for their effective thermal management. This study aims at investigating the effect of non-isothermal heating inside such enclosures with linearly varying temperature distribution on free convection inside square enclosure. The issue of free convection of air interior of a square chamber with linearly varying temperature distributions on the left partition is studied numerically.  The effect of change of Rayleigh number, temperature distributions, on flow and temperature field and rate of transfer of heat are analysed. Rayleigh number is chosen to vary in between 103 and 106. Four different cases of linearly varying temperature distributions are considered. The outcomes are presented as stream line plot, isotherm contour and average Nusselt number. The outcomes depicted that case of linearly increasing temperature along the height gives higher Nusselt number than other cases.

Study of Natural Convection in Inclined Square Enclosures With Uniform Heat Generation

2007 ◽  
Author(s):  
Manish Kulkarni ◽  
Sushanta K. Mitra ◽  
U. N. Gaitonde
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Generation ◽  
Inclination Angle ◽  
Local Nusselt Number ◽  
Internal Heat ◽  
Square Enclosure ◽  
Inclination Angles ◽  
Inclined Cavity

Two-dimensional laminar natural convection in an inclined square enclosure with uniform internal heat generation is studied here. The steady-state solutions are obtained for inclination angles of 45°, 30° and 15° and at Rayleigh number of 1.5 × 105. For these cases, the two counter-rotating rolls of fluid are present in the cavity. Streamlines, isotherms and heat transfer for these results are compared with the existing experimental results and are found to be in reasonably good agreement. It is found that the location of maximum non-dimensional temperature in the inclined cavity is higher than that for pure conduction case. The maximum non-dimensional temperature in the cavity decreases as the Rayleigh number increases. For Ra > 5 × 104, the maximum non-dimensional temperature in inclined cavity is almost independent of the inclination angle. It is also observed that the local Nusselt number at the top wall is greater than the pure conduction solution, whereas that for bottom wall it is lower than the Nusselt number for pure conduction. The effect of Rayleigh number and inclination angle on the local Nusselt number and modified local Nusselt number are also studied. For horizontal cavity, at Rayleigh number greater than or equal to 5 × 104, periodic solutions are obtained. In this case, two unstable secondary rolls are present near the center of top wall, in addition to the primary rolls. The secondary rolls are dissipated and recreated during one period of oscillation.

A Study on Natural Convection in a Cold Square Enclosure With Two Vertical Eccentric Square Heat Sources Using the IB–LBM Scheme

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
S. M. Dash ◽  
S. Sahoo
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Lattice Boltzmann Model ◽  
Immersed Boundary ◽  
Heat Sources ◽  
Square Enclosure ◽  
Thermal Lattice Boltzmann

In this article, the natural convection process in a two-dimensional cold square enclosure is numerically investigated in the presence of two inline square heat sources. Two different heat source boundary conditions are analyzed, namely, case 1 (when one heat source is hot) and case 2 (when two heat sources are hot), using the in-house developed flexible forcing immersed boundary–thermal lattice Boltzmann model. The isotherms, streamlines, local, and surface-averaged Nusselt number distributions are analyzed at ten different vertical eccentric locations of the heat sources for Rayleigh number between 103 and 106. Distinct flow regimes including primary, secondary, tertiary, quaternary, and Rayleigh–Benard cells are observed when the mode of heat transfer is changed from conduction to convection and heat sources eccentricity is varied. For Rayleigh number up to 104, the heat transfer from the enclosure is symmetric for the upward and downward eccentricity of the heat sources. At Rayleigh number greater than 104, the heat transfer from the enclosure is better for downward eccentricity cases that attain a maximum when the heat sources are near the bottom enclosure wall. Moreover, the heat transfer rate from the enclosure in case 2 is nearly twice that of case 1 at all Rayleigh numbers and eccentric locations. The correlations for heat transfer are developed by relating Nusselt number, Rayleigh number, and eccentricity of the heat sources.

Natural Convection in a Nano-Fluid Filled Square Enclosure

2020 ◽  
Vol 847 ◽  
pp. 114-119
Author(s):  
Barbie Leena Barhoi ◽  
Ramesh Chandra Borah ◽  
Sandeep Singh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Control Volume ◽  
Convection Heat Transfer ◽  
Ansys Fluent ◽  
Square Enclosure ◽  
Nano Fluid

The present study relates to numerical investigation of natural convection heat transfer in a nanofluid filled square enclosure. One side of the enclosure is maintained at high temperature and the other side at a low temperature; while the top and bottom sides are adiabatic. The commercial CFD software ANSYS-FLUENT© was used to solve this numerical problem with the governing differential equations discretized by a control volume approach. nanofluids of Cu-water, Al2O3-water and TiO2-water have been simulated for a range of Rayleigh numbers and volume fractions. The results were obtained in the form of streamlines and isotherms. Interpretations of the results are done based on heat transfer rates, volume fraction, Rayleigh number and Nusselt number. It is to be noted that addition of nanoparticles enhances the heat transfer rate. It is also observed that the Nusselt number is highly affected by volume fraction and Rayleigh number.

Combined Effects of Fluid Yield Stress and Geometrical Arrangement on Natural Convection in a Square Duct From Two Differentially Heated Horizontal Cylinders

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Lubhani Mishra ◽  
R. P. Chhabra
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Square Duct ◽  
Bingham Plastic ◽  
Square Enclosure ◽  
Bingham Number ◽  
Heated Cylinder

Abstract Laminar natural convection in Bingham plastic fluids has been investigated from two differentially heated cylinders arranged either one above the other or along the diagonal of the square enclosure. The coupled momentum and energy equations have been solved to elucidate the effect of Rayleigh number (104–106), Prandtl number (10–100), Bingham number (0.01 to Bnmax), and the gap between the two cylinders in terms of the geometric parameters (0 to −0.25 for vertical alignment and 0.15 to 0.35 for diagonal alignment) on the detailed structure of the flow field and the overall heat transfer characteristics of the system. New extensive results are visualized in terms of streamlines, isotherm contours, and variation of the local Nusselt number along various surfaces. Additional insights are developed by examining the shear-rate contours and the yield surfaces delineating the fluid-like and solid-like regions in the flow domain. At high values of the Bingham number, the average Nusselt number reaches its asymptotic value corresponding to the conduction limit. The increasing Rayleigh number promotes fluid-like behavior which promotes heat transfer. The augmentation in heat transfer depends on the volume of fluid participating in the buoyancy-induced flow. For the vertical arrangement, the average Nusselt number (for the heated cylinder) decreases a little as these are moved slightly away from the center of the enclosure, followed by an increase as the two cylinders approach one of the sidewalls; this is so even in the conduction limit. In contrast, when the two cylinders are arranged along the diagonal, the Nusselt number progressively decreases as the gap between the two cylinders increases. Finally, predictive correlations have been developed for the average Nusselt number and the limiting Bingham number thereby enabling their estimation in a new application.

Natural Convection of Viscoplastic Fluids in a Square Enclosure

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
M. A. Hassan ◽  
Manabendra Pathak ◽  
Mohd. Kaleem Khan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Yield Stress ◽  
Average Nusselt Number ◽  
Critical Value ◽  
Square Enclosure ◽  
Bingham Number ◽  
Viscoplastic Fluids

Viscoplastic fluids are special kind of non-Newtonian materials which deform or flow only when applied stresses are more than a critical value known as yield stress. In this work, a numerical investigation of natural convection in a square enclosure filled with viscoplastic fluids has been reported. The enclosure has been partially heated from the bottom wall by a heating source and symmetrically cooled from both the side walls. The rheology of the viscoplastic fluids has been modeled with Bingham fluid model. A scaling analysis has been presented to establish the gross dependence of heat transfer on different values of operating parameters of the problem. The effects of yield stress of the fluid on heat and fluid transport inside the enclosure have been investigated for different values of temperature difference, across the hot and cold surfaces and also for different fluids. The effects of different lengths of heated zone on the flow phenomena and heat transfer characteristics have been investigated for three different values of the heated zones. All the important results have been expressed in terms of Bingham number (Bn), Rayleigh number (Ra), and Prandtl number (Pr). It has been observed that with the increase in Bingham number, the buoyancy induced fluid circulation and convection effect decreases inside the enclosure. For each Rayleigh number, there correspond a critical Bingham number for which the heat transfer inside the enclosure takes place solely by conduction mode. This critical value increases with the increase in Rayleigh number. For fixed value of Bingham number, i.e., fixed value of yield stress, the effects of Rayleigh number and heated length on heat transfer have been observed similar to the case of natural convection in Newtonian fluid. It has been also observed that at high Bingham number the effect of increase in Rayleigh number on average Nusselt number is lesser compared to the effect of increasing Rayleigh number at low Bingham number. Using the present numerical results, a correlation of average Nusselt number as a function of other nondimensional numbers has been established.

Influence of Partition Length on Natural Convection in Partially Divided Square Enclosure

2007 ◽  
Vol 129 (11) ◽  
pp. 1592-1599 ◽  
Author(s):  
C. D. Sankhavara ◽  
H. J. Shukla
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Square Enclosure ◽  
Thermal Boundary Conditions ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Good Agreement

Numerical investigation is carried out for natural convection in square enclosures consisting of partitions protruding from the end walls with different thermal boundary conditions at the end walls and partitions. The vertical walls were maintained isothermal at different temperatures. The Rayleigh number varies from 104 to 106 and the Prandtl number is 0.71. The thickness of the partition is fixed and is equal to one-tenth of the width of the enclosure. Their nondimensional length (l∕H) varies from 0 (a nonpartitioned enclosure) to 0.5 (two separate enclosures). A good agreement was found between the results in the present study and those published previously. The partitions were found to significantly influence the convective heat transfer. The average Nusselt number is less in the presence of partitions, and it decreases with increasing partition length (l∕H) from 0 to 0.5.

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

scholarly journals Lattice Boltzmann Simulation of Natural Convection in an Annulus between a Hexagonal Cylinder and a Square Enclosure

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
L. El Moutaouakil ◽  
Z. Zrikem ◽  
A. Abdelbaki
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Square Enclosure ◽  
Lattice Boltzmann Simulation ◽  
Laminar Natural Convection ◽  
Heat Transfers ◽  
Boltzmann Method ◽  
Vertical Case

Laminar natural convection in a water filled square enclosure containing at its center a horizontal hexagonal cylinder is studied by the lattice Boltzmann method. The hexagonal cylinder is heated while the walls of the cavity are maintained at the same cold temperature. Two orientations are treated, corresponding to two opposite sides of the hexagonal cross-section which are horizontal (case I) or vertical (case II). For each case, the results are presented in terms of streamlines, isotherms, local and average convective heat transfers as a function of the dimensionless size of the hexagonal cylinder cross-section (0.1≤B≤0.4), and the Rayleigh number (103≤Ra≤106).

scholarly journals Effects of Different Boundary Conditions at the Surfaces of the Extended Computational Domain in Computing the Natural Convection Flow in an Open Cavity

2016 ◽  
Vol 64 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Roushanara Begum ◽  
MZI Bangalee
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Open Cavity ◽  
Stream Line ◽  
Convection Flow ◽  
Computational Domain ◽  
Physical Domain ◽  
Natural Convection Flow ◽  
Different Boundary Conditions

Effects of different boundary conditions at the surfaces of the extended computational domain on buoyancy driven natural convection flow in a three dimensional open cavity are studied numerically. This study is carried out for turbulent flow where Rayleigh number is greater than 108. Air is used as working fluid having properties at 25°C temperature and 1atm pressure. To capture the turbulent nature of the flow k - ? model is used. ANSYS CFX software is used to solve the governing equations subject to the corresponding boundary conditions. The methodology is verified through a satisfactory comparison with some published results. Average mass flow, temperature, stream line, contour velocity and velocity profile are studied at different height. An extended computational domain around the physical domain of the cavity at different surrounding conditions is considered to investigate the effect of its existence on the computation. Effects of different surrounding boundary conditions on the physical domain of the cavity are studied and reported.A relation among non-dimensional parameters such as Nusselt number, Rayleigh number, Prandlt number and Reynolds number is also reported.Dhaka Univ. J. Sci. 64(1): 31-37, 2016 (January)

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.

Sign in / Sign up

Export Citation Format

Share Document