Natural Convection in Square Cavities Heating From Below: Investigation of Three Different Values of the Heat Source Length

2003 ◽  
Author(s):  
Massimo Paroncini ◽  
Barbara Calcagni ◽  
Federico Marsili
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Heat Source ◽  
Real Time ◽  
Holographic Interferometry ◽  
Low Noise ◽  
Heat Transfer Analysis ◽  
Double Exposure ◽  
Square Enclosure

The objective of the present study is to gain some insight into fluid motion and heat transfer phenomena in the case of a square enclosure heated from below and symmetrically cooled from the sides; the effects of different values of the heat source is experimentally investigated. The localized heating is a centrally located heat source on the bottom wall; three different values of the heat source length (1/5, 2/5, 3/5 of the wall) are considered. The test cell is a square enclosure filled with air with isothermal side walls at equal temperatures Tc; the remaining vertical walls are realized with glass to allow optical access to the cavity. The top and bottom surfaces of the enclosure are made of plexiglass and, except for the heated section, are considered to be adiabatic. The located heat source is assumed to be isothermal at a temperature Th. The temperature distribution is experimentally measured by real-time and double-exposure holographic interferometry. The real-time technique is used in order to reveal the presence of plume oscillations while the double-exposure technique is used for steady-state measurements. Holographic interferometry shows the typical advantages over the classical optical techniques, such as high precision and sensitivity, very low noise level, and the possibility of displaying the temperature distribution across the whole investigated region. The objective of the heat transfer analysis is the experimental investigation of the Nusselt number distribution around the cavity at various Rayleigh numbers and several dimensions of the heat source. Different convection forms were obtained depending on Ra and on the heat source length. The Nusselt number was evaluated on the heat source surface and it showed a symmetrical form rising near the heat source borders.

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.

scholarly journals Numerical Investigation of Laminar Natural Convection in Inclined Square Enclosure with the Influence of Discrete Heat Source

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Chithra Devaraj ◽  
Eswaramurthi Muthuswamy ◽  
Sundararaj Kandasamy
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Source ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Correlation Coefficients ◽  
Computational Procedure ◽  
Square Enclosure ◽  
Rayleigh Numbers

Natural convection heat transfer in a two-dimensional square enclosure at various angles of inclination is investigated numerically using a finite volume based computational procedure. The heat transfer is from a constant temperature heat source of finite length centred at one of the walls to the cold wall on the opposite side while the remaining walls are insulated. The effect of area ratio of the heat sourceAfrom 0.2 to 1.0, Rayleigh number Ra from 103to 107, and angle of inclination of the enclosureθvarying from 0° to 360° on the flow field and heat transfer characteristics are investigated. Streamline and isothermal line patterns are found to be similar at low Rayleigh numbers whereas at high Rayleigh numbers the differences are significant due to the influence of the parameters considered. Average Nusselt number decreases drastically as the position of the heat source is moved above the horizontal centre line of the enclosure. Correlation of the average Nusselt number which depends on the parameters of interest is obtained in the general formCRamAn. The correlation coefficients are determined by multiple regression analysis for the entire range of Rayleigh numbers analysed and the values found by correlation equations are in good agreement with the numerical results.

Investigation Into Thermal Stress Characteristics of Pipe-in-Pipe Under High Temperature Condition

2018 ◽  
Author(s):  
Si-Hwa Jeong ◽  
Min-Gu Won ◽  
Nam-Su Huh ◽  
Yun-Jae Kim ◽  
Young-Jin Oh ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
High Temperature ◽  
Temperature Distribution ◽  
Heat Transfer Analysis ◽  
Piping System ◽  
Curved Pipe ◽  
High Temperature Condition ◽  
Single Pipe ◽  
Radiation Conditions

In this paper, the thermal stress characteristics of the pipe-in-pipe (PIP) system under high temperature condition are analyzed. The PIP is a type of pipe applied in sodium-cooled faster reactor (SFR) and has a different geometry from a single pipe. In particular, under the high temperature condition of the SFR, the high thermal stress is generated due to the temperature gradient occurring between the inner pipe and outer pipe. To investigate the thermal stress characteristics, three cases are considered according to geometry of the support. The fully constrained support and intermediate support are considered for case 1 and 2, respectively. For case 3, both supports are applied to the actual curved pipe. The finite element (FE) analyses are performed in two steps for each case. Firstly, the heat transfer analysis is carried out considering the thermal conduction, convection and radiation conditions. From the heat transfer analysis, the temperature distribution results in the piping system are obtained. Secondly, the structural analysis is performed considering the temperature distribution results and boundary conditions. Finally, the effects of the geometric characteristics on the thermal stress in the PIP system are analyzed.

Heat Transfer Analysis of Jet Impingement Cooling on a Simulated Ceramic Matrix Composite Surface

2017 ◽  
Author(s):  
Karthik Krishna ◽  
Mark Ricklick
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Matrix Composite ◽  
Ceramic Matrix Composite ◽  
Jet Impingement ◽  
Ceramic Matrix ◽  
Heat Transfer Analysis ◽  
Test Surface ◽  
Composite Surface ◽  
The Impact

Ceramic Matrix Composite is a woven material characterized by a significant level of surface waviness of 35–60μm and surface roughness of 5–6μm. To be implemented in a future gas turbine engine they will be cooled traditionally to increase power and efficiency. To analyze the CMC surface effects on heat transfer rate, an impinging circular jet on a simulated CMC surface is studied experimentally and the CMC surface is represented by a high resolution CNC machined surface. The test parameters are jet to plate distance of 7 jet diameters, oblique impingement angles of 45° and 90° and Reynolds numbers of 11,000 to 35,000. The test surface is broken down into constant temperature segments, and individual segment Nusselt number is determined and plotted for the various impingement cases studied. Area-Averaged results show negligible changes in average Nusselt number as compared to the hydrodynamically smooth surface. The impact of the CMC surface feature is negligible compared to the uncertainty in heat transfer coefficient, and therefore traditional design tools can be utilized.

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 Analysis of transient mixed convection in a horizontal channel partially heated from below

2021 ◽  
Vol 4 (8(112)) ◽  
pp. 16-22
Author(s):  
Mahmoud A. Mashkour
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Source ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Stokes Equations ◽  
Heat Convection ◽  
Horizontal Channel ◽  
Outlet Temperature

The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nuav) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (NuI) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

Slip Gas Flow and Heat Transfer in Confined Porous Media With Different Shape Cylinders

2021 ◽  
Author(s):  
Ammar Tariq ◽  
Zhenyu Liu
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Gas Flow ◽  
Velocity Slip ◽  
Heat Transfer Analysis ◽  
Variable Boundary ◽  
Flow And Heat Transfer ◽  
Multiple Relaxation Time ◽  
Permeability Increase ◽  
Boltzmann Method

Abstract With the recent advances in micro devices, an accurate gas flow and heat transfer analysis become more relevant considering the slip effect. A micro-scale, multiple-relaxation-time (MRT) lattice Boltzmann method with double distribution function approach is used to simulate flow and heat transfer through circular- and diamond-shaped cylinders at the porescale level. The velocity slip and temperature jump are captured at the boundaries using a non-equilibrium extrapolation scheme with the counter-extrapolation method. A pore-scale domain of micro-cylinders comprised of circle and diamond shape are studied. It is found that the permeability increases linearly with an increase in Knudsen number for both circular- and diamond-shaped cylinders. However, the permeability increase for circular obstacle is larger than that of the diamond one. A larger surface area for diamond cylinder will offer more resistance to flow, hence resulting in lower values. For heat transfer, the Nusselt number shows an increase with increasing Reynolds number, however, it decreases with the increase in porosity. Nusselt number values are found to be higher for a circular obstacle. A variable boundary gradient for circular obstacle could be a possible explanation for this difference.

Numerical Thermal Analysis of a Hot Non-circular Rotating Cylinder in the Presence of a Magnetic Field

2021 ◽  
Author(s):  
Hojjat Khozeymeh-Nezhad ◽  
Yaser Basati ◽  
Hamid Niazmand
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Transfer Rate ◽  
Elliptic Cylinder ◽  
Optimal Location ◽  
Elliptical Cylinder ◽  
Square Enclosure ◽  
Cylinder Rotation

Abstract In the present paper for the first time, a Lattice Boltzmann Simulation is performed to analyze the simultaneous effects of a hot rotating elliptic cylinder and the magnetic field on the mixed convection flow in a square enclosure. Complicated flow patterns and isotherms plots are found and analyzed in the concentric annulus between the internal elliptic cylinder and the outer square enclosure. Results indicate that increasing the Reynolds number, instantaneous averaged Nusselt number of the enclosure and its oscillation amplitude increase, while decrease with increasing the Hartmann number especially at its lower values. Furthermore, response surface method is adopted to find the optimal location of the elliptic cylinder. Response surface optimization results reveal that the average Nusselt number shows a decreasing-increasing trend with increasing both non-dimensional parameters of cylinder center (Xc,Yc) Finally, the optimal location of the elliptic cylinder for the maximum heat transfer rate is obtained as Xc=0.65 and Yc=0.35. Moreover, a comparative study is performed to evaluate the heat transfer effects of the elliptical cylinder rotation as compared to circular cylinder. It was found that the elliptical cylinder rotation has a significant effect on the heat transfer enhancement, especially at high values of Re and Ha. As an example, the heat transfer rate for the elliptical cylinder at Re=200 is increased by 13 % and 34% as compared to the circular cylinder at Ha=50 and 100, respectively.

Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Rectangular Channels

1987 ◽  
Vol 109 (4) ◽  
pp. 936-942 ◽  
Author(s):  
G. J. Hwang ◽  
F. C. Chou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Numerical Study ◽  
Fully Developed Flow ◽  
Rectangular Channels ◽  
Laminar Convection

This paper presents a numerical study of the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal rectangular channels with uniform heat input axially, In addition to the Prandtl number, the Grashof number Gr+, and the aspect ratio γ, a parameter Kp indicating the significance of wall conduction plays an important role in heat transfer. A finite-difference method utilizing a power-law scheme is employed to solve the system of governing partial differential equations coupled with the equation for wall conduction. The numerical solution covers the parameters: Pr = 7.2 and 0.73, γ = 0.5, 1, and 2, Kp = 10−4–104, and Gr+ = 0–1.37×105. The flow patterns and isotherms, the wall temperature distribution, the friction factor, and the Nusselt number are presented. The results show a significant effect of the conduction parameter Kp.

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