Free Convection in a square Cavity with thermal Boundary Conditions (original) (raw)
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IJERT-Numerical Investigation of Natural Convection Heat Transfer in a Square Cavity
International Journal of Engineering Research and Technology (IJERT), 2015
https://www.ijert.org/numerical-investigation-of-natural-convection-heat-transfer-in-a-square-cavity https://www.ijert.org/research/numerical-investigation-of-natural-convection-heat-transfer-in-a-square-cavity-IJERTV4IS070206.pdf Natural convection heat transfer in enclosures find many applications such as heating and cooling of building spaces, solar energy utilization, thermal energy storage, cooling of electrical and electronic components etc. In the present study, Numerical Investigation is conducted in a square cavity with one vertical wall maintained at a high temperature and with the opposing vertical wall at a low temperature. The influence of Grashof numbers ranging from 20000 to 200000 for Prandtl number 0.7 (air) is studied. The governing vorticity and energy equations are solved by finite difference methods including Alternating Direction Implicit (ADI) and Successive Over Relaxation (SOR) techniques with C coding. Steady state isothermal lines and streamlines are obtained for all the Grashof numbers considered. In addition, the average Nusselt number, over the hot wall for the range of Grashof numbers is calculated. The contours of streamlines and isothermal lines are presented for all the parameters investigated. Changes in the streamline and isothermal line patterns are observed with the change in Grashof numbers. The results obtained in this study are useful for the design of devices with enclosures subjected to high temperature differences.
Effects of thermal boundary conditions on natural convection flows within a square cavity
International Journal of Heat and Mass Transfer, 2006
A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 5 and Prandtl number Pr, 0.7 6 Pr 6 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.
“Effects Of Heat Source Location On Natural Convection In A Square Cavity”
2012
Natural convection in a closed square cavity has occupied the centre stage in many fundamental heat transfer analysis which is of prime importance in certain technological applications. Infact buoyancy driven convection in a sealed cavity with differentially heated isothermal walls is a prototype of many industrial applications such as energy efficient buildings, operation and safety of nuclear reactor and convective heat transfer associated with electronic cooling equipment. The internal flow problems are considerably more complex than external ones. In electronic systems normally the heat generating bodies exist within the cavity. The effect of the presence of heat source on the mass flow rate and heat transfer is considered in present case for investigation. In order to verify the methodology of using fluent, the commercial software, the available problem in the literature is verified for parametric study on the location of heat source and its strength is considered for study. In present work, the given source is split into two parts and its effect on the flow rate and heat transfer is studied. An attempt is made for the best location of the heat source in the cavity so that it can be used in the electronic equipment generating heat.
Heatline analysis on thermal management with conjugate natural convection in a square cavity
Conjugate natural convection finds various thermal applications in chemical industries, where the heat transfer is controlled by the presence of solid walls such as heat exchanger, nuclear reactors, fin type cooling and solar storage systems. Heat flow distribution within square cavity enclosed by vertical conducting walls of definite thickness ðt 1 and t 2 Þ is analyzed for various fluids (Pr) in this study based on the location of the wall thickness [left wall (case 1)/ right wall (case 2)/ both side walls (case 3)] and conductivity ratios between solid and fluid regions (K). At Ra ¼ 10 5 , circular heatlines are observed near core of the cavity at K¼ 0.
Journal of Intelligent Mechanics and Automation (ISSN Online: 2771-9960), 2022
The aim of the present study is to analyze heat transfer characteristics for natural convection flows in a square enclosure with wavy right wall filled with air(Pr=0.71) having uniform heating on bottom wall and adjacent cold walls with a adiabatic square block inside. This geometry and the following results can be used for analysis in heat management of building architecture, solar collection devices, having walls with surface roughness. The design/methodology/approach of these numerical solutions is the finite element analysis by a commercial software COMSOL Multiphysics version 5.6. The choice of consideration of sinusoidal heating gives a better analysis of heat transfer analysis in this square geometry with wavy wall and with adiabatic block inside has not been investigated by numerical or experimental basis before and therefore, it is this motivation that results in this numerical investigation.
Simulation of Natural Convection in a Square Cavity with Partially Heated and Cooled Vertical Walls
Proceeding of 5th Thermal and Fluids Engineering Conference (TFEC)
Natural convection driven by temperature differences between partially heated and cooled vertical walls in a square cavity is studied numerically. Steady or unsteady cellular flow structures and temperature patterns are illustrated along with the evolution of heat transfer rates in terms of Nusselt number. The cavity is filled with fluids of various Prandtl number, including .024 (liquid metal), .71 (air), 6 (water), and 450 (silicon oil). The effect of Prandtl and Rayleigh numbers on the flow regime and heat transfer is established along with two different thermal boundary conditions.
IJERT-Effects Of Heat Source Location On Natural Convection In A Square Cavity
International Journal of Engineering Research and Technology (IJERT), 2014
https://www.ijert.org/effects-of-heat-source-location-on-natural-convection-in-a-square-cavity https://www.ijert.org/research/effects-of-heat-source-location-on-natural-convection-in-a-square-cavity-IJERTV1IS6332.pdf Natural convection in a closed square cavity has occupied the centre stage in many fundamental heat transfer analysis which is of prime importance in certain technological applications. Infact buoyancy driven convection in a sealed cavity with differentially heated isothermal walls is a prototype of many industrial applications such as energy efficient buildings, operation and safety of nuclear reactor and convective heat transfer associated with electronic cooling equipment. The internal flow problems are considerably more complex than external ones. In electronic systems normally the heat generating bodies exist within the cavity. The effect of the presence of heat source on the mass flow rate and heat transfer is considered in present case for investigation. In order to verify the methodology of using fluent, the commercial software, the available problem in the literature is verified for parametric study on the location of heat source and its strength is considered for study. In present work, the given source is split into two parts and its effect on the flow rate and heat transfer is studied. An attempt is made for the best location of the heat source in the cavity so that it can be used in the electronic equipment generating heat. Nomenclatures AR = Aspect ratios, H/L, Gr = Grashoff Number g = Acceleration due to gravity (m/s 2), Ra = Rayleigh number H = Height of the cavity (m), Pr = Prandtl number h = Convective heat transfer coefficient (W/m 2 K) k = Thermal conductivity (W/m.K), Nu = Nusselt number L = Length of the cavity (m), T = Temperature (K) q = Heat flux (W/m 2) Greek Symbols α = Thermal diffusivity (m 2 /s) β = Volume expansion coefficient (K-1) ρ = Fluid Density (kg/m 3) ν = Kinematic viscosity (m 2 /s) θ = Dimensionless temperature Subscript b = Bottom wall s = Side wall
Study of Natural Convection Heat Transfer in a Closed Wall with Thermal Conditions
Lecture Notes in Mechanical Engineering, 2021
In this study, conjugate natural convection in a square cavity filled with fluids under steady-state condition is numerically investigated with the finite element method. The left side wall is considered as hot wall, and the right wall is considered to be cold. The top and bottom walls are assumed to be adiabatic. Different boundary conditions are introduced on the walls, and a thorough investigation is done in the present study. Numerical simulations have been done for different parameters of Grashof number (10 3-10 7) and Prandtl number. The graph of Nusselt number versus Grashof number and Nusselt number versus Prandtl number is plotted. It is observed that the buoyant forces developed in the cavity due to thermally induced density gradients vary as the value of acceleration due to gravity (g) differs, due to the change in temperature and stream function. Keywords Conjugate natural convection heat transfer Á Square cavity Nomenclature AR aspect ratio (H/L) g acceleration due to gravity (m s −2) H height of square cavity (m) K thermal conductivity (W m −1 K −1) L length of the square cavity (m)
Journal of Mechanical Science and Technology, 2015
Finite element method was used to investigate the effects of heater location and heater size on the natural convection heat transfer in a 2D square cavity heated partially or fully from below and cooled from above. Rayleigh number (5Í10 2 ≤ Ra ≤ 5Í10 5), heater size (0.1 ≤ D/L ≤ 1.0), and heater location (0.1 ≤ x h /L ≤ 0.5) were considered. Numerical results indicated that the average Nusselt number (Nu m) increases as the heater size decreases. In addition, when x h /L is less than 0.4, Nu m increases as x h /L increases, and Nu m decreases again for a larger value of x h /L. However, this trend changes when Ra is less than 10 4 , suggesting that Nu m attains its maximum value at the region close to the bottom surface center. This study aims to gain insight into the behaviors of natural convection in order to potentially improve internal natural convection heat transfer.
Journal of Naval Architecture and Marine Engineering, 2011
In this study natural convection flow in a square cavity with heat generating fluid and a finite size heater on the vertical wall have been investigated numerically. To change the heat transfer in the cavity, a heater is placed at different locations on the right vertical wall of the cavity, while the left wall is considered to be cold. In addition, the top and bottom horizontal walls are considered to be adiabatic and the cavity is assumed to be filled with a Bousinessq fluid having a Prandtl number of 0.72. The governing mass, momentum and energy equations along with boundary conditions are expressed in a normalized primitive variables formulation. Finite Element Method is used in solution of the normalized governing equations. The parameters leading the problem are the Rayleigh number, location of the heater, length of the heater and heat generation. To observe the effects of the mentioned parameters on natural convection in the cavity, we considered various values of heater locations, heater length and heat generation parameter for different values of Ra varying in the range 102 to 105. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the mentioned parameters. The results showed that the flow and thermal fields through streamlines and isotherms as well as the rate of heat transfer from the heated wall in terms of Nusselt number are strongly dependent on the length and locations of the heater as well as heat generating parameter.