Effect of Variable Thermal Conductivity on Buoyant Convection in a Cavity with Internal Heat Generation (original) (raw)
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Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top
Journal of The Institution of Engineers (India): Series C, 2020
The prime objective of the present numerical study is to analyse buoyancy-driven thermal flow behaviour inside an enclosure with the application of nonlinear heating from top surface which is commonly essential in glass industries. A fluid-filled square cavity with sinusoidal heating from top surface, adiabatic bottom wall and constant temperature side walls is considered here. The thermal flow behaviour has been numerically observed with the help of relevant parameters like stream functions, isotherms and Nusselt number. For the present investigation, Rayleigh number (Ra), Prandtl number (Pr) and heating frequency of the wall (x) are varied from 10 3 to 10 6 , 0.7 to 7 and 0.5 to 2, respectively. It has been noticed from the investigation that flow dynamics drastically alter with Ra, x and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by x and Pr. Keywords Free convection Á Buoyancy Á Rayleigh number Á Pr number Á Sinusoidal heating Greek letters a Thermal diffusivity (m 2 s-1) b Volumetric expansion coefficient (K-1) q Kinetic viscosity (m 2 s-1) t Density of fluid (kg m-3) h Dimensionless temperature x Heating frequency of the top wall
Mixed Convection and Heat Transfer Studies in Non-Uniformly Heated Buoyancy Driven Cavity Flow
Open Journal of Fluid Dynamics, 2017
We analyse the mixed convection flow in a cavity flow which is driven by buoyancy generated due to a non-uniformly heated top wall which is moving uniformly. A fourth order accurate finite difference scheme is used in this study and our code is first validated against available data in the literature. The results are obtained for different sets of Reynolds number Re , Prandtl number Pr and Grashof number Gr which are in the ranges 100-3000, 0.0152-10 and 10 2-10 6 respectively. Here Gr is related to the Richardson number according to 2 Ri Gr Re =. While increasing the Richardson number, the growth of upstream secondary eddy (USE) is observed together with a degradation of downstream secondary eddy (DSE). When mixed convection is dominant, the upstream secondary eddy and the downstream secondary eddy merge to form a large recirculation region. When the effect of Pr is studied in the forced convection regime, 1 Ri , the temperature in the central region of the cavity remains nearly a constant. However, in the mixed convection regime, the temperature in cavity undergoes non-monotonic changes. Finally, using the method of divided differences, it is shown that numerical accuracy of the derived numerical scheme used in this work is four.
“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.
NATURAL CONVECTION FLOW IN A SQUARE CAVITY WITH TEMPERATURE DEPENDENT HEAT GENERATION
Unsteady natural convection laminar flows in a square cavity formed by insulated bottom and top walls, uniformly heated left wall and the cooled right wall has been investigated numerically. The governing equations are transformed into non-dimensional form and the resulting partial differential equations are solved applying upwind finite difference method together with Successive Over-Relaxation (SOR) scheme. The effect of the heat generation and the Rayleigh number on streamlines and isotherms as well as on the rate of heat transfer from the heated wall of the cavity are presented.
International Journal of Heat and Mass Transfer, 2011
A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra e = 10 3-10 5 , while the influence of the heat source was evaluated through the relation R = Ra i /Ra e , investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra e whereas these features are absent at higher Ra e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.
Buoyancy convection in a cavity with mutually orthogonal heated plates
Buoyancy driven convection in a square cavity induced by two mutually orthogonal arbitrarily placed heated thin plates is studied numerically under isothermal and isoflux boundary conditions. The flow is assumed to be two-dimensional. The coupled governing equations were solved by the finite difference method using the Alternating Direction Implicit technique and Successive Over Relaxation method. The steady state results are depicted in terms of streamline and isotherm plots. It is found that the resulting convection pattern is stronger for the isothermal boundary condition. A better overall heat transfer can be achieved by placing one of the plates far away from the center of the cavity for isothermal boundary condition and near the center of the cavity for isoflux boundary condition.
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.
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.
Natural convection in an enclosed cavity
Journal of Computational Physics, 1984
We are concerned with the problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated. An application of the dynamic A.D. I. method to obtain nUMerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid.