Optimal Conditions of Natural and Mixed Convection in a Vented Rectangular Cavity with a Sinusoidal Heated Wall Inside with a Heated Solid Block (original) (raw)
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Finite element method is used to solve two-dimensional governing mass, momentum and energy equations for steady state, mixed convection problem inside a vented square cavity. The cavity consists of adiabatic left, top and bottom walls and heated right vertical wall; but it also contains a heat conducting horizontal square block located somewhere inside the cavity. Forced flow conditions are imposed by providing an inlet at the bottom of the left wall and an exit at the top of the right wall, through which the working fluid escape out of the cavity. The aim of the study is to describe the effect of such block on the flow and thermal fields. The investigations are conducted for various values of geometric size, location and thermal conductivity of the block under constant Reynolds and Prandtl numbers. Various results such as the streamlines, isotherms, heat transfer rates in terms of the average Nusselt number, average fluid temperature in the cavity and the temperature at the center of solid block are presented for different parameters. It is observed that the block size and location have significant effect on both the flow and thermal fields but the solid-fluid thermal conductivity ratio has insignificant effect on the flow field. The results also indicate that the average Nusselt number at the heated surface, the average temperature of the fluid inside the cavity and the temperature at the center of solid block are strongly dependent on the configurations of the system studied under different geometrical and physical conditions.
International Journal of Engineering Science, 2005
A penalty finite element analysis with bi-quadratic rectangular elements is performed to investigate the influence of uniform and non-uniform heating of wall(s) on natural convection flows in a square cavity. In the present investigation, one vertical wall and the bottom wall are uniformly and non-uniformly heated while the other vertical wall is maintained at constant cold temperature and the top wall is well insulated. Parametric study for a wide range of Rayleigh number (Ra), 10 3 6 Ra 6 10 6 and Prandtl number (Pr), 0.2 6 Pr 6 100 shows consistent performance of the present numerical approach to obtain the solutions as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented in terms of local Nusselt number.
Mixed Convection in a Vented Cavity with Heat Conducting Square Block
We present a numerical study of steady laminar mixed convection flow in a two dimensional vented cavity containing a heat conducting square solid block on its center. The flow in the cavity is induced by the combined shear force and buoyancy force resulting from the motion through air-stream at the inlet and heating of the right wall of the cavity. Parametric studies for the effects of governing parameters on the fluid flow and heat transfer inside the cavity are carried out numerically. Numerical computations are performed by a finite element scheme based on the Galerkin method of weighted residuals. The flow phenomena are discussed for a range of governing parameters namely Richardson and Reynolds numbers. The numerical results indicate the strong influence of the above parameters on the flow structure and heat transfer characteristics inside the vented cavity.
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.
2012
This paper reports a numerical study of flow behaviors and natural convection heat transfer characteristics in an inclined open-ended square cavity filled with air. The cavity is formed by adiabatic top and bottom walls and partially heated vertical wall facing the opening. Governing equations in vorticity-stream function form are discretized via finite-difference method and are solved numerically by iterative successive under relaxation (SUR) technique. A computer program to solve mathematical model has been developed and written as a code for MATLAB software. Results in the form of streamlines, isotherms, and average Nusselt number, are obtained for a wide range of Rayleigh numbers 10 3-10 6 with Prandtl number 0.71 (air) , inclination angles measured from the horizontal direction 0º-60º , dimensionless lengths of the active part 0.4-1 ,and different locations of the thermally active part at the vertical wall. The Results show that heat transfer rate is high when the length of the...
Purpose – The purpose of this paper is to optimize the heat transfer rate in square cavity by attaching fin at the bottom wall. Design/methodology/approach – The problem is formulated and solved using finite element method. Accuracy of the method is validated by comparisons with previously published work. Findings – It was found that attaching fin reduces heat transfer rate in the cavity. Originality/value – Although the problem is not very original it is important in that many applications have heating on adjacent walls.
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.
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.
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.
Applied Mathematical Modelling
A numerical study has been executed to analyze the effects of Reynolds and Prandtl number on mixed convective flow and heat transfer characteristics inside a ventilated cavity in presence of a heat-generating solid circular obstacle placed at the center. The inlet opening is at the bottom of the left wall, while the outlet one is at the top of the right wall and all the walls of the cavity are considered to be adiabatic. Galerkin weighted residual finite element method is used to solve the governing equations of mass, momentum and energy. Results are presented in terms of streamlines, isotherms, the average Nusselt number, the Drag force and the average fluid temperature in the cavity for different combinations of controlling parameters namely, Reynolds number, Prandtl number and Richardson number. The results indicate that the flow and thermal fields as well as the heat transfer rate, the Drag force and the average fluid temperature in the cavity depend significantly on the mentioned parameters.