A numerical study of three-dimensional laminar mixed convection past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective flow over a three-dimensional cavity that lies at the bottom of a horizontal channel. The vertical walls of the cavity are isothermal and all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar and incompressible. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall over a wide range of the Grashof number (10³–10⁶) and two Reynolds numbers Re = 100 and 1000. The computed thermal and flow fields are displayed and discussed in terms of the velocity fields, streamlines, the temperature distribution and the averaged Nusselt number at the heated and cooled walls. It is found that the flow becomes stable at moderate Grashof number and exhibit a three-dimensional structure, while for both high Reynolds and Grashof numbers the mixed convection effects come into play, push the recirculating zone further upstream and the flow becomes unsteady with Kelvin–Helmholtz instabilities at the shear layer.     

Numerical simulation of double-diffusive mixed convective flow in rectangular enclosure with insulated moving lid

The present study is concerned with the mixed convection in a rectangular lid-driven cavity under the combined buoyancy effects of thermal and mass diffusion. Double-diffusive convective flow in a rectangular enclosure with moving upper surface is studied numerically. Both upper and lower surfaces are being insulated and impermeable. Constant different temperatures and concentration are imposed along the vertical walls of the enclosure, steady state laminar regime is considered. The transport equations for continuity, momentum, energy and spices transfer are solved. The numerical results are reported for the effect of Richardson number, Lewis number, and buoyancy ratio on the iso-contours of stream line, temperature, and concentration. In addition, the predicted results for both local and average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for 0.1 ≤ Le ≤ 50 and Prandtl number Pr = 0.7. Through out the study the Grashof number and aspect ratio are kept constant at 10⁴ and 2 respectively and ?10 ≤ N ≤ 10, while Richardson number has been varied from 0.01 to 10 to simulate forced convection dominated flow, mixed convection and natural convection dominated flow.     

Effect of Nanoparticles on the Hysteresis Loop in Mixed Convection within a Two-Sided Lid-Driven Inclined Cavity Filled with a Nanofluid

The present work deals with numerical modeling of mixed convection flow in a two-sided lid driven inclined square enclosure filled with water-Al₂O₃ nanofluid. The limiting cases of a cavity heated from below and cooled from above and the one differentially heated are recovered respectively for inclination angles 0° and 90°. The moving walls of the cavity are pulled in opposite directions with the same velocity and maintained at constant but different temperatures while the remaining walls are kept insulated. The numerical resolution of the studied problem is based on the lattice Boltzmann method. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and enclosure inclination angle on fluid flow and heat transfer characteristics. The governing parameters of this problem are the Richardson number (varied from 0.1 to 10⁶), the nanoparticles volume fraction (varied from 0 to 0.04) and the inclination angle (varied from 0° to 180°). The critical conditions leading to the transition from monocellular flow to multicellular flow and vice versa are determined. In the common ranges of Richardson number and inclination angle where both monocellular and tri-cellular patterns coexist, the heat transfer is seen to be strongly reduced by the latter.     

Comparison of Mixed Convection in a Square Cavity with an Oscillating versus a Constant Velocity Wall

This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.     

Second law analysis in a three dimensional lid-driven cavity

Three dimensional analyses of laminar mixed convection and entropy generation in a cubic lid-driven cavity have been performed numerically. Left side of cavity moves in + y (Case I) or −y (Case II) direction. The cavity is heated from left side and cooled from right while other surfaces are adiabatic. Richardson number is the main parameter which changes from 0.01 to 100. Prandtl number is fixed at Pr = 0.71. Results are presented by isotherms, local and mean Nusselt number, entropy generation due to heat transfer and fluid friction, velocity vectors and Bejan number. Total entropy generation contours are also presented. It is found that direction of lid is an effective parameter on both entropy generation and heat and fluid flow for low values of Richardson number but it becomes insignificant at high Richardson number.     

Mixed convective heat transfer enhancement in a ventilated cavity by flow modulation via rotating plate

The present study numerically explores the mixed convection phenomena in a differentially heated ventilated square cavity with active flow modulation via a rotating plate. Forced convection flow in the cavity is attained by maintaining external fluid flow through an opening at the bottom of the left cavity wall while leaving it through another opening at the right cavity wall. A counter-clockwise rotating plate at the center of the cavity acts as an active flow modulator. Moving mesh approach is used for the rotation of the plate and the numerical solution is achieved using arbitrary Lagrangian-Eulerian finite element formulation with a quadrilateral discretization scheme. Transient parametric simulations have been performed for various frequency of the rotating plate for a fixed Reynolds number (Re) of 100 based on maximum inlet flow velocity while the Richardson number (Ri) is maintained at unity. Heat transfer performance has been evaluated in terms of spatially averaged Nusselt number and time-averaged Nusselt number along the heated wall. Power spectrum analysis in the frequency domain obtained from the fast Fourier transform analysis indicates that thermal frequency and plate frequency start to deviate from each other at higher values of velocity ratio (>4).     

Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity

The current numerical study is conducted to analyze mixed convection heat transfer in lid-driven cavity with a sinusoidal wavy bottom surface. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The implications of Richardson number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number increases with an increase in both the amplitude of the wavy surface and Reynolds number. Furthermore, optimum heat transfer is achieved when the wavy surface is designated with two undulations while subjected to low Richardson numbers.     

Evolution to chaotic mixed convection in a multiple ventilated cavity

The characteristics of transition from laminar to chaotic mixed convection in a two-dimensional multiple ventilated cavity is analyzed in this paper. The horizontal air streams enter the cavity from the two inflow-openings near the top of both vertical walls, while the outflow openings are near the bottoms of both vertical walls. The results obtained for a range of the Richardson number, Ri, from 0.01 to 5 at Pr = 0.71, the Reynolds number, Re, from 1000 to 2500 and the inlet flow angle, φ, based on 0°, 20°, 45° and 70°. The results show that, as Ri increases, the solution may exhibit a change from steady-state to periodic oscillation, and then to non-periodic oscillatory state. However, the flow inside the cavity becomes steady-state again as Richardson number increases further. The results also show that the effect of inlet flow angle on the oscillations of mixed convection is evident, the configuration with φ = 0° is the most unstable among the four values of φ. The non-periodic oscillatory solution at Re = 2500 is studied by means of phase portraits, correlation dimension, Kolmogorov entropy and Lyapunov exponents to detect chaos. The phase portraits show the evolution of the attractor from a stable fixed point to a limited cycle to chaos, and finally, to a stable fixed point again, and the correlation dimension, Kolmogorov entropy and the largest Lyapunov numbers all show that the behavior of mixed convection in this dynamical system lies on a low-dimensional chaotic attractor according to the non-periodic oscillatory solution.     

Combined convection flow in triangular wavy chamber filled with water–CuO nanofluid: Effect of viscosity models

This work is focused on the numerical modeling of steady laminar combined convection flow in a vertical triangular wavy enclosure filled with water–CuO nanofluid. The left and right vertical walls of the cavity take the form of a triangular wavy pattern. The bottom and top horizontal walls are mechanically driven. The lower and upper surfaces move to the right and left direction at the same constant speed respectively. They maintain constant temperature lower than both vertical walls. Two different nanofluid models namely, the Brinkman model and the Pak and Cho correlation are employed. The developed equations are given in terms of the Navier Stokes and the energy equation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by the Galerkin's finite-element method. Comparisons with published work are performed and found to be in good agreement. A parametric study is conducted and a selective set of graphical results is presented. The effects of the Reynolds number, Richardson number and the nanoparticles volume fraction on the flow and heat transfer characteristics in the cavity are displayed to compare the predictions obtained by the two different nanofluid models. Heat transfer enhancement can be obtained significantly due to the presence of nanoparticles. The rate of heat transfer is accentuated moderately by falling the Richardson number and rising the Reynolds number as well as the solid volume fraction.     

Heat and fluid flow characteristics inside differentially heated square enclosures with single and multiple sliding walls

Fluid flow and heat transfer characteristics of differentially heated lid driven cavities are numerically modeled and analyzed in the present study. One‐, two‐, and four‐sided lid driven cavity configurations are considered with the vertical walls being maintained at different temperatures and the horizontal walls being thermally insulated. Eight different cavity configurations are considered depending on the direction of wall motion. The Prandtl number Pr is taken to be 0.7, the Grashof number is taken to be 10⁴, while two values for the Richardson number Ri are considered, 0.1 and 10. It is found that both the Richardson number and the cavity configuration affect the heat and fluid flow characteristics in the cavity. It is concluded that for Ri=0.1, a four‐sided driven cavity configuration with all walls rotating in the same direction would triple the value of the average Nusselt number at the cold wall when compared to a one‐sided driven cavity configuration. However, for Ri=10, the cavity configuration has minimal effect and all eight cases result in an average Nusselt number value at the cold wall ranging between 1.3 and 1.9. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/htj.20264     

Mixed Convection Heat Transfer Analysis in an Enclosure with Two Hot Cylinders: A Lattice Boltzmann Approach

The aim of this work is to study laminar mixed convection heat transfer characteristics within an obstructed enclosure by using the Lattice Boltzmann method. Flow is driven by a top cold lid while other walls are stationary and adiabatic. Hot cylinders are located at different places inside the cavity to explore the best arrangement. Comparison of streamlines, isotherms, average Nusselt number are presented to evaluate the influence of Richardson number and location of cylinders on flow field and heat transfer. Results indicate that heat transfer decreases with a rise of Richardson number for all considered arrays of cylinders. Among them, horizontally‐located cylinders at the top of the cavity have the greatest heat transfer at all Richardson numbers. Horizontally located cylinders at the bottom of the cavity have the lowest heat transfer at Richardson numbers of 0.1 and 1 while the lowest heat transfer rate belongs to cross diagonal located cylinders at a Richardson number of 10.     

A numerical study of mixed convection in a two-sided lid-driven tall cavity containing a heated triangular block for non-Newtonian power-law fluids

The study of hydrodynamics and thermal characteristics inside a lid-driven cavity has been one of the most captivating problems in computational fluid dynamics. In this numerical work, the mixed convection phenomenon inside a two-dimensional, tall lid-driven cavity with top and bottom lids moving in opposite directions, +x and –x, respectively, has been explored for non-Newtonian power-law fluids. The cavity contains a uniformly heated equilateral triangular obstacle at its geometric center.  Numerical experimentation is performed for a range of flow governing parameters, such as aspect ratio (0.25, 0.5, and 0.75), Prandtl number (1, 50, and 100) Richardson number (0.1, 1, and 10), power-law index (0.6–1.4) and Grashof number of 10⁴. The physical perceptions of the cavity are explained by using streamline and isotherm contours. The fluid movement is limited adjacent to the moving wall concerning the Richardson number at the lower Prandtl number. With a rise in the aspect ratio of the cavity, the flow-pattern becomes more dispersed inside the cavity. Heat transfer enhancement is observed at a lower aspect ratio equal to 0.25.     

Control of mixed convection in lid-driven enclosures using conductive triangular fins

Control of mixed convection (combined forced and natural convection) in a lid-driven square cavity is performed using a short triangular conductive fin. A numerical technique is used to simulate the flow and temperature fields. The vertical walls of the cavity are differentially heated. Both the top lid and the bottom wall are adiabatic. The fin is located on one of the motionless walls of the cavity. Three different cases have been studied based on the location of the fin. In this context, Cases I, II and III refer to the fin on the left, bottom and right walls, respectively. Results are presented for +x and −x directions of the top lid in horizontal axis and different Richardson numbers as Ri = 0.1, 1.0 and 10.0. It is observed that the triangular fin is a good control parameter for heat transfer, temperature distribution and flow field.     

Fuzzy-based estimation of mixed convection heat transfer in a square cavity in the presence of an adiabatic inclined fin

In this study, heat transfer from a square cavity in the presence of a thin inclined adiabatic fin is estimated using inputs–outputs generated from a CFD code with a fuzzy based identification procedure. The Reynolds number based on cavity length is 300 and the Richardson number is varied between 1 and 30. The top and bottom walls of the cavity are kept at constant temperature while the vertical walls are assumed to be adiabatic. The fin height, fin inclination angle, and Richardson number are considered as the input and the spatial averaged Nusselt number is taken as the output for the fuzzy model. Two data sets are used. One data set which contains 45 cases is used for estimation and another data set which contains 10 cases (not used in estimation) is used for validation purposes. The predictions using fuzzy model compare well with the CFD computations.     

Effect of moving wall direction on mixed convection in an inclined lid-driven square cavity with sinusoidal heating

ABSTRACT

The aim of the present study is to investigate the effect of the moving wall’s direction on mixed convective flow and heat transfer in an inclined lid-driven square cavity. Sinusoidal heating is applied on the left wall while the right wall is cooled at a constant temperature. The bottom and top walls are taken to be adiabatic. The results are presented graphically in the form of streamlines, isotherms, velocity profiles, and Nusselt numbers to understand the influence of the different directions of the moving wall, Richardson number, and cavity inclination. It is observed that the flow field and temperature distribution in the cavity are affected by the moving wall’s direction. It is also observed that the heat transfer is more pronounced at low Richardson number when the wall is moving to the left.     

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

Mixed convection in a lid-driven triangular enclosure filled with nanofluids

This paper presents the results of a numerical study on the mixed convection in a lid-driven triangular enclosure filled with a water–Al₂O₃ nanofluid. A comparison study between two different scenarios of upward and downward left sliding walls is presented. The effects of parameters such as Richardson number, solid volume fraction and the direction of the sliding wall motion on the flow and temperature fields as well as the heat transfer rate are examined. The results show that the addition of Al₂O₃ nanoparticles enhances the heat transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the downward sliding wall motion results in a stronger flow circulation within the enclosure and hence, a higher heat transfer rate.     

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.     

Numerical Simulation of Steady Mixed Convection Around Two Heated Circular Cylinders in a Square Enclosure

In this paper, a numerical study has been carried out to investigate the steady-state mixed convection around two heated horizontal cylinders in a square two-dimensional enclosure. The cylinders are located at the middle of the enclosure height and the walls of the cavity are adiabatic. Streamlines and isotherms are produced and the effects of cylinder diameter, Reynolds number, and Richardson number on the heat transfer characteristics are numerically analyzed. The average Nusselt number over the surface of cylinders and average nondimensional temperature in the enclosure are also presented. The results show that both heat transfer rates from the heated cylinders and the dimensionless fluid temperature in the enclosure increase with increasing Richardson number and cylinder diameter. However, the trend of average Nusselt number and nondimensional temperature variation is completely opposite when Reynolds number increases. In addition, by increasing the cylinders diameter and Richardson number, the left cylinder is less affected by the inlet flow than right one.