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.     

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.     

MHD mixed convection of Cu–water nanofluid in a two-sided lid-driven porous cavity with a partial slip

ABSTRACT

A numerical simulation of magneto-hydrodynamic mixed convection flow and heat transfer of Cu–water nanofluid in a square cavity filled with a Darcian porous medium with a partial slip is numerically investigated. The left and right walls of the cavity are moving up with a constant speed in vertical direction, and the partial slip effect is considered along these walls. The top and bottom walls of the cavity are assumed to be adiabatic. The right vertical wall of the cavity is assumed to be kept at a lower temperature, while the left vertical wall is kept at a higher temperature. The developed equations of the mathematical model are nondimensionalized and then solved numerically subject to appropriate boundary conditions by the finite-volume method. A parametric study is performed and a set of graphical results is presented and discussed to demonstrate interesting features of the solution.     

HYDROMAGNETIC COMBINED CONVECTION FLOW IN A VERTICAL LID-DRIVEN CAVITY WITH INTERNAL HEAT GENERATION OR ABSORPTION

The problem of unsteady, laminar, combined forced-free convection flow in a square cavity in the presence of internal heat generation or absorption and a magnetic field is formulated. Both the top and bottom horizontal walls of the cavity are insulated while the left and right vertical walls are kept at constant and different temperatures. The left vertical wall is moving in its own plane at a constant speed while all other walls are fixed. A uniform magnetic field is applied in the horizontal direction normal to the moving wall. A temperature-dependent heat source or sink is assumed to exist within the cavity. The governing equations and conditions are solved numerically by the finite-volume approach along with the alternating direct implicit (ADI) procedure. Two cases of thermal boundary conditions corresponding to aiding and opposing flows are considered. Comparisons with previously published work are performed and the results are found to be in excellent agreement. A parametric study is conducted and a set of representative graphical results is presented and discussed to illustrate the influence of the physical parameters on the solution.     

Laminar Mixed-Convection Heat Transfer in a Lid-Driven Cavity with Modified Heated Wall

In this numerical study, steady laminar mixed-convection heat transfer in a two-dimensional square lid-driven cavity with a modified heated wall is investigated over a range of Richardson numbers, including 0.01, 1, and 10. The heated bottom wall of the cavity is characterized by rectangular, triangular, and sinusoidal wave shapes. The cooled top wall of the cavity is sliding with constant velocity, while the vertical walls are kept stationary and adiabatic. The governing equations are solved using a finite-volume technique. The results are presented in the form of streamlines, isotherms, and Nusselt number plots. The effects of the number of undulations and the amplitude on the flow field and heat transfer are also investigated. The predicted results demonstrate that the heat transfer enhancement is generally observed with the modification of the heated wall, while the improvement is found to be more profound for the case of rectangular wave and at low Richardson number.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

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.     

Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall

Double — diffusive natural convection in fluid saturated porous medium has been investigated using a generalised porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases.     

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.     

MULTIGRID COMPUTATION OF NATURAL CONVECTION IN ENCLOSURES WITH A CONDUCTIVE BAFFLE

Conjugate heat transfer has been investigated in a two-dimensional square enclosure with a conducting vertical baffle of finite thickness and varying height. The horizontal end walls are assumed to be adiabatic, and the vertical watts are at constant but different temperatures. Calculations are made by a staggered, finite volume multigrid procedure. The performance of the multigrid method in accelerating the convergence rate is remarkable by comparison with the usual iterative method. The influence of inserting a baffle into the buoyancy-driven square cavity on the heat transfer, as well as on the temperature distribution and velocity field, has been obtained for various Rayleigh numbers Ra, solid /fluid conductivity ratio k? dimensionless baffle height H, and baffle location L. Predicted flow patterns and isotherms indicate that the effect of inserting baffles of varying height upon the overall heat transfer and local temperature profiles in the cavity is limited, except when the height of baffle is large (H > 0.5). The effect of conductivity is also found to be marginal. However, both the height and the conductivity become very important when the baffle is located very near the hot wall or cold walls.     

Analysis of Non-Darcy Models for Mixed Convection in a Porous Cavity Using a Multigrid Approach

This article investigates the performance of two models; namely the Brinkman-Forchheimer Darcy model (BFDM) and the Brinkman-extended Darcy model (BDM), in a problem involving mixed convection in a square cavity filled with a porous medium using the multigrid method. The left and right walls, moving in opposite directions, are maintained at different constant temperatures, while the top and bottom walls are thermally insulated. The transport equations were solved numerically by the finite-volume method on a colocated grid arrangement using a quadratic upwind interpolation for convective kinematics (QUICK) scheme. The influence of the key parameters, namely the Darcy number (Da) and Grashof number (Gr) on the flow and heat transfer pattern is examined. Further, the issue of reliability of the results is addressed. The results demonstrate that BDM over-predicts the momentum and heat transfer rates compared with BFDM, which is in conformity with the fact that the additional term present in the BFDM hinders convective effects. The full approximation storage (FAS) multigrid method achieves considerable acceleration of convergence for the present relatively unexplored problem.     

Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids

The behaviour of nanofluids is investigated numerically inside a two-sided lid-driven differentially heated square cavity to gain insight into convective recirculation and flow processes induced by a nanofluid. A model is developed to analyze the behaviour of nanofluids taking into account the solid volume fraction χ. The transport equations are solved numerically with finite volume approach using SIMPLE algorithm. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. The left and the right moving walls are maintained at different constant temperatures while the upper and the bottom walls are thermally insulated. Three case were considered depending on the direction of the moving walls. Governing parameters were 0.01 < Ri < 100 but due to space constraints only the results for 0.1 < Ri < 10 are presented. It is found that both the Richardson number and the direction of the moving walls affect the fluid flow and heat transfer in the cavity. Copper–Water nanofluid is used with Pr = 6.2 and solid volume fraction χ is varied as 0.0%, 8%, 16% and 20%. Detailed results are presented for flow pattern and heat transfer curves.     

Magneto-Convective Transport of Nanofluid in a Vertical Lid-Driven Cavity Including a Heat-Conducting Rotating Circular Cylinder

Numerical simulations are performed for the two-dimensional magneto-convective transport of Cu–H₂O nanofluid in a vertical lid-driven square cavity in the presence of a heat-conducting and rotating circular cylinder. The left wall of the cavity is allowed to translate at a constant velocity in the vertically upward direction. Both left and right walls are maintained at isothermal but different temperatures. The top and bottom walls of the enclosure are thermally insulated. At the central region of the cavity is a heat-conducting circular cylinder which can rotate either clockwise or counterclockwise. A constant horizontal magnetic field of amplitude B₀ is applied perpendicular to the vertical walls. The nanofluid is electrically conducting, while the solid walls are considered electrically insulated. Simulations are performed for various controlling parameters, such as Richardson number (0.01 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), dimensionless rotational speed of the cylinder (Ω = ±1), and nanoparticle concentration (0 ≤ ? ≤ 0.3), while Reynolds number based on lid velocity is fixed at a specific value (Re = 100). The flow and thermal fields are found to be susceptible to changes in the magnetic field and mixed convective strength, as well as nanoparticle concentration. However, the direction of cylinder rotation is observed to have little or no influence quantitatively on global hydrodynamic and thermal parameters.     

Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation

An analysis is presented for the effects of chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of heat generation. The plate moves with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Analytical expressions are computed numerically. Numerical calculations are carried out the purpose of the discussion of the results which are shown on graphs and the effects of the various dimensionless parameters entering into the problem on the velocity, angular velocity, temperature, concentration. Also, the results of the skin-friction coefficient, the couple stress coefficient and the rates of the heat and mass transfers at the wall are prepared with various values of fluid properties and the flow conditions are studied.     

Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition

Numerical simulations of the conduction-combined forced and natural convection (mixed convection) heat transfer and fluid flow have been performed for 2-D lid-driven square enclosure divided by a partition with a finite thickness and finite conductivity. Left vertical wall of enclosure has two different orientations in positive or negative vertical coordinate. Buoyancy forces are taken into account in the system. Horizontal walls are adiabatic while two vertical walls are maintained isothermal temperature but the temperature of the left moving wall is higher than that of the right stationary wall. Thus, heat transfer regime between moving lid and partition is mixed convection. Conduction occurs along the partition. And, pure natural convection is formed between the partition and the right vertical wall. This investigation covers a wide range of Richardson number which is changed from 0.1 to 10, thermal conductivity ratio varies from 0.001 to 10. It is observed that higher heat transfer was formed for higher Richardson number for upward moving wall for all values of thermal conductivity ratio. When forced convection becomes effective, the orientation of moving lid becomes insignificant. Heat transfer is a decreasing function of increasing thermal conductivity ratio for all cases and Richardson numbers.     

Free convection in a wavy cavity filled with a porous medium

The steady-state free convection inside a cavity made of two horizontal straight walls and two vertical bent-wavy walls and filled with a fluid-saturated porous medium is numerically investigated in the present paper. The wavy walls are assumed to follow a profile of cosine curve. The horizontal walls are kept adiabatic, while the bent-wavy walls are isothermal but kept at different temperatures. The Darcy and energy equations (in non-dimensional stream function and temperature formulation) are solved numerically using the Galerkin Finite Element Method (FEM). Flow and heat transfer characteristics (isothermal, streamlines and local and average Nusselt numbers) are investigated for some values of the Rayleigh number, cavity aspect ratio and surface waviness parameter. The present results are compared with those reported in the open literature for a square cavity with straight walls. It was found that these results are in excellent agreement.     

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.     

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     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. 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 importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh 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.     

Jet impingement onto a conical cavity: Effects of annular nozzle outer angle and jet velocity on heat transfer and skin friction

Jet impingement onto a conical cavity results in complicated flow structure in the region of the cavity. Depending on the nozzle geometric configurations and jet velocities, enhancement in the heat transfer rates from the cavity surface is possible. In the present study, annular nozzle and jet impingement onto a conical cavity are considered and heat transfer rates from the cavity surfaces are examined for various jet velocities, two outer angles of the annular nozzle, and two cavity depths. A numerical scheme adopting the control volume approach is used to simulate the flow situation and predict the heat transfer rates. It is found that increasing jet velocity at the nozzle exit modifies the flow structure in the cavity while altering the heat transfer rates and skin friction; in which case, increasing nozzle outer angle and jet velocity enhances the heat transfer rates and skin friction.