Natural convection in rectangular enclosures with adiabatic fins attached on the heated wall

The heat transfer by natural convection in vertical and inclined rectangular enclosures with fins attached to the heated wall is numerically studied using the energy and Navier-Stokes equations with the Boussinesq approximation. The range of study covers 10⁴Ra2×10⁵,A=H/L=2.5 to ,B=l/L=0 to 1,C=h/L=0.25 to 2 andPr=0.72. The inclination angle from the vertical was from 0 to 60 degree. The variation of the local Nusselt numberNu _loc along the enclosure height and the average Nusselt numberNu as a function ofRa are computed. Streamlines and isotherms in the enclosure are produced. The results show thatB is an important parameter affecting the heat transfer through the cold wall of the enclosure. The heat transfer is reduced for decreasingC and it passes from a maximum for an inclination angle. The results show that the heat transfer can generally be reduced using appropriate geometrical parameters in comparison with a similar enclosure without fins.Die Wärmeübertragung bei freier Konvektion in vertikalen und geneigten rechtwinkligen Behältern mit Rippen an den beheizten Wänden wird unter Verwendung der Energie- und Navier-Stokes-Gleichungen sowie der Boussinesq-Approximation numerisch untersucht. Der Bereich der Studie liegt bei 10⁴Ra2·10⁵,A=H/L=2,5 bis ,B=l/L=0 bis 1,C=h/L=0,25 bis 2 undPr=0.72. Der Neigungswinkel der Wand liegt zwischen 0 und 60 Grad. Die Veränderung der lokalen Nusselt-Zahl entlang der Höhe der Behälterwände und die mittlere Nusselt-Zahl in Abhängigkeit derRa-Zahl werden berechnet. Strömungslinien und Isothermen werden im Behälter erzeugt. Die Ergebnisse zeigen, daßB ein wichtiger Parameter für die Wärmeübertragung an der nicht beheizten Wand des Behälters ist. Die übertragene Wärmemenge verringert sich mit abnehmendemC und durchschreitet ein Maximum für eine bestimmte Wandneigung. Die Ergebnisse zeigen, daß im Vergleich zu einer Anordnung ohne Rippen, die Wärmeübertragung bei geeigneten geometrischen Parametern allgemein reduziert werden kann.     

Transient natural convection in a rectangular enclosure with one heated side wall

This paper describes a numerical and theoretical study of the transient natural convection heating of a two-dimensional rectangular enclosure filled with fluid. The heating is applied suddenly along one of the side walls, while the remaining three walls are maintained insulated. It is shown that the process has two distinct phases, an early period dominated by conduction and a late period dominated by convection. The scaling laws for the heat transfer rate and the effectiveness (energy storage fraction) are determined based on scale analysis. These theoretical results are confirmed by numerical experiments conducted in the domain Ra = 10³−10⁶, Pr = 7, A = 1, where Ra is the Rayleigh number based on height and initial temperature difference, Pr is the Prandtl number, and A is the height/length ratio of the enclosure. Correlations for heat transfer rate and effectiveness are constructed by comparing the theoretical scaling laws with the numerical results.     

Natural convection in inclined rectangular enclosures with perfectly conducting fins attached on the heated wall

The natural convection heat transfer in inclined rectangular enclosures with perfectly conducting fins attached to the heated wall is numerically studied. The parameters governing this problem are the Rayleigh number (10²≤Ra≤2×10⁵), the aspect ratio of the enclosures (2.5≤A=H′/L′≤∞), the dimensionless lengths of the partitions (0≤B=?′/L′≤1), the aspect ratio of micro-cavities (A≤C=h′/L′≤0.33), the inclination angle (0≤φ≤60^°) and the Prandtl number (Pr=0.72). The results indicate that the heat transfer through the cover is considerably affected by the presence of the fins. At low Rayleigh numbers, the heat transfer regime is dominated by conduction. When B≈0.75 and C≈0.33, the heat transfer through the cold wall decreases considerably. This trend is enhanced when the enclosure is inclined. Useful engineering correlations are derived for practical applications.     

An experimental study of the effect of wall temperature nonuniformity on natural convection in an enclosure heated from the side

An experimental study of natural convection in a parallelepipedal enclosure induced by a single vertical wall is described. The upper half of this wall was warm and the lower half cold. The other enclosure walls were insulated. The temperature and flow measurements were performed in the high Rayleigh number regime (10¹⁰<Ra<5×10¹⁰) by using water as the working fluid. The Rayleigh number was based on the enclosure height and the temperature difference between the warm and the cold part of the driving wall. The flow field featured two flat cells, one filled with warm fluid along the top horizontal wall, and the other filled with cold fluid along the bottom horizontal wall. Each of these cells was surrounded by an additional cell as tall as half the enclosure height. The above flow structure prohibited extensive thermal contact between warm and cold fluid, thus limiting the role of convection on the heat transfer process in the cavity. The findings of this study differ significantly from the findings of previous studies based on the ‘classical’ enclosure model possessing two isothermal vertical walls, the one warm and the other cold, and support the view that the use of ‘more realistic‘ temperature boundary conditions in enclosure natural convection needs careful examination.     

Free convection enhancement between inclined wall and air in presence of expired jets at temperature difference of 40 K

This paper aims to determine the heat transfer enhancement in natural convection between a downward-facing inclined wall, heated by Joule effect, and air in the presence of small air pulsating expired jets, in conditions of medium temperature difference between wall and air, namely 40 K. Experimental measurements have been taken both with and without pulsating expired jets. The wall is kept in condition of uniform temperature. The expired jets blow out perpendicularly from the wall surface. An infrared thermo-camera was used to check the wall temperature uniformity. Hot-wire anemometer and visualization with smoke were used to find information on the air velocity field.The wall inclination angle which maximizes the convective heat exchange near the leading edge has been investigated too.     

Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects

The effect of double-diffusive natural convection of water in a partially heated enclosure with Soret and Dufour coefficients around the density maximum is studied numerically. The right vertical wall has constant temperature θ_c, while left vertical wall is partially heated θ_h, with θ_h > θ_c. The concentration in right wall is maintained higher than left wall (C_c < C_h) for case I, and concentration is lower in right wall than left wall (C_h > C_c) for case II. The remaining left vertical wall and the two horizontal walls are considered adiabatic. Water is considered as the working fluid. The governing equations are solved by control volume method using SIMPLE algorithm with QUICK scheme. The effect of the various parameters (thermal Rayleigh number, center of the heating location, density inversion parameter, Buoyancy ratio number, Schmidt number, and Soret and Dufour coefficients) on the flow pattern and heat and mass transfer has been depicted. Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters mentioned above.     

Free convection from a vertical plate with nonuniform surface heat flux and embedded in a porous medium

An analysis is presented for the calculation of heat transfer due to free convective flow along a vertical plate embedded in a porous medium with an arbitrarily varying surface heat flux. By applying the appropriate coordinate transformations and the Merk series, the governing energy equation is expressed as a set of ordinary differential equations. Numerical solutions are presented for these equations which represent universal functions and several computational examples are provided.     

Free convection from one thermal and solute source in a confined porous medium

This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 ⩽ N ⩽ + 10, 0 ⩽ R _t ⩽ 200, 10⁻² ⩽ Le ⩽ 200, and 0.125 ⩽ L ⩽ 0.875, where N, R _t , Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment.     

Combined radiation and natural convection in a rectangular cavity with a transparent wall and containing a non-participating fluid

This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e. transparent) fluid. One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls. The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non-isothermal walls. A two-band radiation model has been employed. Results are presented for a square cavity with a vertical hot wall at 150 °C, the ambient at 20 °C and 10⁴ ? Ra ? 3 × 10⁵, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers.     

Numerical simulation for 2D double-diffusive convection (DDC) in rectangular enclosures based on a high resolution upwind compact streamfunction model I: numerical method and code validation

Applied Mathematics and Mechanics - A high resolution upwind compact streamfunction numerical algorithm for two-dimensional (2D) double-diffusive convection (DDC) is developed. The unsteady...     

On the Reynolds-number independence of mixed convection in a vertical channel subjected to asymmetric wall temperatures with and without flow reversal

The problem of mixed convection in a vertical channel with asymmetric wall temperatures including situations of flow reversal is studied numerically. The SIMPLER algorithm with a staggered grid system is employed to solve the corresponding numerical equations formulated by the finite-volume method. A second-order upwind scheme is used to model the convective term, and a suitable grid distribution is introduced. The ranges of the parameters studied are 0 r_t 1, 1 Re 1000, and 0 Gr/Re 500.

The numerical results, with the streamwise coordinate scaled by the Reynolds number (Re), show that solutions for the velocity and temperature fields are independent of the Reynolds number when Re 50, even in the presence of flow reversal. These solutions, however, are dependent on r_t and Gr/Re. Subsequently, correlations are proposed for the bulk temperature distribution and the local Nusselt numbers along the hot wall and the cold wall.     

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

The effect of nonlinear mixed convection in stretched flows of rate-type non-Newtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.     

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.     

A numerical method for forced convection in porous and homogeneous fluid domains coupled at interface by stress jump

A numerical method was developed for flows involving an interface between a homogeneous fluid and a porous medium. It is based on the finite volume method with body‐fitted and multi‐block grids. The Brinkman–Forcheimmer extended model was used to govern the flow in the porous medium region. At its interface, the flow boundary condition imposed is a shear stress jump, which includes the inertial effect, together with a continuity of normal stress. The thermal boundary condition is continuity of temperature and heat flux. The forced convection through a porous insert over a backward‐facing step is investigated. The results are presented with flow configurations for different Darcy numbers, 10^?2 to 10^?5, porosity from 0.2 to 0.8, Reynolds number from 10 to 800, and the ratio of insert length to channel height from 0.1 to 0.3. The heat transfer is improved by using porous insert. To enhance the heat transfer with minimal frictional losses, it is preferable to have a medium length of insert with medium Darcy number, and larger Reynolds number. The interfacial stress jump coefficients β and β₁ were varied from ?1 to 1, and within this range the average and local lower‐wall Nusselt numbers are not sensitive to the parameters. Copyright © 2007 John Wiley & Sons, Ltd.     

Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.     

The laminar free‐convection boundary‐layer flow about a heated and rotating down‐pointing vertical cone in the presence of a transverse magnetic field

This paper deals with the study of the laminar free‐convection boundary‐layer flow about a heated and rotating down‐pointing vertical cone in the presence of a transverse magnetic field. Two cases of heat transfer analysis are discussed. These are: (i) the rotating cone with prescribed surface temperature and (ii) the rotating cone with prescribed surface heat flux. By means of similarity transformation, the governing partial differential equations are reduced into highly non‐linear ordinary differential equations. The resulting non‐linear system has been solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in a series form. The influence of various pertinent parameters is also seen on the velocity and temperature fields. Copyright © 2010 John Wiley & Sons, Ltd.     

Free and forced oscillations of a frictionless liquid in a long rectangular tank with structural obstructions at the free liquid surface

Summary If a free liquid surface is partly covered with a solid wall, the natural frequencies and the response of the liquid in the container may be drastically changed. The fundamental natural frequency of a frictionless and incompressible liquid in an infinitely long rectangular container is determined for increasing structural coverage of the free surface. With increasing coverage of the surface by a rigid structural member, the natural frequencies increase drastically and reduce the sloshing motion. The response to translational excitation is evaluated also numerically. The procedure may be applied to arbitrary coverages of a three-dimensional rectangular container, and may also be used as a test case for purely numerical procedures such as the finite element method. Received 13 July 1999; accepted for publication 26 October 1999