Interactions of thermally induced acoustic waves with buoyancy induced flows in rectangular enclosures

Acoustic waves are generated when a compressible-fluid is exposed to a rapidly varying heat flux along a confining wall. For an enclosure, these waves reverberate and eventually decay. Buoyancy-induced flows generated within an enclosure can be affected by the acoustic waves generated. The interactions of the acoustic waves produced by rapid heating of a wall with the buoyancy-induced flow in air filled rectangular enclosures are investigated numerically. For the present simulations, the bottom wall of the enclosure is heated rapidly with varying heating rates, while the top wall is held at the initial temperature of the air. The vertical walls of the enclosure are considered insulated. The compressible unsteady Navier–Stokes equations are solved by an explicit flux-corrected transport algorithm for the convection terms and by a central-differencing scheme for the viscous and conduction terms.     

Numerical oscillatory on the simulation of thermoacoustic waves

The SIMPLE algorithm for compressible flows is introduced to predict the thermoacoustic wave in a one‐dimensional closed region. The thermoacoustic waves are generated by an impulsive rise of the temperature on the left wall, while the other walls are kept at the initial temperature. Four different schemes are employed to deal with the convection‐diffusion terms, i.e., CD, FUD, QUICK, and MUSCL. The calculations and analysis show that numerical oscillation occurs under all four schemes, affected by the intensity of the waves, type of schemes, and other factors. The results are beneficial for the further investigation of the thermoacoustic waves and high efficiency scheme development. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(5): 265– 275, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20162     

A Study of Free Convection Induced by a Vertical Wavy Surface with Heat Flux in a Porous Enclosure

Free convection induced by a vertical wavy surface with uniform heat flux in a porous enclosure has been analyzed numerically using the finite element method (FEM). The flow and the convection process in the cavity is found to be sensitive to the flow parameter Rayleigh number (Ra), and geometrical parameters like wave amplitude (a), wave phase (φ), and number of waves (N) in the vertical dimension of the cavity. The study reveals that small sinusoidal drifts from the smoothness of a vertical wall with a phase angle of 60^o and high frequency enhances the free convection from a vertical wall with uniform heat flux.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

Conjugate natural convection in a square enclosure: effect of conduction in one of the vertical walls

Steady, laminar, natural convection flow in a square enclosure has been analysed numerically. One vertical wall of the enclosure is thick, with a finite thermal conductivity, while the other three walls are taken to be of zero thickness. The problem is conjugate and the main focus of the study is on examining the effect of conduction in the wall on the natural convection flow in the enclosure. Three separate models to account for the wall conduction are investigated : (i) the complete conjugate case in which conduction in the thick vertical wall is assumed to be fully two-dimensional; (ii) a one-dimensional model in which conduction in the wall is assumed to be in the horizontal direction only; and (iii) a lumped parameter approach which assumes the solid-fluid interface temperature to be uniform. A Boussinesq fluid with Prandtl number of 0.7 (air) and Grashof numbers ranging from 10³ to 10⁷ are considered. For Grashof number > 10⁵, the temperature distribution in the wall shows significant two-dimensional effects and the solid-fluid interface temperature is found to be quite non-uniform. This non-uniformity tends to make the flow pattern in the enclosure asymmetric. In the parametric range investigated, all three models predict nearly the same value for the overall heat transfer.     

Natural convection in an enclosure with non-uniform wall temperature

A numerical study of natural convection in an enclosure was investigated. The heated wall of the enclosure is divided into two of the higher and lower temperature regions and the temperature of the cold wall is maintained at a constant. The parameters of Rayleigh number and length ratio are mainly considered. The results show that the local Nusselt number distribution varies drastically at the intersection of the higher and lower temperature regions, and the flow is strongly affected by the above two parameters.     

A segregated spectral element method for thermomagnetic convection of paramagnetic fluid in rectangular enclosures with sinusoidal temperature distribution on one side wall

An accurate segregated spectral element method is developed to simulate the thermomagnetic convection in an air-filled rectangular enclosure, which has spatially varying sinusoidal temperature distribution on the left wall with all the other walls insulated. The numerical scheme is based on spectral elements in space and the semi-implicit method for pressure linked equations algorithm is adopted to decouple the flow variables. The validation tests with analytical solution and natural convection verify the high accuracy of the algorithm. The fluid flow and heat transfer characteristics in the enclosure are systematically studied, including the influences of magnetic strength, aspect ratio, and position of the heating part. The results show that the addition of an external magnetic field significantly increases the heat transfer rate in the enclosure, and the fluid on the right side is well heated to form a uniform temperature field.     

Lattice Boltzmann Simulation of Natural Convection in a Differentially Heated Square Enclosure Containing Heat Generating Low‐Prandtl Number Fluid

Lattice Boltzmann simulations were conducted for the free convective flow of a low‐Prandtl number (Pr = 0.0321) fluid with internal heat generation in a square enclosure having adiabatic top and bottom walls and isothermal side walls. The problem of free convection with volumetric heat source has represented itself in connection with advanced engineering applications, such as water‐cooled lithium–lead breeder blankets for nuclear fusion reactors and liquid metal sources of spallation neutrons for subcritical fission systems. A single relaxation time (SRT) thermal lattice Boltzmann method (LBM) was employed. While applying SRT, a D2Q9 model was used to simulate the flow field and temperature field. Results have been obtained for various Rayleigh numbers characterizing internal and external heating from 10³ to 10⁶. Flow and temperature fields in terms of stream function and isotherms in the enclosure were predicted for these cases. The temperature of the fluid in the enclosure was found higher than the heated wall temperature at high values of internal Rayleigh numbers. The internal heat generation affected the rate of heat transfer significantly as two convection loops are observed in the enclosure. The average Nusselt number at the heated and cold wall was determined for all the cases.     

Effects of corrugation frequency and aspect ratio on natural convection within an enclosure having sinusoidal corrugation over a heated top surface

Natural convection of a two-dimensional laminar steady-state incompressible fluid flow in a modified rectangular enclosure with sinusoidal corrugated top surface has been investigated numerically. The present study has been carried out for different corrugation frequencies on the top surface as well as aspect ratios of the enclosure in order to observe the change in hydrodynamic and thermal behavior with constant corrugation amplitude. A constant flux heat source is flush mounted on the top sinusoidal wall, modeling a wavy sheet shaded room exposed to sunlight. The flat bottom surface is considered as adiabatic, while the both vertical side walls are maintained at the constant ambient temperature. The fluid considered inside the enclosure is air having Prandtl number of 0.71. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results in terms of isotherms, streamlines and average Nusselt numbers are obtained for the Rayleigh number ranging from 10³ to 10⁶ with constant physical properties for the fluid medium considered. It is found that the convective phenomena are greatly influenced by the presence of the corrugation and variation of aspect ratios.     

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 10⁵ to 10⁸ with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed except for the density where Boussinesq’s approximation has been considered. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh number with corrugation amplitude and frequency.     

Two-dimensional natural convection in a porous triangular enclosure with a square body

A two-dimensional numerical solution for steady-state buoyancy induced convection in a right-triangular enclosure with a square body is obtained using finite difference technique. The solid body is located far from the origin with the distance of 0.3 in both directions. It is considered that the temperature of the bottom wall of triangular enclosure is higher than that of inclined wall while the vertical wall is insulated. To obtain the effects of the presence of a square body on heat transfer and fluid flow inside the enclosure, four different temperature boundary conditions were applied for the body as heated, cooled, neutral and adiabatic at different Ra numbers. It is observed that fluid flow and temperature fields strongly depend on thermal boundary conditions of the body.     

Inverse determination of building heating profiles from the knowledge of measurements within the turbulent slot-vented enclosure

Slot ventilated enclosure flows have been simulated, respectively in displacement ventilation and mixed ventilation covering from the forced convection dominated flow to the natural convection dominated flow. Direct convection simulation together with the turbulent streamlines and turbulent heatlines demonstrate that the enclosure flow pattern, indoor thermal level and heat transfer potential will depend on the interactions of external forced flow and thermal buoyancy driven flows, i.e., Reynolds number and Grashof number. In subsequent inverse convection modeling, the inverse determination of enclosure wall heat flux profiles was conducted by the use of adjoint methodology, in which the direct, sensitivity and adjoint problems are formulated and solved by finite volume method. The effects of the supplying air flow rate, thermal source strength, ventilation mode, flux functional forms, and the measurement errors on the accuracy of inverse turbulent convection estimation have been investigated. The inverse solutions of turbulent convections are of low level accuracy as the flow becomes thermal-driven turbulent flows, and they deteriorate as the noise levels increase. This work is of fundamental importance for the room air flow design and measurements involving the turbulent thermal convections.     

Nonzero Mean Oscillatory Flow in Symmetrically-Heated Shallow Enclosures: An Analysis of Acoustic Streaming

The effects of symmetric heating on a nonzero mean oscillatory fluid motion, namely acoustic streaming, in air-filled shallow enclosures and associated thermal convection in transient regime are investigated numerically. The fluid motion is driven by periodic vibration of the enclosure left wall. The vertical walls of the enclosure are adiabatic while the horizontal walls are heated symmetrically. A control-volume method-based explicit time-marching flux-corrected transport algorithm is used to simulate the transport phenomena in the enclosure. A symmetric temperature gradient strongly affects the acoustic streaming structures and velocities. The variation of the steady flow field becomes more noticeable and drastic with increasing wall temperature.     

Visualization investigation of the flow and heat transfer in thermoacoustic engine driven by loudspeaker

Heat transfer process in thermoacoustic engine is affected by acoustic oscillation which makes it different from the heat transfer in steady flow. This study pays attention to the flow and heat transfer characteristics of thermoacoustic engine driven by loudspeaker. Thermal infrared imager and particle image velocimetry (PIV) were used to investigate the temperature and flow fields under two heat levels (150 °C and 200 °C). The radial and axial temperature distribution was analyzed through dimensionless temperature. To explore the appropriate working frequency, resonance characteristic was discussed. The experimental results illustrated that the first resonance frequency is the most effective driving frequency where thermoacoustic system shows the best performance. Heat transfer mode changed from natural convection to forced convection with the addition of acoustic oscillation. Original temperature field induced by heat convection was destroyed and temperature gradient redistributed as parabolic after sound addition.     

Brownian motion of nanoparticles in a triangular enclosure with natural convection

This paper presents the results of a numerical study on the natural convection in a right triangular enclosure, with a heat source on its vertical wall and filled with a water–CuO nanofluid. The effects of parameters such as Rayleigh number, solid volume fraction, heat source location, enclosure aspect ratio and Brownian motion on the flow and temperature fields as well as the heat transfer rate, are examined. The results show that when Brownian motion is considered in the analysis, the solid volume fraction, the heat source location and the enclosure aspect ratio affect the heat transfer performance differently at low and high Rayleigh numbers. At high Rayleigh numbers, an optimum value for the solid volume fraction is found which results in the maximum heat transfer rate. This is in contradiction to the results of the analysis in which Brownian motion is neglected.     

Numerical simulation of double diffusive mixed convection in an open enclosure with different cylinder locations

This article reports numerical simulation of the double diffusive mixed convection around a cylinder in an open enclosure with an inlet and exit ports. The temperature and mass concentration of the cylinder are higher than those of the inlet flow and the cylinder can be at three different locations (lower, middle and upper) in the enclosure. The inlet flow with low temperature and mass concentration is located at the lower-left wall of the enclosure and the exit is at the upper-right wall. Other walls are assumed to be adiabatic. Effects of Lewis number Le, buoyancy ratio Br, and cylinder locations on the double diffusive mixed convection are investigated at Richardson number Ri = 1.0 and 0.01 while Prandtl number Pr is kept at 0.7. Streamlines, isotherms, isoconcentrations, and the average and local Sherwood number at different parameters are reported to characterize the double diffusive mixed convection phenomena in the open enclosure.     

Finite element simulation of mixed convection heat and mass transfer in a right triangular enclosure

A simulation of mixed convection heat and mass transfer in a right triangular enclosure is investigated numerically. The bottom surface of the enclosure is maintained at uniform temperature and concentration that are higher than that of the inclined surface. Moreover, the left wall of cavity moves upward (case 1) and downward (case 2) directions, which have constant flow speed, and is kept adiabatic. The enclosure represents the most common technology utilizing solar energy for desalination or waste-water treatment. A simple transformation is employed to transfer the governing equations into a dimensionless form. A finite-element scheme is used for present analysis. Comparison with the previously published work is made and found to be an excellent agreement. The study is performed for pertinent parameters such as buoyancy ratio, Richardson number and the direction of the sliding wall motion. The effect of aforesaid parameters on the flow and temperature fields as well as the heat and mass transfer rate examined. The results show that the increase of buoyancy ratio enhances the heat and mass transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the direction of the sliding wall motion can be a good control parameter for the flow and temperature fields.     

EFFECT OF HEATED WALL POSITION ON MIXED CONVECTION IN A CHANNEL WITH AN OPEN CAVITY

Mixed convection in an open cavity with a heated wall bounded by a horizontally insulated plate is studied numerically. Three basic heating modes are considered: (a) the heated wall is on the inflow side (assisting flow); (b) the heated wall is on the outflow side (opposing flow); and (c) the heated wall is the horizontal surface of the cavity (heating from below). Mixed convection fluid flow and heat transfer within the cavity is governed by the buoyancy parameter, Richardson number (Ri), and Reynolds number (Re). The results are reported in terms of streamlines, isotherms, wall temperature, and the velocity profiles in the cavity for Ri=0.1 and 100, Re=100 and 1000, and the ratio between the channel and cavity heights (H/D) is in the range 0.1-1.5. The present results show that the maximum temperature values decrease as the Reynolds and the Richardson numbers increase. The effect of the H/D ratio is found to play a significant role on streamline and isotherm patterns for differentheating configurations. The present investigation shows that the opposing forced flow configuration has the highest thermal performance in terms of both maximum temperature and average Nusselt number.     

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 shallow wavy enclosure

This paper presents the simulation of free convection heat transfer and fluid flow in a horizontal and shallow wavy enclosure. Its bottom wall is varied with a sinusoidal function while the top wall is flat. The wavy wall has constant hot temperature and ceiling is cold as verticals are insulated. The simulations are performed using CFDRC software. Results are presented in terms of streamlines, isotherms and Nusselt number for different aspect ratios, non-dimensional wave length and Rayleigh number. The obtained results showed that heat transfer is increased with the decreasing non-dimensional wave length and it is increased with the increasing of aspect ratio and Rayleigh number.