Investigation of Mixed Convection in a Ventilated Cavity in the Presence of a Heat Conducting Circular Cylinder

The study is aimed to investigate the mixed convective transport within a ventilated square cavity in presence of a heat conducting circular cylinder. The fluid flow is imposed through an opening at the bottom of the left cavity wall and is taken away by a similar opening at the top of the right cavity wall. The cylinder is placed at the center of the cavity. Two cases are considered depending on the thermal conditions of the cavity walls. In the first case, the left and right vertical walls are kept isothermal with different temperatures and the top and bottom horizontal walls are considered as thermally insulated. For the second case, the top and bottom walls are maintained at different constant temperatures and the left and right walls are considered adiabatic. Heat transfer due to forced flow, thermal buoyancy, and conduction within the cylinder are taken into account. Effect of the cylinder size (0.1 ≤ D ≤ 0.5) and the solid–fluid thermal conductivity ratio (0.1 ≤ K ≤ 10) are explored for various values of Richardson number (0 ≤ Ri ≤ 5) at fixed Reynolds (Re = 100) and Prandtl (Pr = 0.71) numbers. The fluid dynamic and thermal transport phenomena are depicted through streamline and isotherm plots. Additionally, the global thermal parameters such as the average Nusselt number and average fluid temperature of the cavity are presented. It is found that the aforementioned parameters have significant influences on the fluid flow and heat transfer characteristics in the cavity.     

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady natural convection flow from a horizontal cylindrical annulus filled with a non-Darcy porous medium has been studied. The unsteadiness in the problem arises due to the impulsive change in the wall temperature of the outer cylinder. The Navier–Stokes equations along with the energy equation governing the unsteady natural convection flow have been solved by the finite-volume method. The effect of time variation on the heat transfer is more pronounced only in a small time interval immediately after the start of the impulsive motion and the steady state is reached after certain time. The results show that the annulus completely filled with a porous medium has the best insulating effectiveness. Convection in the horizontal annulus is confined mostly at top and bottom regions. Hence, only these regions should be insulated. In case of annulus partially filled with a porous material, insulating the region near the outer cylinder is more effective than insulating the region near the inner cylinder. The effect of Darcy number on the heat transfer is more pronounced than that of the Grashof number.     

Thermal instability in a plane channel with internal heating and horizontal Poiseuille throughflow

The effect of a basic Poiseuille throughflow on the thermal instability of a horizontal fluid layer bounded by two plane parallel walls is studied. An unstable thermal stratification is studied, entirely due to a uniform internal heat generation in the fluid, whereas the thermal boundary conditions do not impress any temperature difference across the fluid layer. Two cases are investigated: a symmetric case where both boundaries are perfectly conducting; a non-symmetric case where the lower boundary is adiabatic and the upper boundary is perfectly conducting. A linear stability analysis is carried out and the eigenvalue problem is solved numerically for arbitrary oblique rolls, and by a symbolic weighted residual method in the special case of longitudinal rolls. The main result is that the basic Poiseuille flow does not influence the thermoconvective instability at the onset of the least stable modes, i.e. the longitudinal rolls. Thus, the critical conditions are just the same as for a fluid at rest in the basic state. Although the focus is on the thermoconvective instability, it is proved that, even in the presence of the internal heat generation, Squire’s theorem holds for the hydrodynamic instability of the plane Poiseuille flow.     

Enhancement of convection heat-transfer in a rectangular duct

Characteristics of wall-to-air heat transfer for a fully developed forced convection have been studied in a large rectangular packed duct with 160 cm heated length, 40 cm width, and for low bed equivalent diameter to particle diameter ratio. The separation distance between the top and bottom walls is 10 cm. A uniform heat flux is supplied at the top wall, while the bottom wall is insulated. Raschig rings in two and spherical packing in three sizes have been used in the air flow passage to investigate the enhancement of heat transfer due to packing. Temperature profiles for the steady and unsteady states have been measured. In modeling, the Ergun equation and energy equations are solved to calculate the temperature profile for the steady-state only. It has been found that the introduction of the packing into the air flow passage increases the wall-to-fluid heat transfer approximately three times compared with that of empty bed. This finding can enhance the rational use of energy from solar air heaters, chemical reactors, electronic cooling and many other engineering applications.     

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.     

Production of hot air with quasi uniform temperature using concentrated solar radiation

The design of a hot air solar generator for different uses has been simulated while investigating the flow induced by a hot disc placed at the entrance of the open ended vertical cylinder. Ambient air (Pr = 0.7) enters the bottom of the cylinder with constant velocity and temperature, and flows up through the cylinder as a result of natural convection. The cylindrical wall is heated by thermal radiation emitted by the disc. The pressure drop due to acceleration of the flow to the cylinder-inlet causes the appearance of thermosyphon effect around the thermal plume. At the top part of the cylinder, the flow exploration shows the full development of the turbulence and the uniformity of thermal and hydrodynamic fields. The study of the thermal spectral density indicates that the turbulent structures seem to be sufficiently small not to be sensitive to viscosity, but large enough to be sensitive to Archimedes effects.     

Visualization of mixed convective vortex rolls in an impinging jet flow of air through a cylindrical chamber

In this study a combined buoyancy and inertia driven vortex flow in an air jet impinging onto a heated circular plate confined in a cylindrical chamber simulating that in a vertical single-wafer rapid thermal processor for semiconductor manufacturing is investigated experimentally by flow visualization. A copper plate is used here to simulate the wafer for its better uniformity of the surface temperature and air is used to replace the inert gases. We concentrate on how the inlet gas flow rate, temperature difference between the wafer and air jet, and chamber pressure affect the vortex flow. The results show that typically the flow in the chamber is in the form of two-roll structure characterized by a circular vortex roll around the air jet along with another circular roll near the side wall of the chamber. Both rolls are somewhat deformed. The rolls are generated by the reflection of the jet from the wafer and by the deflection of the wall boundary layer flow along the wafer surface by the upward buoyancy due to the heated wafer. At low buoyancy and inertia the vortex rolls are steady and axisymmetric. At increasing buoyancy associated with the higher temperature difference and chamber pressure, the inner roll becomes slightly smaller and the outer roll becomes correspondingly bigger. Moreover, at a higher gas flow rate the inner roll is substantially bigger. Based on the present data, a correlation equation is provided to predict the location where the two rolls contact each other, providing the approximate size of the rolls. Moreover, at high buoyancy and inertia the flow becomes time dependent and does not evolve to a steady state.     

Optimization of Mixed Convection in a Lid-Driven Enclosure with a Heat Generating Circular Body

The physical model considered here is a lid-driven enclosure with bottom heating and top cooling conditions, and a heat generating circular body is placed at the center. The vertical walls of the cavity are kept thermally insulated, and the top lid moves at a constant speed. The steady two-dimensional governing equations for the physical problem are transformed in a dimensionless form with dimensionless governing parameters that decide the fluid flow and heat transfer characteristics in the system. The solution of these transport equations is obtained numerically with the finite element approach using the Galerkin method of weighted residuals. The parametric study has been carried out for variation of the heat generation parameters, the Reynolds numbers, solid-fluid thermal conductivity ratios as well as the Richardson numbers. The working fluid is assigned as air with a Prandtl number of 0.71 throughout the simulation. Results are presented in the form of streamlines, isotherms, average Nusselt number, bulk temperature, and drag force for the afore mentioned parameters. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as average Nusselt number, average bulk temperature, and drag force. An optimum combination of the governing parameters would result in higher heat transfer and lower drag force.     

Characteristics of vortex flow in a low speed air jet impinging onto a heated disk in a vertical cylindrical chamber

An experiment combining flow visualization and transient temperature measurement is carried out to investigate the characteristics of the mixed convective vortex flow resulting from a low speed air jet impinging onto a heated horizontal circular disk confined in a vertical adiabatic cylindrical chamber. Attention is focused on the conditions leading to the onset of the inertia and buoyancy driven vortex rolls and the effects of governing nondimensional groups on the steady and time dependent vortex flow. More specifically, experiments are conducted for the jet Reynolds number varied from 0 to 1082 and Rayleigh number from 0 to 18,790 for two different injection pipes. The results show that typically the steady vortex flow in the processing chamber consists of two inertia-driven and one buoyancy-driven circular vortex rolls. The secondary inertia-driven roll only appears at high jet Reynolds numbers. At low buoyancy-to-inertia ratio Gr/Re_j² the vortex rolls are steady and axisymmetric. But at certain high Gr/Re_j² the vortex flow becomes unstable and the vortex rolls are somewhat deformed. Besides, new vortex rolls can be induced by the additional thermal rising from the heated disk and the splitting of the primary inertia-driven roll. The temporal characteristics of the time periodic vortex flows are examined in detail. In the region dominated by the new rolls the flow oscillates significantly. Finally, empirical equations are proposed to correlate the oscillation frequency of the time periodic flow, and the size and location of the vortex rolls. Furthermore, the conditions for the onset of the buoyancy driven rolls are given. A flow regime map is provided to delineate the temporal state of the vortex flow.     

Structure of mixed convective longitudinal vortex air flow driven by a heated circular plate embedded in the bottom of a horizontal flat duct

In this study experimental flow visualization combined with transient temperature measurement are conducted to investigate the structure of the buoyancy driven longitudinal vortex rolls in low Reynolds number mixed convective air flow through a horizontal flat duct with an isothermally heated circular disk embedded in the bottom plate of the duct for the Reynolds number ranging from 15.1 to 99.2 and Rayleigh number from 3506 to 29,493. How the circular geometry of the heated surface affects the longitudinal vortex flow characteristics is investigated in detail. The results indicate that the longitudinal vortex rolls (L-rolls) in the duct core are induced at more upstream locations than those near the duct sides, which is completely opposite to those induced in a duct with a uniformly heated bottom. Besides, the thermals driven by the circular heated surface are not evenly spaced in the spanwise direction and are slightly asymmetric. It is of interest to note that at a given Rayleigh number Ra the thermals are unstable at high Reynolds numbers, suggesting the existence of the inertia driven instability. Thus the L-rolls evolved from these thermals are also unstable with the presence of nonperiodic generation and disappearance of new L-rolls. But at slightly lower Re the thermals and L-rolls are steady and regular. The vortex flow becomes unstable and irregular for a further reduction in the Reynolds number, which obviously results from the buoyancy driven instability. The simultaneous presence of these two instability mechanisms explains the appearance of the reverse steady-unsteady transition in the vortex flow.Based on the present data, a flow regime map is given to delineate various L-roll patterns driven by the circular heated plate. In addition, the boundaries separating these patterns are empirically correlated. Empirical correlations for the onset points of the L-rolls are also provided.     

TEMPERATURE FIELD WITH THERMAL CYLINDERS IN BUOYANT FLOW IN STABLY STRATIFIED AIR

ABSTRACT

The aim of this work is to clarify characteristics of time-dependent temperature behavior in a buoyant flow in stably stratified air in an enclosure. For this aim, the two-dimensional, laminar, time-dependent continuity equation, Navier-Stokes equations with the buoyancy term, and energy equation are solved numerically by finite-difference methods. The computed results at unstratified condition agree well with the previous results, and validate the numerical accuracy. The present computational methods and procedures are therefore valid, and have sufficient grid resolution. As a result, at an adiabatic ceiling of the enclosure or in stably stratified air in the enclosure, a thermal cylinder with high temperature is discovered to occur intermittently near the plume front, and moves upward. However, a thermal cylinder never occurs at unstratified condition. Furthermore, a thermal cylinder exists in both the instantaneous crossover (COI) region at adiabatic condition and the time-averaged crossover (COM) region at stratified condition. In other words, when a thermal cylinder exists, the region with a thermal cylinder is certainly either COM or COI.     

四气门柴油机气缸内气流运动的实验研究

在稳流气道试验台上,使用热线风速仪和自行设计制作的气缸内流场测试系统,对二气门和四气门柴油机模型气缸盖下气缸内流场进行了测量。分析了两种柴油机气缸内流场的形成状况和不同的形成原因。     

Low Rayleigh number flow in a heat generating porous media

A numerical analysis has been performed for the steady-state temperature and stream function distributions in a short cylinder, having an isothermal side and top, an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid, since conduction was the expected mode of heat transfer at low heat generation rates for a lead sphere air porous media system. The solution of the non-dimensionalized momentum and energy equations resulted in small Rayleigh numbers (2×10⁻⁶ to 0.2) indicating the heat transfer is by conduction. Solutions for the stream lines and isotherms were obtained using a transient explicit finite-difference approximation using a mean bed thermal conductivity.     

Effects of connecting pipes in thermosyphonic solar systems

The influence of thermal insulation of pipes in thermosyphonic systems is simulated. In spite of their normally small heat transfer area, these pipes are capable of triggering a reverse flow which causes a substantial drop in the overall efficiency. A clear recommendation of this paper is that at least the upper pipe should be properly insulated. The system's efficiency dependence on the high difference between the collector's top and the tank's bottom is studied. The results indicate that this height should be in the range of 30–80 cm.     

环形腔内密度极值流体Rayleigh-Bénard对流三维数值模拟

为了了解环形腔内流体密度倒置参数对导热态一次分岔临界条件及流动结构的影响,采用有限容积法对侧壁为导热边界条件时具有密度极值流体Rayleigh-Bénard对流进行了三维数值模拟。选用工质为冷水,其普朗特数为11.67。结果表明,随着半径比的增加,系统更加稳定,Rayleigh-Bénard对流发生的临界Ra逐渐增大,流动发生时周向对流涡卷数增加;随着密度倒置参数的增加,导热态一次失稳时的临界Ra显著增加,且大于常规流体中流动发生的临界Ra;在较大的密度倒置参数下,发现了Rayleigh-Bénard对流中的分层现象。     

Viscous dissipation and thermoconvective instabilities in a horizontal porous channel heated from below

A linear stability analysis of the basic uniform flow in a horizontal porous channel with a rectangular cross section is carried out. The thermal boundary conditions at the impermeable channel walls are: uniform incoming heat flux at the bottom wall, uniform temperature at the top wall, adiabatic lateral walls. Thermoconvective instabilities are caused by the incoming heat flux at the bottom wall and by the internal viscous heating. Linear stability against transverse or longitudinal roll disturbances is investigated either analytically by a power series formulation and numerically by a fourth order Runge-Kutta method. The special cases of a negligible effect of viscous dissipation and of a vanishing incoming heat flux at the bottom wall are discussed. The analysis of these special cases reveals that each possible cause of the convective rolls, bottom heating and viscous heating, can be the unique cause of the instability under appropriate conditions. In all the cases examined, transverse rolls form the preferred mode of instability.     

The Effect of a Magnetic Field on the Melting of Gallium in a Rectangular Cavity

The role of magnetic field and natural convection on the solid–liquid interface motion, flow, and heat transfer during melting of gallium on a vertical wall is reported in this paper. The classical geometry consisting of a rectangular cavity with uniform but different temperatures imposed at two opposite side walls, insulated top, and bottom walls is considered. The magnetic field is imposed in the horizontal direction. A numerical code is developed to solve for natural convection coupled to solid–liquid phase transition and magnetic effects. The corresponding streamlines and isotherms predicted by the numerical model serve to visualize the complicated flow and temperature field. The interplay between the conduction and convection modes of heat transfer stimulated by the combination of the buoyancy-driven flow and the Lorentz force on the fluid due to the magnetic field are studied. The results show that the increase of Rayleigh number promotes heat transfer by convection, while the increase of Hartmann number dampens the strength of circulating convective currents and the heat transfer is then mainly due to heat conduction. These results are applicable in general to electrically conducting fluids and we show that magnetic field is a vital external control parameter in solid–liquid interface motion.     

Natural convection heat transfer by heated partitions within enclosure

In this study, natural convection heat transfer and fluid flow of two heated partitions. within an enclosure have been analysed numerically. The right side wall and the bottom wall of the enclosure were insulated perfectly while the left side wall and top wall were maintained at the same uniform temperature. The partitions were placed on the bottom of the enclosure and their temperatures were kept higher than the non-isolated walls. The effects of position and heights of the partitions on heat transfer and flow field have been investigated. Computations for Rayleigh number in the range of 10⁴ and 10⁶ have been conducted. Using the control volume approach, finite difference equations are obtained with non-staggered grid arrangement, a computer program based on the SIMPLEM algorithm was developed. The finite difference equations were solved iteratively with a line-by-line Thomas algorithm.     

MHD Mixed Convection in a Lid-Driven Cavity Including Heat Conducting Solid Object and Corner Heaters with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a top sided lid-driven square enclosure is numerically simulated in this paper following a finite volume approach based on the SIMPLEC algorithm. The enclosure is heated by corner heaters which are under isothermal boundary conditions with different lengths in bottom and right vertical walls. The lid is having lower temperature than heaters. The other boundaries of the enclosure are insulated. A uniform magnetic field is applied along the horizontal direction. A heat conducting horizontal solid object (a square cylinder) is placed centrally within the outer enclosure. Shear forces through lid motion, buoyancy forces due to differential heating and magnetic forces within the electrically conducting fluid inside the enclosure act simultaneously. Heat transfer due to forced flow, thermal buoyancy, Joule dissipation and conduction within the solid object are taken into account. Simulations are conducted for various controlling parameters such as the Richardson number (0.1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50) and Joule heating parameter (0 ≤ J ≤ 5) keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number and bulk fluid temperature are also plotted to show the effects of Ha, J and Ri on them.