Computational and experimental studies of convective fluid motion and heat transfer in inclined non-rectangular enclosures

Computational and experimental studies of the fluid motion and heat transfer characteristics of an incompressible fluid contained in a non-rectangular inclined enclosure are described in this paper. The enclosure has two 45° inclined side walls one of which was heated and the other cooled. The remaining two sides of the enclosure are parallel and insulated. The enclosure was rotated about the long axis in steps of 30° through 360°. Experiments were performed to study the effects of Rayleigh number, aspect ratios and orientation of the enclosure. The computational method uses a mesh transformation technique coupled with the introduction of ‘false transient’ parameters for the steady state solution of the problem. The experimental method uses smoke for flow visualization studies. With aspect ratios of 3 and 6, the results indicate that the heat transfer and fluid motion within the enclosure is a strong function of both the Rayleigh number and the cavity orientation angle. A minimum and a maximum mean Nusselt number occurred as the angle of inclination was increased from 0 to 360°. A transition in the mode of circulation occurred at the angle corresponding to the minimum or maximum rate of heat transfer. Stream lines and isotherms are presented for the most representative cases     

Natural convection in an inclined quadrantal cavity heated and cooled on adjacent walls

Natural convective flow and heat transfer in an inclined quadrantal cavity is studied experimentally and numerically. The particle tracing method is used to visualize the fluid motion in the enclosure. Numerical solutions are obtained via a commercial CFD package, Fluent. The working fluid is distilled water. The effects of the inclination angle, ? and the Rayleigh number, Ra on fluid flow and heat transfer are investigated for the range of angle of inclination between 0° ? ? ? 360°, and Ra from 10⁵ to 10⁷. It is disclosed that heat transfer changes dramatically according to the inclination angle which affects convection currents inside, i.e. flow physics inside. A fairly good agreement is observed between the experimental and numerical results.     

矩形倾斜腔体中的两种对流斑图和分区

为了研究矩形倾斜腔体中普朗特数Pr=0.72的流体对流斑图和分区,本文基于流体力学方程组进行了数值模拟。在相对瑞利数r=6.0的情况下,观察了倾角θ=10°和θ=60°时对流斑图随着时间的发展,发现系统存在单圈型对流和多圈型对流两种斑图。流线随着倾角的变化说明:随着倾角增加,对流圈数逐渐减少,对流波长逐渐增加,对流波数减小;然后,随着对流圈数显著地减少,系统由多圈型对流过渡到单圈型对流。根据模拟计算结果,给出了多圈型对流过渡到单圈型对流的临界倾角θc随着相对瑞利数r变化的关系曲线。对流在θ-r平面上分为两个区域:θ<θc时系统是单圈型对流,θ>θc时系统是多圈型对流。对流最大振幅A和努塞尔数Nu随着倾角θ的变化曲线被临界倾角θc分成两段,它们有不同的变化规律。因此,临界倾角也可以由对流最大振幅A或努塞尔数Nu的变化曲线来确定。     

Natural convection in cavities containing internal sources

 Numerical predictions are reported for buoyancy-induced circulations in a 2D closed cavity with internal heat sources. Two cases are considered: (A) two vertical plates with uniform heat generation, forming a short vertical channel within the enclosure; and, (B) a rectangular heating block with uniform wall temperature, placed central in the enclosure. Air, with a Prandtl number 0.71, is considered as the working fluid. The vertical enclosure walls are isothermal, while the horizontal enclosure walls are adiabatic. Results are presented for two values of the Grashof number, one below the stability limit for laminar flow, and one well above it. In those latter cases, the long-term behaviour of the numerical solution is time-dependent, i.e. no steady-state can be reached. Heat transfer results are compared with predictions from standard correlations for isolated surfaces. Received on 17 January 2000     

A numerical study of three-dimensional laminar natural convection in a vented enclosure

A three-dimensional numerical investigation of steady laminar natural convection in vented enclosures is carried out. A discrete flush-type heat source mounted on the substrate is used to simulate an electronic component. Four different vent locations are investigated. Combined natural convection in the air and conduction in the heat source, the substrate, and the enclosure walls are solved. Solutions are obtained for Rayleigh numbers ranging from 10⁴ to 10⁶, different substrate thermal conductivity ratios, and varied vent sizes. The calculation domain is extended beyond the cubic enclosure in x-, y-, and z-directions. Appropriate boundary conditions are prescribed on the extended computational domain. The resulting flow and temperature patterns are discussed. Also, the local and overall heat transfer from the heat source and the substrate, in terms of Nusselt numbers and the surface temperatures, are presented to illustrate the vent effects.     

Natural convection flow under a magnetic field in an inclined square enclosure differentialy heated on adjacent walls

Steady, laminar, natural-convection flow in the presence of a magnetic field in an inclined square enclosure differentially heated along the bottom and left vertical walls while the other walls are kept isothermal was considered. The governing equations were solved numerically for the stream function, vorticity and temperature ratio using the differential quadrature method for various Grashof and Hartmann numbers, inclination angle of the enclosure and direction of the magnetic field. The orientation of the enclosure changes the temperature gradient inside and has a significant effect on the flow pattern. Magnetic field suppresses the convective flow and its direction also influences the flow pattern, causing the appearance of inner loops and multiple eddies. The surface heat flux along the bottom wall is slightly increased by clockwise inclination and reduced by half by the counterclockwise inclination. The surface heat flux along the upper portion of the left side wall is reversed by the rise of warmer fluids due to the convection currents for no inclination and clockwise inclination of the enclosure.     

Natural convection in a partitioned enclosure heated from below

Cubic spline collection numerical method has been developed to determine two dimensional natural convection in a partitioned enclosure heated from below. The both sides of impermeable partition are considered to have continuity in heat flux and temperatures. The governing equations are solved with aid of the SADI procedure. Parametric studies of the effects of the partition and Rayleigh number on the fluid flow and temperature fields have been performed. Results show that the location of the partition and Rayleigh number have a significant influence on the flow and heat transfer characteristics.

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Freie Konvektion in einem von unten beheizten, unterteiltem Hohlraum

Zusammenfassung Eine numerische dreidimensionale SplineMethode zur Berechnung der zweidimensionalen Naturkonvektion in einem von unten beheizten, unterteiltem Hohlraum wird vorgestellt. Der Wärmestrom und die Temperatur auf beiden Seiten der undurchlässigen Trennwand werden als konstant betrachtet. Mit Hilfe der SADI-Prozedur werden die beschreibenden Gleichungen gelöst. Über den Einfluß der Unterteilung und der Rayleigh-Zahl auf die Strömung des Fluids und das Temperaturfeld wird eine Parameter-Studie durchgeführt. Die Ergebnisse zeigen, daß die Anordnung der Unterteilung und die Rayleigh-Zahl einen entscheidenden Einfluß auf das Wärmeübertragungsverhalten haben.

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Nomenclature A aspect ratio=L/H - g gravitational acceleration - H enclosure height - H₁ distance between the top wall of enclosure and the partition - H₂ distance between the bottom wall of enclosure and the partition - k thermal conductivity of fluid - L enclosure length - m number of vertical grid lines - n number of horizontal grid lines - Nu Nusselt number - P pressure - Pr Prandtl number - Q heat transfer across enclosure - Ra Rayleigh number based onH - t time - T dimensional temperature - T _H temperature of warm horizontal wall - T _L temperature of cold horizontal wall - T ₀ average temperature=T(_H+T_L)/2 - T temperature difference between the hot and cold wall =T _H–T_L - u, U dimensional and dimensionless horizontal velocity - , V dimensional and dimensionless vertical velocity - x, X dimensional and dimensionless horizontal coordinate - y, Y dimensional and dimensionless vertical coordinate - fluid thermal diffusivity - coefficient of thermal expansion - viscosity - kinematic viscosity=/g9 - density - , dimensional and dimensionless stream function - dimensionless temperature - , dimensional and dimensionless vorticity - dimensionless time     

Numerical investigation of natural convection inside an inclined parallel‐walled channel

Steady two‐dimensional natural convection in an inclined parallel‐walled channel was investigated numerically. The full elliptic forms of conservation equations were solved together and the velocity vectors, temperature contours and local and average Nusselt number distribution were obtained. The comparisons of local and average Nusselt number with published experimental and numerical results indicate very good agreement. Results are presented for a single aspect ratio, L/b=24, over the range of Rayleigh number of 3–1000 and angle of inclination 0–90°. The results indicate that the overall channel average Nusselt number is reduced as the inclination angle is increased. Significant reductions in the overall Nusselt number are exhibited at high angle of channel inclination. Copyright © 2005 John Wiley & Sons, Ltd.     

Natural convection in an inclined porous enclosure with an off-center diathermal partition

A numerical study has been made of natural convection in an inclinded porous enclosure with an off-center diathermal partition. A temperature difference is imposed between the two isothermal end walls and the other two walls are assumed to be adiabatic. Numerical results are obtained for Rayleigh numbers (Ra) in the range of 10 to 500, the dimensionless partition location ( \(\bar S\) ) ranging from 0.125 to 0.875, the aspect ratios (A) of the enclosure ranging from 0.5 to 5, and the inclination angles (φ) of ?60, ?30, 0, 30, 60 degrees. It is found that the partition location has strong influence at lowRa and relatively weaker influence at highRa. The average Nusselt number reaches the minimum value when the partition is in the middle of the vertical enclosure, and the maximum Nusselt number occurs around φ = 30 degrees.     

Natural convection in partially cooled tilted cavities

Two-dimensional numerical simulations of laminar natural convection in a partially cooled, differentially heated inclined cavities are performed. One of the cavity walls is entirely heated to a uniformly high temperature (heat source) while the opposite wall is partially cooled to a lower temperature (heat sink). The remaining walls are adiabatic. The tilt angle of the cavity is varied from 0° (heated from left) to −90° (heated from top). The fast false implicit transient scheme (FITS) algorithm, developed earlier by the same authors, is modified to solve the derived variables vorticity-streamfunction formulation. The effects of aspect ratio (AR), sink–source ratio and tilt angle on the average Nusselt number are examined through a parametric study; solutions are obtained for two Grashof numbers, 10⁵ and 10⁷. Flow patterns and isotherms are used to investigate the heat transfer and fluid flow mechanisms inside the cavity. © 1998 John Wiley & Sons, Ltd.     

Buoyancy-driven flow in an enclosure containing time periodic internal sources

A computational study is carried out to investigate the effect of the sinusoidally driven heat source on the fluid flow and heat transfer within a two-dimensional square cavity. The cavity, which has solid walls of constant temperature, is filled with a fluid including uniformly distributed internal heat source. In addition, the effects of the different periods of the sinusoidally driving heat source on heat transfer are investigated and presented as figures.     

Double-diffusive natural convection in a porous enclosure partially heated from below and differentially salted

This paper reports numerical results of two-dimensional double-diffusive natural convection in a square porous cavity partially heated from below while its upper surface is cooled at a constant temperature. The vertical walls of the porous matrix are subjected to a horizontal concentration gradient. The parameters governing the problem are the thermal Rayleigh number (Ra=100 and 200), the Lewis number (Le=0.1, 1 and 10), the buoyancy ratio (−10N10) and the relative position of the heating element with respect to the vertical centerline of the cavity (δ=0 and 0.5). The effect of the governing parameters on fluid characteristics is analyzed. The multiplicity of solutions is explored and the existence of asymmetric bicellular flow is proved when the heated element is shifted towards a vertical boundary (δ=0.5). The solutal buoyancy forces induced by horizontal concentration gradient lead to the elimination of the multiplicity of solutions obtained in pure thermal convection when N reaches some threshold value which depends on Le and Ra.     

Natural convection in an inclined enclosure with a fluid layer and a heat-generating porous bed

Multiple steady-state solutions of natural convection in an inclined enclosure with a fluid layer and a heat-generating porous bed is investigated numerically by the finite volume method. The conservation equations for the porous layer are based on a general flow model which includes both the effects of flow inertia and friction. The flow in fluid layer is modeled by Navier–Stokes equations. The method of pseudo arc-length continuation is adapted in studying the effects of tilt angle on flow pattern and heat transfer. It is found that, in the whole domain of tilt angle, there exist two groups of solutions with quite different flow pattern and heat transfer behavior. The effects of aspect ratio on flow pattern and heat transfer have also been studied. Received on 04 March 1997     

Natural convection in a square enclosure with an internal isolated vertical plate

Numerical computations were performed for the average Nusselt number at an internal vertical plate situated in a square enclosure, with the inner plate and the bounding wall of the enclosure maintained at uniform but different temperatures. Natural convection occurred in the air which occupied the enclosure space. The position of the inner vertical plate within the enclosure was varied parametrically. The plate height-cavity height ratio was 0.513. For narrow distance between the inner plate and the bounding wall the inner plate Nusselt number was enhanced. Aside from this, the plate average Nusselt number was remarkably insensitive to the plate position. The effect of the Rayleigh number on the velocity and temperature fields and local Nusselt numbers are also discussed. The agreement between the predicted flow pattern forRa=1.1×10⁶ and the flow visualization result was reasonably good.

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Natürliche Konvektion in einem quadratischen Horizontalschacht, der eine freistehende, senkrechte Platte enthält

Zusammenfassung Eine numerische Untersuchung liefert mittlere Nußelt-Zahlen an einer, in einem quadratischen Horizontalschacht freistehenden, senkrechten Platte, wobei deren Temperatur und die der umgebenden Wände jeweils konstant gehalten werden. Im Luftraum dazwischen stellte sich freie Konvektion ein. Die Position der Platte war veränderlich, ihre Höhe blieb mit 51.3% der Schachthöhe konstant. Rückte die Platte nahe an eine Schachtwand, so erhöhte sich die Nußelt-Zahl auf der dieser zugewandten Seite, während die Gesamt-Nußelt-Zahl bezüglich der Platte fast konstant bleibt. Es wird auch der Einfluß der Rayleigh-Zahl auf das Geschwindigkeitsund Temperaturfeld diskutiert. BeiRa=1.1·10⁶ stimmten die Ergebnisse aus der Berechnung gut mit den experimentellen Befunden einer Strömungsvisualisation überein.

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Nomenclature a distance between vertical plate and side-wall of enclosure thermal diffusivity (in definition ofu _r) - b distance between vertical plate and bottom of enclosure - g gravitational acceleration - G characteristic flow rate - H height of vertical plate - k thermal conductivity - k _f fluid thermal conductivity - K relative thermal conductivity,k/k _f - L width of square enclosure - M _res mass residual - Nu local Nusselt number - Nu _m average Nusselt number - Nu _L local Nusselt number of left side of vertical plate - Nu _R local Nusselt number of right side of vertical plate - Nu _B local Nusselt number of bottom side of vertical plate - Nu _T local Nusselt number of top side of vertical plate - p effective pressure - P dimensionless pressure,P=p/[(Ra Pr)(a/H)²] - Pr Prandtl number - Ra Rayleigh number,Ra=gTH ³ Pr/ ² - T temperature - T _i temperature of internal plate - T _o temperature of enclosure surface - u, v velocity components inx-, y-direction - U, V dimensionless velocities,U=u/u _r, V=v/u_r - u _r reference velocity,u _r=(Ra Pr)^1/2/(a/H) - X, {iyY} dimensionless coordinates,X=x/H, Y=y/H Greek symbols heat transfer coefficient - volume expansion coefficient - thickness of plate - kinematic viscosity - density - dimensionless temperature, (T _i–T)/(T _i–T_o)     

Transient heat flux measurement of natural convection in an inclined enclosure with time-periodically-varying wall temperature

The transient natural convection in an inclined enclosure filled with water is studied experimentally for the time-periodically-varying wall temperature on one side wall and constant average temperature on the opposing side wall. This system has no temperature difference between the opposing two side walls in time-averaged sense. The temperatures of two opposing walls and the heat flux across the enclosure are measured by a heat flux meter. Based on the experimental results, the effects of time-periodically-varying wall temperature and inclined angles of the enclosure on heat transfer characteristics are studied. The experimental results show that, with the upper wall temperature oscillating, the heat flux across the enclosure is also periodically varied with time, and the net heat flux is from the lower wall to the upper wall. Numerical computations are also conducted and numerical results are qualitatively assured by the experimental measurements.     

Transient mixed convection flow of a second grade viscoelastic fluid past an inclined backward facing step

The transient mixed convection of a second-grade viscoelastic fluid past an inclined backward facing step was studied numerically. The combined effects of the Reynolds number, the elastic effect, the inclined angle of the flow channel on the reattachment length, and the phenomena of heat transfer are examined during the development of the flow field. The Gauss-Seidal method with successive over relaxation was implemented to solve the stream-vorticity and energy equations. The results indicate that the reattachment length increases to the maximum as the inclined angle increases up to 150° or 180°. At these cases, the point of reattachment is close to the point of the local maximum value of Nu_x or is overshooting it. It is observed that the reattachment length increases as the Reynolds number increases or the elastic coefficient decreases. In the meantime, the contact point of the isotherm on the upper plate moves upward and is close to upstream flow as the inclined angle is around 150°.     

线圈绕Y轴倾斜时方腔内空气磁力与重力耦合对流的数值模拟

数值分析了微重力与重力环境下圆形载流线圈绕Y轴倾斜时方腔内空气热磁对流。磁场计算采用毕奥萨伐定律;控制方程基本变量采用控制容积法离散,求解采用SIMPLE算法。计算过程中Ra数的变化范围为104~105,线圈倾斜角yeuler的变化范围为-90°~90°,磁场力数γ数的变化范围为0~200。获得了空气热磁对流的流场和温...     

Binary-mixture convection in connected channels heated from below

Supercritical binary-mixture flows in connected channels of finite depth are studied theoretically and experimentally. It is shown that, in contrast to uniform fluids, in the mixture the convection excitation is “hard” and specific transient flows and oscillation regimes are observed. A mechanism explaining the phenomena observed is proposed and confirmed by a theoretical solution of the problem. The amplitude curves and the channel distributions of the velocity, temperature, and admixture concentration are obtained. These illustrate the competition between the thermodiffusion and thermo-gravitational convection mechanisms.     

Local mass transfer measurements in an inclined enclosure at high Rayleigh number

An electrochemical technique is used to study local mass transfer coefficients on surfaces of inclined enclosures over the range 1.1×10⁴ < Ra_H < 1.4×10¹⁰ for a nominal Schmidt number of 2280. Scaling with gcos instead of g in the Rayleigh number correlates the data well at low angles of inclination; however, as either the aspect ratio or the angle of inclination increase, the longitudinal density stratification causes the data to deviate from a power law scaling.