Isothermal Side Walls Research Articles

Heat transfer in a high vertical enclosure with fins attached to one of the side walls

A numerical model is developed of heat transfer in a high vertical narrow enclosure in the presence of fins on one of the isothermal side walls. The Navier—Stokes equations were solved numerically in two-dimensional formulation. It is demonstrated that the mean coefficient of heat transfer over the channel surface for adiabatic fins first increases with the number of fins to reach a maximum and then decreases by approximately 30% compared to smooth walls. For heat-conducting fins, the enhancement of heat transfer may be as high as 200% or more.

Double Diffusive Convection of Water in a Rectangular Partitioned Enclosure with Temperature Dependent Species Diffusivity

The double diffusive convection of cold water around its density maximum in a rectangular partitioned enclosure with isothermal side walls and insulated top and bottom is studied numerically. A thin partition is attached to the hot wall. The species diffusivity of the fluid is assumed to vary linearly with temperature. The two-dimensional flow equations expressed by stream function-vorticity formulation along with the energy and concentration equations are solved by finite difference scheme. The effects of position and height of the partition, and variable species diffusivity are analyzed for various Grashof numbers. The heat and mass transfer characteristics are analyzed using the streamlines, isotherms and isomasslines. It has been found that adding partition on the hot wall reduces the heat transfer. Also found that the density inversion of the water has a great influence on the natural convection. We concluded that placing partition at the middle of the hot wall has marked effect on flow pattern and heat transfer in the enclosure.

Natural convection in cavities with constant flux heating at the bottom wall and isothermal cooling from the sidewalls

Natural convection in rectangular cavities is studied numerically using a finite volume based computational procedure. In many applications, especially for cooling of electronic components, a natural convection configuration is encountered where a constant flux heating element at the bottom surface are cooled from the isothermal sidewalls while the top wall can be considered adiabatic. The present study is based on such a configuration where a constant flux heat source is symmetrically embedded at the bottom wall. The length of the heat source is varied from 20 to 80% of the total length of the bottom wall. The non-heated parts of the bottom wall are considered adiabatic. The Grashof number is varied from 10 3 to 10 6. The study includes computations for cavities at various aspect ratios, ranging from 0.5 to 2, and inclination angles of the cavity from 0° to 30°. The effects aspect ratio, inclination angles, and heat source length on the convection and heat transfer process in the cavity are analysed. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface under different conditions.

Mixed convection in rectangular cavities at various aspect ratios with moving isothermal sidewalls and constant flux heat source on the bottom wall

Mixed convection heat transfer in a two-dimensional rectangular cavity with constant heat flux from partially heated bottom wall while the isothermal sidewalls are moving in the vertical direction is studied numerically. The enclosure represents a practical system such as an air-cooled electronic device, where cooling from the sides is expected to be an efficient electronic cooling option. The heat source represents a heater or an electronic component located at the bottom in such an enclosure. Several different values of the heat source length, the aspect ratio of the cavity, as well as symmetric and asymmetric placement of the heat source are considered. All computations are done for a range of Richardson number from 0.1 to 10. The influence of the Richardson number, heat source length, placement of the heat source, and aspect ratio of the cavity, on the maximum temperature and the Nusselt number at the heat source surface is investigated. Results are presented in the form of streamline and isotherm plots as well as the variation of the maximum temperature and Nusselt number at the heat source surface under different conditions. The pressure–velocity coupling in the governing equations is achieved using the well-known SIMPLE method for numerical computation. The computational procedure is based on finite volume collocated mesh. The linear algebraic system of equations is solved sequentially using the strongly implicit procedure (SIP).

Low-Prandtl number natural convection in volumetrically heated rectangular enclosures III. Shallow cavity, AR=0.25

Following previous studies for enclosures of aspect ratios 4 and 1, direct numerical two-dimensional simulations were conducted for the free convection flow of a low-Prandtl number fluid with internal heat generation in a shallow cavity (AR=0.25) having adiabatic top and bottom walls and isothermal side walls. The Prandtl number was 0.0321 and the Grashof number, Gr, based on power density and cavity width, ranged from 10 6 to 10 11. The flow was steady for Gr up to 3×10 9, time-periodic for Gr≈10 10 and chaotic for Gr⩾3×10 10. In both the steady and the periodic regimes, the flow was instantaneously symmetric with respect to the vertical centreline of the enclosure; in the chaotic regime the instantaneous flow was asymmetric, but bilateral symmetry was recovered in the time-averaged velocity and temperature fields. For Grashof numbers above ∼10 7, the Nusselt number (overall/conductive heat transfer) increased roughly as Gr 1/5, i.e., slightly more markedly than for the previous aspect ratios and in agreement with the behaviour expected in the separated-boundary layer regime.

Low-Prandtl number natural convection in volumetrically heated rectangular enclosures: II. Square cavity, AR=1

Following a previous study for a slender enclosure ( AR=4), direct numerical two-dimensional simulations were conducted for the free convective flow of a low-Prandtl number fluid ( Pr=0.0321) with internal heat generation in a square cavity having adiabatic top and bottom walls and isothermal side walls. The Grashof number, Gr, based on conductive maximum temperature and cavity width, ranged from 10 5 to 10 9. For Gr up to ∼10 7, the flow was steady and exhibited left–right symmetry. For Gr≈3×10 7, the spatial symmetry was broken and asymmetric steady-state flow patterns were obtained. For Gr≈5×10 7, the asymmetric flow became time-periodic. Finally, for Gr≥10 8, chaotic flow was predicted; the time-averaged velocity and temperature fields were still markedly asymmetric at Gr=10 8, but reattained bilateral symmetry at higher Gr (10 9), when developed two-dimensional turbulence was observed. For Grashof numbers above ∼10 6, the friction coefficient averaged along the vertical walls scaled roughly with Gr −1/3 (as in the AR=4 cavity), while the Nusselt number (overall/conductive heat transfer) increased roughly as Gr 1/7, i.e. slightly less markedly than in the slender cavity.

THERMOSOLUTAL CONVECTION IN A PARTIALLY DIVIDED SQUARE

Convection in a partially divided square enclosure with combined horizontal temperature and concentration gradients was studied experimentally. An electrochemical system was employed to impose the concentration gradients. The concentration and temperature differences were achieved by heating the cathode and cooling the anode. The partition plate was adiabatic and was oriented parallel to the isothermal sidewalls. Thermal Grashof numbers ranging from 6.94 x 10 5 to 1.1 x 10 6 , solutal Grashof numbers from 7.02 x 10 6 to 1.62 x 10 7 , and partition ratios of 0.125 and 0.25 were investigated. Because of the large difference between the thermal and solutal diffusion rates, the flow had double-diffusive characteristics. Various flow patterns were observed under different experimental conditions. It was demonstrated that the partition ratio has strong effects on both the mass transfer rate and the flow pattern

Low-Prandtl number natural convection in volumetrically heated rectangular enclosures: I. Slender cavity, AR = 4

Natural convection in a volumetrically heated rectangular enclosure filled with a low-Prandtl number ( Pr=0.0321) fluid was studied by direct numerical two-dimensional simulation. The enclosure had isothermal side walls and adiabatic top/bottom walls. The aspect ratio was 4 and the Grashof number Gr, based on conductive maximum temperature and cavity width, ranged from 3.79 × 10 4 to 1.26 × 10 9. According to the value of Gr, different flow regimes were obtained: steady-state, periodic, and chaotic. The first instability of the steady-state solution occurred at Gr≈3×10 5; the resulting time-periodic flow field consisted of a central rising plume and of convection rolls, periodically generated in the upper corners of the cavity and descending regularly along the vertical isothermal walls. Transition from periodic to chaotic motion occurred at Gr≈1×10 6; up to the highest Grashof numbers studied, the fluid motion exhibited a recognizable dominating frequency, associated with the process of roll renewal and scaling as Gr 1/2. The flow field still consisted of a meandering rising plume and of downcoming convection rolls, but these coherent structures were now irregular in shape, size and velocity. For Grashof numbers larger than ∼10 6 (chaotic flow), the friction coefficient averaged along the vertical walls was found to scale as Gr −1/3 and the Nusselt number (overall/conductive heat transfer) as Gr 1/6.

Measurement and prediction of natural convection velocities in triangular enclosures

Free convection velocities were predicted with a finite element method and measured using laser velocimetry in three isosceles triangular enclosures with base angles of 30 °, 45 °, and 60 °. Three Grashof numbers were tested for each geometry, which ranged from 189 × 10 6 to 10.3 × 10 6 . Velocity data were measured near the two isothermal side walls and the isothermal bottom wall. Data were nondimensionalized by the same parameters used to nondimensionalize inclined plate data. Flows were laminar for all cases. For a given base angle, the nondimensional data and predictions collapsed to single curves best for either of the side walls with typical variations of 5 percent; nondimensional predictions and data collapsed poorly for the bottom walls, with typical variations of 20 percent. Hot and cold side-wall data exhibited similitude and typical differences between nondimensional results for the two side walls were 10 percent. For varying base angles, side-wall results failed to reduce to single curves with variations of typically 50 percent. Absolute differences between predicted and measured peak velocities ranged from 6 to 35 percent. Differences between predicted and measured velocities for base angles of 30 and 60 ° tended to be positive, whereas, differences for a base angle of 45 °, tended to be negative.

Experimental and Theoretical Investigations of Heat Transfer in Closed Gas-Filled Rotating Annuli

The prediction of the temperature distribution in a gas turbine rotor containing closed, gas-filled cavities, for example in between two disks, has to account for the heat transfer conditions encountered inside these cavities. In an entirely closed annulus, forced convection is not present, but a strong natural convection flow exists, induced by a nonuniform density distribution in the centrifugal force field. Experimental investigations have been made to analyze the convective heat transfer in closed, gas-filled annuli rotating around their horizontal axes. The experimental setup is designed to establish a pure centripetal heat flux inside these annular cavities (hot outer, and cold inner cylindrical wall, thermally insulated side walls). The experimental investigations have been carried out for several geometries varying the Rayleigh number in a range usually encountered in cavities of turbine rotors (107 < Ra < 1012). The convective heat flux induced for Ra =1012 was found to be a hundred times larger compared to the only conductive heat flux. By inserting radial walls the annulus is divided into 45 deg sections and the heat transfer increases considerably. A computer program to simulate flow and heat transfer in closed rotating cavities has been developed and tested successfully for annuli with isothermal side walls with different temperatures giving an axial heat flux. For the centripetal heat flux configuration, three-dimensional steady-state calculations of the sectored annulus were found to be consistent with the experimental results. Nevertheless, analysis of unsteady calculations show that the flow can become unstable. This is analogous to the Be´nard problem in the gravitational field.

Natural Convection in a Partitioned Cubic Enclosure

Numerical solutions are obtained for fluid flow and heat transfer in a cubic enclosure with a vertical adiabatic partition. The two zones of the enclosure are connected by a single rectangular opening. The partition is oriented parallel to the isothermal sidewalls, one of which is heated and the other cooled while the remaining walls are adiabatic. Results have been presented for air for the Rayleigh numbers in the range 104−107. The width of the opening is held fixed while the height, relative to the enclosure height, is varied from 0.25 to 0.75. The effects of various parameters on the flow structure and heat transfer are investigated. The results of the three-dimensional simulation have also been compared with those for the corresponding two-dimensional configurations.

A Computational and Experimental Study of Natural Convection and Surface/Gas Radiation Interactions in a Square Cavity

Interactions of natural convection and surface/gas radiation in a nongray gas filled square cavity are investigated in the present paper, both computationally and experimentally. A schematic of the cross sectional view of the cavity is depicted. The cavity is heated from the isothermal side wall located at x = H, which is maintained at a temperature of T{sub H}, and cooled from the opposing side wall with a temperature of {Tc} located at x = 0. All the interior surfaces are assumed to be nonslip and radiatively black for the computations. Various thermal boundary conditions are specified for the horizontal walls. Carbon dioxide gas is considered as the medium. The overheat ratio {delta} (defined as T{sub H} {minus} {Tc})/T{sub o}, where T{sub o} is the reference film temperature, ({Tc} + T{sub H})/2 has been limited to small values ({delta} < 0.2) in the experimental study of natural convection-radiation interactions in the past (Kurosaki et al., 1982). In the present investigation, significantly higher values of {delta} are used in the computations and experiments.

Non-Boussinesq effects on transitions in Hele–Shaw convection

Mode jumping between buoyancy-induced convection patterns in a slender Hele–Shaw cell (height&amp;gt;width) is studied with a center manifold projection technique at a critical aspect ratio, where both the single-roll and double-roll convection patterns destabilize simultaneously. In contradiction to some experimental observations, the Boussinesq model with insulated or isothermal side wall conditions indicates that the single-roll mode never surrenders its stability and yields to the double-roll mode as the Rayleigh number is increased. By adding the temperature dependence of fluid density and conductivity to the heat equation, it is shown that the single-roll mode can now undergo secondary bifurcations. Hysteretic jumps to the double-roll mode and smooth transitions to a mixed mode, and even to a time-periodic convection pattern, are then possible.

Radiative influence on the stability of fluids enclosed in vertical cavities

This paper examines the stability of natural convection of a radiating fluid contained in a vertical slot having isothermal side walls at different temperatures. An absorbing-emitting, non-grey but nonscattering fluid is considered and the P1 approximation is used to describe the radiative flux in the energy equation. The base flow equations and the linear stability equations were solved by a spectral tau method. The effect of radiation on the critical values are presented as functions of the interaction parameter, the optical thickness of the fluid, the non-greyness parameter and the wall emissivities over a wide range of stratification parameter. The energetics of the critical disturbance modes were also calculated. For all the cases investigated, it is found that the instabilities set in as a single travelling wave the moving direction of which depends on the wall emissivities. The predictions of the stability analysis are verified by finite difference calculations of multicellular flows of radiating fluids.

A Numerical Study of Laminar Natural Convection in Shallow Cavities

Heat transfer by natural convection in a horizontal cavity with adiabatic horizontal walls and isothermal side walls is investigated numerically for high aspect ratios (width/height). Comparison is made with existing analytical and experimental results. Agreement is generally good at moderate and high Prandtl numbers to which most previous works have been restricted. Improvements of the existing correlation have been proposed in regions of discrepancy. Extension to the low Prandtl number case, including the range of liquid metals, has been made on the basis of an analytical model for high Rayleigh numbers as well as by numerical solution of the full equations. The agreement between the two is found to be very good. A correlation for the heat transfer is proposed for each of the two different cases of high and low Prandtl number.

The Measurement of Natural Convective Heat Transfer in Triangular Enclosures

Heat transfer rates were experimentally measured for laminar convection air flows in two-dimensional triangular enclosures with two side walls which were heated and cooled and an adiabatic bottom. Both local and overall heat transfer data were obtained by the use of a Wollaston prism schlieren interferometer. The angle between the two isothermal side walls was varied between 60 and 120 deg, which resulted in a variation in aspect ratio (enclosure height/base width) between 0.29 and 0.87, while the Grashof number was varied between 2.9 × 106 and 9.0 × 106. Results are compared to previously obtained isothermal inclined flat plate data and rectangular enclosure data. Present results agree with rectangular enclosure results. One deviation from local rectangular enclosure data was found in the apex regions of the triangular enclosures, where complex thermal and flow interactions occurred due to proximity of the two side walls.

Velocity Measurements in Two Natural Convection Air Flows Using a Laser Velocimeter

Velocities in two laminar free convection air flow fields were measured using a laser velocimeter. Velocities were first measured in the boundary layer around a heated vertical flat plate and results compare within two percent of theoretical and previous experimental (streak photography) data. Second, velocities were measured throughout a two-dimensional triangular enclosure, which consisted of two isothermal side walls (one heated and one cooled), an insulated bottom, and glass end plates. Enclosure data are compared to simple inclined isothermal plate data and are also presented so that the flow patterns can be observed.

Numerical Study of Natural Convection in a Vertical Rectangular Enclosure

The steady-state natural convection of a fluid in a vertical rectangular cavity with isothermal side walls and adiabatic top and bottom walls is considered for 6 × 104 ≤ Ra ≤ 3.6 × 105 with Pr = 1, 6, 2000, and at an aspect ratio of 5.0. The governing nonlinear fourth-order equation in the stream function and the coupled second-order energy equation are solved numerically by a stable and rapidly converging iteration scheme. The computed flow distributions, including the appearance of multicellular flows, the temperature profiles, and the heat transfer predictions compare favorably with experimental results and with other numerical studies.

Stability of natural convection in a vertical slot

The stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically. Both the conduction and boundary-layer régimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows. Theoretical predictions of the critical Rayleigh number and of the form of the secondary flow are verified by experimental measurements.