Natural convection in V-shaped and L-shaped corners

Experiments were performed to investigate convection in two types of corners. One, the V corner, is formed by two 45° inclined, upward-facing, heated plates which intersect at 90°. The other, the L corner, is formed by an upward-facing, heated horizontal plate which intersects with a heated vertical plate. In both cases, the two plates had the same uniform temperature which was varied parametrically. The variations of the surface-to-ambient temperature difference and of the plate length yielded a Rayleigh number range from 2 × 10⁶ to 1.5 × 10⁹. Apparatus modifications were also made to investigate the possible role of end effects. The heat transfer experiments were supplemented by flow visualization. The Nusselt numbers for all cases were amenable to power-law correlations with the Rayleigh number. The values of the Nusselt number at the walls of the V corner and at the horizontal wall of the L corner were greater than those for the counterpart single plates.     

CONJUGATE NUMERICAL COMPUTATION FOR THE NATURAL CONVECTION OF LIQUID METAL HEATED FROM BELOW

ABSTRACT

The oscillatory Rayleigh-Benard convection in a shallow layer of liquid metal (Pr = 0.023), sandwiched between two copper plates, was numerically computed for three computational domains simultaneously. The horizontal cross section is square and the aspect ratio (fluid layer width/height) is 10. This conjugate solution suggested that the hot plate temperature oscillates almost simultaneously with the fluid temperature and throughout the whole hot copper plate with almost uniform temperature. The oscillatory temperature amplitude provided the upper and lower limits in the Rayleigh number and the Nusselt number estimated from the relationship, constant = Ra* = Nu ? Ra, where Ra* is a modified Rayleigh number based on the uniform heat flux. This group of data provided quite similar characteristics to the previous experimental observation by Yamanaka et al. for the oscillatory change of the Nusselt number and to the one by Rossby for the time-averaged values.     

Experimental study of flow and heat transfer characteristics of natural convection in an enclosure with horizontal parallel heated plates

We conducted an experimental investigation of natural convection in an enclosure containing horizontal parallel heated plates. Our experimental setup was as follows: Two heated plates were arranged vertically in an enclosure. The temperature of the ceiling was maintained at a constant low temperature, while the other sides satisfied thermal insulation boundary conditions. We examined flow characteristics in the enclosure and heat transfer around the horizontal heated plates. In the region between the cooled ceiling and the upper heated surface, vortex motion occurred when the accompanying flow from the lower region interfered with the ascending flow. Heat transfer around the heated surface was enhanced by this vortex motion. In other regions, the flow circulated along the heated surfaces in all cases. Generally speaking, for each flow pattern, the Nusselt number was proportional to some power of the modified Rayleigh number.     

Natural Convection Heat Transfer of a Rectangular Block within a Vertical Enclosure

A numerical solution of the natural convection heat transfer between two cold and hot isolated vertical plates is presented for different horizontal and vertical location ratios of an enclosure. Results show that: a) flow configurations of cold and hot plates are different; b) the increase of vertical location ratio, toward that corresponding to the enclosure middle value, is considerably diminishing the temperature differences between heating and cooling conditions; c) the effect of vertical location ratio variation is more prominent on heat transfer for cold and hot plates than that of the horizontal location ratio variation; d) the average Nusselt number, obtained from the hot isolated plate, is 20–39% larger than that of the cold plate under the same conditions when the isolated plate varies horizontally; e) for a narrow distance between the inner plate and the bounding wall, the inner plate Nusselt number is enhanced, but aside from this, the plate average Nusselt number is insensitive to the plate position; and f) different trends are found to affect heat transfer for cold and hot plates when the isolated plate varies vertically. The optimal vertical location can be found at specific Rayleigh number for the hot plate and cold plate.     

Effects of side-wall temperature on the flow pattern of Rayleigh-Bénard cells in an enclosure

Experimental and numerical studies relating to the effects of side-wall temperatures on the flow pattern of Rayleigh-Bénard cells in a rectangular enclosure with an aspect ratio of 6:2:1 (length: width: height) are presented. Experiments were carried out using air at Rayleigh number less than or equal to 16,000. We were able to demonstrate that the flow patterns always consist of a steady even or odd number of roll-cells with axes almost parallel to the short or long side of the enclosure for all side-wall temperatures. The results of numerical calculations based on the steady three-dimensional Boussinesq equations are in quantitative agreement with the observed flow patterns. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(6): 462–471, 1998     

Heat transfer in a PEMFC flow channel

A numerical method was applied to the heat transfer performance in the flow channel for a proton exchange membrane fuel cell (PEMFC) using the finite element method (FEM). The heat transfer enhancement has been analyzed by transversely installing a baffle plate and a rectangular cylinder to manage flow pattern in the flow channel of the fuel cell. Case studies include baffle plates (gap ratios from 00.05 to 0.2) and the rectangular cylinder (width-to-height ratios from 0.66 to 1.66 with a constant gap ratio of 0.2; various gap ratios from 0.05 to 0.3 with a constant width-to-height ratio 1.0) at constant Reynolds number. The results show that the transverse installation of a baffle plate and a rectangular cylinder in the flow channel can effectively enhance the local heat transfer performance of a PEMFC. The installation of a rectangular cylinder has a better effective heat transfer performance than a baffle plate; the larger the width of the cylinder is the better effective heat transfer performance becomes.     

Natural convection from narrow horizontal plates at moderate Rayleigh numbers

The present work deals with the natural convection flow and heat transfer from a horizontal plate cooled from above. Experiments are carried out for rectangular plates having aspect ratios between φ=0.036 and 0.43 and Rayleigh numbers in the range 290?Ra_w?3.3×10⁵. These values of Ra_w and φ have been selected below those commonly considered in previous research in view of a future application to the design of printed circuit boards. The plates are made of two different metals, copper and steel. The choice of a metal is relevant to the present problem because the plates are heated by means of an electric current. Important variations of the surface temperature are observed along the transverse direction for the steel plates. The surface of the copper plates is almost isothermal because of the high thermal conductivity of the metal.Calculations for a semi-infinite plate are carried out to predict the transverse profiles of the surface temperature and heat flux and to visualize the structure of the flow. Three-dimensional calculations are also used at a qualitative level to observe the changes in the flow structure due to the finite length of the plate. Present results are compared with both previous experimental work and analyses that are based on boundary layer theory. It is shown that analyses for an infinite boundary layer are not completely applicable to the present problem because of its different physics. The most relevant feature of the natural convection flow, which is not predicted by boundary layer analyses, is a thermal plume rising near the center of the plate.Present heat transfer results differ from previous experimental work because of the lower Rayleigh numbers and aspect ratios investigated here. The Nusselt number is found to depend on Ra_wⁿ, with the exponent n=0.17 being lower than most of the values reported in the literature. This comparatively low value is related to the transverse conduction of heat through the air, which becomes increasingly significant as Ra_w approaches zero. It is shown that such a low-Ra_w effect can be accounted for in a physically consistent manner by adding a constant term to the heat transfer correlation. On the other hand, it is found that the Nusselt number does not significantly depend on the aspect ratio in the range of φ investigated contrary to what has been previously reported for wider plates.     

FULLY DEVELOPED MIXED CONVECTION IN A HORIZONTAL CHANNEL HEATED UNIFORMLY FROM ABOVE AND BELOW

Abstract

Calculations were performed for fully developed, laminar, mixed convection flow in a horizontal, parallel plate channel heated uniformly at the top and bottom plates. Spanwise conduction within the plates was considered, and calculations were performed for Pr = 0.7, 0 < Ra? < 2.5 × 10⁴, and values of a nondimensional conductance ratio in the range 10^?5 < γ < 10³. It is shown that mixed convection heat transfer enhancement is restricted to the lower surface and that the attendant secondary flow induces large spanwise surface temperature variations for which the maximum temperature exceeds values associated with the upper surface. Increased conduction within the bottom plate weakens the secondary flow and decreases spanwise temperature variations. Results of the calculations have important implications in situations for which there is interest in maintaining reduced temperatures, as well as large heat transfer enhancement, at the bottom plate.     

Fluid Flow and Infrared Image Analyses on Endwall Fitted with Short Rectangular Plate Fin

An experimental investigation is carried out to study fluid flow and heat transfer characteristics on the endwall fitted with arrays ( 7×7 ) of short rectangular plate fins of different pattern (co-angular and zigzag) for different pitch ratio. Experiments were conducted in a rectangular duct of 50 mm height for an air flow of Reynolds number ranged from 18750 to 62500 based on the equivalent diameter and air velocity of the duct. Infrared image analysis technique was employed to make clear the characteristics of local heat transfer coefficients on fin base, endwall and overall surface. Flow pattern around the short rectangular plates were visualized by inducing fluorescent dye in a water channel and longitudinal vortices were observed. Increasing the distance between plates in flow direction causes heat transfer enhancement for co-angular pattern, while decreasing the distance causes heat transfer enhancement for zigzag pattern. Zigzag pattern with pitch ratio 2 is found to be more effective in heat transfer enhancement than any other cases investigated.     

Numerical Investigation on the Steady State Natural Convection in a Horizontal Open-Ended Cavity with a Heated Upper Wall

In this article, the investigation is focused on a configuration made of two horizontal parallel plates with the upper plate heated at uniform heat flux and the lower one adiabatic. Results are presented in terms of velocity and temperature fields, and both the temperature and the velocity profiles at different sections are shown. They are reported at two Rayleigh numbers, 10³ and 10⁵, and for two aspect ratio values, 1 and 10. Results are also shown in terms of the upper and lower wall temperature profiles. Correlations for average Nusselt numbers and maximum dimensionless wall temperature, in terms of Rayleigh number and aspect ratio, are given for 10³ ≤ Ra ≤ 10⁵ and 1 ≤ L/b ≤ 10.     

Natural convection heat transfer in the open space between two horizontal circular planes with different temperatures

A vertical cylinder maintained at room temperature is located right above a horizontal circular heated plane to constitute a narrow air space between the plane and the cylinder bottom surface. Natural convection heat transfer in the space is experimentally investigated. Average heat transfer coefficients of the heated plane are presented with the variation of space distance and Rayleigh number, and are compared with the predictions of the correlation equations which have been proposed for the space between two infinite parallel plates. Visualized flow patterns above the heated plane are also shown. The relation between the flow pattern and the heat transfer coefficient is discussed to clarify the mechanism of heat transfer in the narrow space. As a result, a heat transfer correlation is proposed, which is applicable over a wide range of space distances. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 521–531, 2001     

The Effect of Plate Size on the Natural Convective Heat Transfer Intensity of Horizontal Surfaces

Abstract

Natural convective heat transfer from flat horizontal isothermal plates has been investigated for more than a century. In the present study, the influence of the size of the plate on the heat flux is investigated. Two ranges of the heat transfer intensity are proposed for this problem: for the plates with characteristic length smaller than 0.1–0.2 m, the heat transfer coefficient is inversely proportional to the plate width; for plates wider than 0.2 m, the heat flux is not influenced by the plate width. The explanation for the discrepancy between the two ranges of natural convective heat transfer based on analysis and comparison of experimental data available in the literature has been proposed.     

Effect of gap thickness on a rectangular-cell compound-honeycomb solar collector

Compound-honeycomb solar collectors employ a honeycomb to suppress natural convection and air gaps between the honeycomb and the absorber plate or the glazing to reduce conductive and radiative heat losses. Results of an experimental study on the effect of the thickness of these gaps on the total heat transfer across a compound honeycomb confined between two isothermal and low emissivity boundaries are presented. The honeycomb consists of rectangular cells with elevation aspect ratio 6.3 and plan aspect ratio 82 (15.8 mm thick, 206 mm wide and 2.5 mm deep), constructed from parallel glass strips. Plots of Nusselt number versus Rayleigh number are given for compound honeycombs with air gaps of thickness 1.6 mm, 3.3 mm, 6.4 mm and 9.6 mm above and below the honeycomb and for a compound-honeycomb layer with an air gap of thickness 6.4 mm below the honeycomb. Measurements are reported for tilt angles of 0°, 30° and 60° where the long dimension of the rectangular cells in the honeycomb is horizontal. As the air gaps' thickness increase, coupled conductive-radiative heat transfer is reduced, while the critical Rayleigh number is also reduced and convective heat transfer increases. However, even for relatively thick air gaps, the decrease in critical Rayleigh number is moderate, and the rectangular-cell compound honeycomb is found to be an effective convection suppressor. A compound honeycomb with air gaps above and below the honeycomb is shown to be superior in suppressing convection to a compound honeycomb of equal total thickness with only one air gap below the honeycomb.     

Numerical simulation of natural convection heat transfer in the open space between two horizontal circular planes

Numerical simulations were conducted for natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier–Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer values are shown to be in good agreement with the experimentally obtained ones reported in a previous paper. From the obtained isotherms, streamlines, and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance: one is a simple convection due to a single renewal flow which replaces heated air with ambient air and the other is a combined convection due to several vortex flows and a renewal flow. Furthermore, the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 485–502, 2001     

Improvement of the basic correlating equations and transition criteria of natural convection heat transfer

In this paper, improvements in the basic physical laws of natural convection heat transfer were implemented in two major respects by incorporating recent research findings in this field. A preferred transition criterion was adopted in this paper to correlate all of the experimental data. Since transition correlations are primarily flow stability problems, the Grashof number, instead of the Rayleigh number, was found to be the preferred criterion. Furthermore, in the case of natural convection heat transfer from a horizontal cylinder, a series of experimental data in the high‐Rayleigh‐number regions recently became available. These data made it possible to establish new reliable correlations and also to test the validity of previous correlations. It is concluded that the previous correlation for a horizontal cylinder in high‐Rayleigh‐number regions was based on unreliable experimental results. The transition correlation for a horizontal cylinder occurred at much higher values of Rayleigh number than the previous recommendation. In the case of natural convection heat transfer from a vertical plate, more accurate property values for air under pressurized conditions are now available. This made it possible to replot the reliable data of Saunders. From this result and the experimental result of Warner and Arpaci, a new set of basic correlations in natural convection heat transfer for laminar, transitional, and turbulent regimes are recommended. These recommendations reflect a better understanding of the basic physical laws in the field of heat convection. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 293–300, 2001     

Natural convection in a periodically finned vertical channel

This paper presents the experimental results of natural convection in a rectangular cross-sectional vertical channel. Along the channel fins connected to both plates are placed, periodically. The channel walls are maintained at uniform heat flux. Rayleight number and Nusselt number are obtained based on channel width. The ratio of the channel length to the channel width, L/b, is 66. The experiments are performed for modified Rayleigh number, (b/L)RA, ranges from 20 to 90. Results shows that Nusselt number for finned channel are less than those of the smooth channel.     

Jet impingement cooling of a horizontal surface in a confined porous medium: Mixed convection regime

In the present article the jet impingement cooling of heated portion of a horizontal surface immersed in a fluid saturated porous media is considered for investigation numerically. The jet direction is considered to be perpendicular from the top to the horizontal heated element; therefore, the external flow and the buoyancy driven flow are in opposite directions. The governing parameters in the present problem are Rayleigh number, Péclet number, jet width and the distance between the jet and the heated portion normalized to the length of the heated element. The results are presented in the mixed convection regime with wide ranges of the governing parameters with the limitation of the Darcy model. It is found for high values of Péclet number that increasing either Rayleigh number or jet width lead to increase the average Nusselt number. Narrowing the distance between the jet and the heated portion could increase the average Nusselt number as well.No steady-state solution can be found in some cases; when the external jet flow and the flow due to buoyancy are in conflict for domination. The results from the unsteady governing equations in these cases show oscillation of the average Nusselt number along the heated element with the time without reaching steady state.     

Fluid flow and heat transfer of natural convection over upward‐facing,horizontal, heated plate shrouded by a parallel insulated plate

The present paper describes experimental results on the fluid flow and heat transfer of natural convection between a horizontal, heated plate facing upward and an insulated cover plate. The experiments were carried out with water. The width of the test plates W and their gaps H were changed from W = 50 to 250 mm and H = 10 to 30 mm and ∞ (no cover plate). The visualization studies with dye and liquid crystal thermometry revealed that the roll cells whose axes are perpendicular to the flow direction appear and become dominant over the heated plate on decreasing the gap. These roll cells inhibit the heat transfer, and thus, the heat transfer coefficients become smaller than those without a cover plate. It was found that the flow and heat transfer in the region near the plate edges are unaffected by the cover plate. The conditions of the above reduced heat transfer were determined empirically. Moreover, nondimensional correlations for the local and the overall heat transfer coefficients of the heated plates are proposed based on the present heat transfer results. © 2000 Scripta Technica, Heat Trans Asian Res, 29(4): 333–346, 2000     

Flow patterns and heat transfer enhancement in low-Reynolds–Rayleigh-number channel flow

This paper presents an experimental study on buoyancy-induced flow patterns and heat transfer characteristics of airflow through a horizontal rectangular channel. The channel had an aspect ratio of six, and its bottom and sidewalls were heated, whereas the top of the channel was cooled. The experiments were conducted at the Reynolds numbers 40 and Rayleigh numbers ranging from 100 to 4200. The Nusselt number and the temperature distributions on the top surface of the channel were measured simultaneously at different thermal/flow conditions, and the heat transfer characteristics of the channel was evaluated, together with the flow patterns in the channel. The results showed that due to the heated sidewalls, which was an `imperfect' factor comparing with the classic Rayleigh–Bénard channel, the longitudinal vortex rolls can occur at the Rayleigh number Ra=100, starting with number of rolls N=2 and then N=4 as the Ra increases, rather than the N=6 mode for the same channel with `perfect' sidewalls. In the present study, the six-roll mode occurred at Ra=1730 and above, but an initial trigger was required. Otherwise the four-roll mode would continue to be the dominant flow pattern at high Rayleigh numbers. It was demonstrated that significant heat transfer enhancement could be achieved in low Reynolds and Rayleigh number flow if the longitudinal vortex rolls were excited in the channel.     

Hydromagnetic Double-Diffusive Laminar Natural Convection in a Radiatively Participating Fluid

ABSTRACT

Two-dimensional hydromagnetic double-diffusive convection of a radiatively participating fluid confined in a rectangular enclosure is studied numerically for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10⁵, Le = 2. Uniform temperatures and concentrations are imposed along the vertical walls, while the horizontal walls are assumed to be adiabatic and impermeable. The damping and stabilization effects of an external horizontal magnetic field are studied for three different optical thicknesses of the semitransparent fluid as well as for an opaque medium. For moderate optical thickness, a steady compositionally dominated flow is observed for all values of Hartmann number considered, and the magnetic damping is remarkably lower than in the opaque medium, for which the flow is always thermally dominated. For optically thin and optically thick media, the thermally dominated flow is stabilized and becomes compositionally dominated as soon as the Hartmann number is increased.