Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels

Combined effect of laminar flow mixed convection and surface radiation heat transfer for thermally developing airflow in a vertical channel heated from a side has been experimentally examined with different thermal and geometric parameters. The channel boundary is made of two isothermal walls and two adiabatic walls, the isothermal parallel wall is heated uniformly and the opposite cold wall temperature is maintained equal to the inlet conditions. The heated wall temperature ranged from 55 to 100°C, Reynolds number ranged from 800 to 2900 and the heat flux was varied from 250 to 870 W/m². To cover the wide range of Reynolds numbers, two aspect ratios of square and rectangular section were used. Surface radiation from the internal walls is considered through two emissivities i.e. 0.05 and 0.85, to represent weak and strong radiation effects, respectively. From the experiments, surface temperature and Nusselt number distributions of convection and radiation heat transfer are obtained for different heat flux values. Flow structure inside the channel is visualized to observe the flow pattern. The results show the combined effect of laminar flow mixed convection and surface radiation on the total heat transfer rate within the channel. The accumulating buoyancy force and airflow moves together vertically in the upward direction to give significant heat transfer enhancement in the vertical orientation of the channel.     

A mathematical model of a solar chimney

A simple mathematical model of a solar chimney is proposed. The physical model is similar to the Trombe wall. One side of the chimney is provided with a glass cover which with the other three solid walls of the chimney form a channel through which the heated air could rise and flow by natural convection. Openings provided at the bottom and top of the chimney allow room air to enter and leave the channel. Steady state heat transfer equations were set up to determine the boundary temperatures at the surface of the glass cover, the rear solar heat absorbing wall and the air flow in the channel using a thermal resistance network. The equations were solved using a matrix-inversion solution procedure. The thermal performance of the solar chimney as determined from the glass, wall and air temperatures, air mass flow rate and instantaneous heat collection efficiency of the chimney are presented. Satisfactory correlation was obtained with experimental data from other investigators. Further experimental investigation is currently under way.     

Numerical study of natural convection in asymmetrically heated channel considering thermal stratification and surface radiation

This article consists in a numerical study of the influence of thermal stratification and surface radiation on laminar airflow induced by natural convection in vertical, asymmetrically heated channels. Several cases are investigated to spotlight their influence on fluid dynamics and thermal quantities. Thermal stratification is obtained by a weak gradient of temperature outside of the channel, and then the temperature at the bottom end of the channel is considered as a function of time. Significant effects on vertical velocities, mass flow, and flow structure are shown. Surface radiation is also considered but appears less predominant than thermal stratification for the selected conditions of this article. The impact on heat transfer is also evaluated for each studied configuration. It is observed that local and mean Nusselt numbers weakly increase for the investigated cases.     

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     

Shear-driven flows of locally heated liquid films

This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater’s upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of “ripples” on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas–liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid–gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.     

Assessment of thermal characteristics of square wavy plates

In this paper, the thermal characteristics and air flow behavior over heated square plate of wavy configurations are assessed. Two cases of heated wavy configurations were considered, one having an elliptical and other with the sinusoidal cross‐sectional shape to augment heat transfer rate over the plate. To explore the impact of wavy configurations of plate on convective heat transfer, the Rayleigh numbers in the range of 10⁴ to 10¹³ were considered. The steady‐state two‐dimensional momentum and energy equations were solved using a validated numerical model. The numerical results in terms of Nusselt numbers, Rayleigh numbers, aspect ratio (AR), and flow/temperature distribution over the plate are presented. The variations in the heat transfer coefficient and temperature contours with Rayleigh number and AR of waves were concentrated for both the elliptical and sinusoidal configurations of the plate. The results obtained indicate that the enhancement in heat transfer rate from the heated plate depends on the Rayleigh number, the AR of waves, plate configuration, and the Prandtl number.     

NATURAL CONVECTION IN VERTICAL PARALLEL PLATES WITH AN UNHEATED ENTRY OR UN HEATED EXIT

This study aims to investigate the effects of the unhealed entry or unheated exit section on the free convection heat transfer in airflow in vertical parallel plate channels resulting from the thermal boundary conditions of uniform heat flux (VHF) and uniform wall temperature (UWT). Results of average Nusselt number and dimensionless volume flow rate are presented in terms of the ratio of the length of heated section to the full channel length and a Rayleigh number, ranging from the limit for the fully developed flow to that for single-plate behavior. Analytical equations for dimensionless volume flow rate and average Nusselt number for both unheated restrictions and both thermal boundary conditions have been developed for the fully developed flow limit. The numerical solutions are shown to approach asymptotically the approximate solution for fully developed flow as the Rayleigh number approaches 1 or less. An important finding of the study is that an unheated exit characterizes greater total heat transfer and volume flow rate than an unheated entry does. The presence of the unheated entry or unheated exit severely affects the convection process, especially at low Rayleigh number. A notable effect of an unheated exit on convection characteristics was found for the case of UHF at high Rayleigh number.     

EFFECT OF BUOYANCY ON FORCED CONVECTION IN A CUSPED DUCT

ABSTRACT

In the event of a loss of coolant accident in a pressurized water reactor, swelling of the fuel rod cladding will lead to reduction of the subchannel flow area and worsening of the core heat transfer in the region of the blockage. The four-cusped duct is an ideal geometry for the simulation of such a channel blockage. Understanding the characteristics of flow and heat transfer in the cusped duct is essential for better design of the emergency core cooling system. Thus, in this paper, combined natural and forced convection in a vertical cusped duct has been investigated in the region of both hydrodynamically and thermally fully developed flow. The thermal boundary condition imposed on the cusped duct is the axial uniform heat flux with peripheral uniform temperature. The results indicate that the fluid flow and heal transfer in the comer region of the cusped duct are improved because of the influence of natural convection. As the Rayleigh number increases, the friction factor and Nusselt number increase accordingly. It was also found that the critical Rayleigh number is 1200, at which flow reversal occurs in the buoyancy-assisted flow ( heated upflow). The velocity, temperature, and local Nusselt number distribution are presented for a range of Rayleigh numbers.     

COMBINED RADIATION AND LAMINAR MIXED CONVECTION IN THE THERMAL ENTRANCE REGION OF HORIZONTAL ISOTHERMAL RECTANGULAR CHANNELS

The interaction of thermal radiation with laminar mixed convection for a gray fluid in the thermal entrance region of a horizontal isothermally heated rectangular channel is numerically investigated. The vorticity-velocity formulation of the Navier-Stokes equation and the integral formulation for radiation solved by finite-element nodal approximation are employed. The effects of radiation and convection on local Nusselt number, the development of bulk temperature, and the friction factor are examined. Secondary flow induced by the buoyancy effects leads to a significant enhancement in heat transfer in the entrance region. The result shows that the existence of secondary flow causes fluctuations in local Nusselt number and this phenomenon is reduced by the effect of thermal radiation and a large aspect ratio.     

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.     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Transient numerical analysis of a multi-layered porous heat exchanger including gas radiation effects

Thermal characteristics of a new type of multi-layered porous heat exchanger (PHE) are identified in the present study. This system works based on the energy conversion between gas enthalpy and thermal radiation. It has a five-layered structure consisting of two high temperature, two heat recovery and one low temperature sections. These sections are separated from each other by four quartz glass windows. In the two high temperature sections, the enthalpy of high temperature gas flow is converted to thermal radiation that is emitted toward the three adjacent layers where the low temperature air flows are effectively heated by the reverse conversion from thermal radiation into gas enthalpy. The gaseous radiation is also considered, such that in each section, a transient theoretical analysis is conducted for a one-dimensional system where convection, conduction and radiation take place simultaneously in both gas and solid phases. The coupled energy equations for the gas flows and porous layers based on the two-flux radiation model are solved numerically to identify the transient heat transfer characteristics of the system. It is shown that this type of porous heat exchanger has a very high efficiency especially when the porous layers have high optical thicknesses.     

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     

Free convection suppression using honeycomb cellular materials

It is well-known that an undisturbed layer of air forms an effective insulating barrier against heat transfer because of its low thermal conductivity. In confined air spaces any initiation of free convection will inevitably lead to an increase in the rate of heat transfer across the gap for a fixed temperature difference. To delay the onset of convection for horizontal layers of fluid it has been shown theoretically and experimentally that the introduction of cell walls will effectively raise the critical Rayleigh number by providing more shear surfaces within the fluid. This paper reports on some of the earlier work dealing with the horizontal cell (this being vertical cellular constraining walls within a horizontal fluid layer) and extends the theory to cover the case of the inclined cell and the vertical cell. The photographic results of flow visualization studies are also presented as it is felt that an inspection of the flow patterns leads to a fuller understanding of the problem. Whereas the concept of the critical Rayleigh number is quite valid for the horizontal layer of fluid heated from below, it is shown to be inadequate for the inclined fluid layer as would be found in an inclined solar absorber of the flat plate type. Instead, the solutions of the equations show that convection must be initiated for any temperature gradient to be established between the absorber plate and the glass cover plate. Although the honeycomb may be effective in suppressing convection in the horizontal case, the effect of such constraints on the fluid in the inclined case is negligible as far as suppression of natural convection is concerned.     

Performance of solar air heater ducts with different types of ribs on the absorber plate

Repeated ribs are considered an effective technique to enhance forced convection heat transfer in channels. In order to establish the performance of rib-roughened channels, both heat transfer and friction characteristics have to be accounted for. In the present paper, heat transfer coefficients and friction factors have been experimentally investigated for a rectangular channel having one wall roughened by repeated ribs and heated at uniform flux, while the remaining three walls were smooth and insulated. Angled continuous ribs, transverse continuous and broken ribs, and discrete V-shaped ribs were considered as rib configurations. Different performance evaluation criteria, based on energy balance or entropy generation analysis, were proposed to assess the relative merit of each rib configuration. All the rib-roughened channels performed better than the reference smooth channel in the medium-low range of the investigated Reynolds number values, which is that typically encountered in solar air heater applications.     

Numerical investigation of heat and mass transfer from an evaporating meniscus in a heated open groove

The process of evaporation from a meniscus into air is more complicated than in enclosed chambers filled with pure vapor. The vapor pressure at the liquid–gas interface depends on both of the evaporation and the vapor transport in the gas environment. Heat and mass transport from an evaporating meniscus in an open heated V-groove is numerically investigated and the results are compared to experiments. The evaporation is coupled to the vapor transport in the gas domain. Conjugate heat transfer is considered in the solid walls, and the liquid and gas domains. The flow induced in the liquid due to Marangoni effects, as well as natural convection in the gas due to thermal expansivity and vapor concentration gradients are simulated. The calculated evaporation rates are found to agree reasonably well with experimentally measured values. The convection in the gas domain has a significant influence on the overall heat transfer and the wall temperature distribution. The evaporation rate near the contact lines on either end of the meniscus is high. Heat transfer through the thin liquid film near the heated wall is found to be very efficient. A small temperature valley is obtained at the contact line which is consistent with the experimental observation.     

Three-Dimensional Study of Natural Convection in a Horizontal Channel With Discrete Heaters on One of Its Vertical Walls

Three-dimensional natural convection in a horizontal channel with an array of discrete flush-mounted heaters on one of its vertical walls is numerically studied. Effects of thermal conductivities of substrate and heaters and convection on outer sides of the channel walls on heat transfer are examined. The substrate affects heat transfer in a wider range of thermal conductivities than do the heaters. At lower heater thermal conductivities a higher heat portion is transferred by direct convection from the heaters to the adjacent coolant. However, higher substrate conductivity is associated with higher heat portion transferred through the substrate. The innermost heater column is found to become the hottest heater column due to the lower coolant accessibility. The heat transfer in the channel is strongly influenced by convection on the outer sides of the channel walls. Correlations are presented for dimensionless temperature maximum and average Nusselt number.     

Numerical simulation of natural convection in a horizontal enclosure with a heat-generating conducting body

The physical model considered here is a horizontal layer of fluid heated below and cold above with heat-generating conducting body placed at the center of the layer. The dimensionless thermal conductivities of body considered in the present study are 0.1, 1 and 50. The dimensionless temperature difference ratios considered are 0.0, 0.25, 2.5 and 25. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral methodology for variety of Rayleigh number from 10³ to 10⁶. Multi-domain technique is used to handle square-shaped heat-generating conducting body. The fluid flow, heat transfer and time- and surface-averaged Nusselt number are investigated for various ranges of Rayleigh number, thermal conductivity ratio and dimensionless temperature difference ratio. The results for the case of conducting body with heat generation are also compared to those without heat generation to see the effects of heat generation from the conducting body on the fluid flow and heat transfer in the enclosure.     

An autonomous system for thermal convection of viscoelastic fluids in a porous layer using a thermal nonequilibrium model

Thermal convection of viscoelastic fluids saturating a horizontal porous layer heated from below is analyzed using a thermal nonequilibrium model to take account of the interphase heat transfer between the fluid and the solid. The viscoelastic character of the flow is considered by a modified Darcy’s law. An autonomous system with five differential equations is deduced by applying the truncated Galerkin expansion to the momentum and heat transfer equations. The effects of interphase heat transfer H on the thermal convection of viscoelastic fluids in a porous medium are analyzed and discussed. The results show that the weak interphase heat transfer tends to stabilize the steady convection.