LAMINAR FULLY DEVELOPED MIXED CONVECTION IN INCLINED TUBES UNIFORMLY HEATED ON THEIR OUTER SURFACE

The problem of conjugate heat transfer involving mixed convection laminar ascending flow of water in inclined circular tubes uniformly heated on their outer surface has been studied numerically using a unified formulation for the solid and fluid domains. The highly coupled governing equations were discretized using the control volume approach, and solved according to the SIMPLER algorithm. Results have clearly demonstrated that the conduction within the tube wall has an important influence on both the hydrodynamic and thermal fields. High wall thermal conductivity or large thickness reduces the temperature stratification within the fluid and intensifies the secondary motion, consisting of two symmetrical vortices. The effects of wall conduction are particularly significant for horizontal tubes for which the average Nusselt number is bounded by two limits corresponding to the cases of infinite wall thermal conductivity and zero wall thermal conductivity. For Gr = 2 × 10⁵ these limits are 10.42 and 9.03, respectively. These effects are negligible for tubes inclined at 30° and for Grashof number below 3 × 10⁴.     

NATURAL CONVECTION ABOVE AN ARRAY OF OPEN CAVITIES HEATED FROM BELOW

Abstract

The effect of buoyancy on the flow and heat transfer that develop between a horizontal cold surface and an infinite two-dimensional array of open cavities heated from below is studied numerically. In earlier investigations the steady-state features of this problem were studied for the case of unbounded flow above the cavities. The resulting flow pattern was found to be symmetrical with respect to the centerlines of the cavities. In the present work it is shown that the symmetry of the flow can be destroyed due to the presence of an upper wall. The evolutionary path to steady-state flow is examined, and sustained oscillatory behavior has been observed in several cases. The solution structure is governed by five parameters, i.e., the geometric parameters A = l'/H', B = h'/H', and C = L'/H', the Rayleigh number Ra = gβ ΔT' H' ³/av, and the Prandtl number Pr = v/α. For a geometry with A = ½z, B = ¼, and C = 1, a complicated solution structure is observed upon increasing the Rayleigh number. For Ra ≤ 4 × 10³, a steady symmetric two-cell pattern is observed. This pattern becomes asymmetric for 4 × 10³ < Ra ≤ 9 × 10⁴, periodic for Ra ≤ 3 × 10⁵ and chaotic above that. The transition to periodic convection occurs at lower Rayleigh numbers with decreasing B.     

FREE CONVECTION IN OPEN-TOP ENCLOSURES FILLED WITH A POROUS MEDIUM HEATED FROM BELOW

Free convection is studied for porous medium-filled enclosures that are open for fluid flow at the top. For such setups a mixed boundary condition for the transport variable at the top is examined, which is different from the classical approach (Lapwood problem) in systems where flow is governed by Darcy's law. While the latter led to open and to closed paths within each convection cell, the mixed boundary condition induces open convection cells only. By numerical means, the onset of convection, total heat and mass transfer, and the transition from the first to the second mode are examined. At 16.5, the critical Rayleigh number for the onset of convection in the system with mixed boundary condition is much lower than the classical value.     

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.     

HEAT TRANSFER AUGMENTATION OF MIXED CONVECTION THROUGH VORTEX SHEDDING FROM AN INCLINED PLATE IN A VERTICAL CHANNEL CONTAINING HEATED BLOCKS

A numerical analysis is made of the unsteady flow and heat transfer characteristics of mixed convection in a vertical block-heated channel with and without installing an inclined plate above an upstream block. Parameter studies including the inclined plate angle, Reynolds number (ranging from 260 to 530), and Grashof number (in the range of 0-3,200,000) on heat transfer performance have been explored in detail. The results show that the installation of an inclined plate in the vertical block-heated channel can effectively augment the blocks' heat transfer performance in the channel.     

MIXED CONVECTION FROM A MULTIBLOCK HEATER IN A CHANNEL WITH IMPOSED THERMAL MODULATION

Enhancement of mixed-convection heat transfer in a multiblock heater arrangement in a channel is studied. At the most upstream heated block, a time-periodic heat generation is present, while the heat generation is constant in other heater blocks. The explicit effect of using thermal modulation (time-periodic heat generation) at the upstream heater is examined by acquiring comprehensive numerical solutions. The heat transfer enhancement is pronounced at the heaters at far downstream, and the augmentation is maximized when resonance is realized. The resonance frequency is close to the natural frequency of the system, which scales with the time for the main stream to travel through the interblock region. Plots are illustrated to demonstrate the formations of a pair of circulations downstream of the most upstream heater, which leads to identifying the natural frequency. The increase in the overall pressure drop is calculated. The benefit of heat transfer augmentation, as opposed to the increased pressure drop, is assessed to justify the use of thermal modulation in the upstream heater.     

NUMERICAL INVESTIGATION OF MIXED CONVECTION HEAT TRANSFER IN A HORIZONTAL CHANNEL WITH A BUILT-IN SQUARE CYLINDER

Structures of laminar wakes and heat transfer in the presence of thermal buoyancy art investigated from the numerical solution of complete Navier-Stokes and energy equations in a two-dimensional horizontal channel with a built-in square cylinder. Results show that mixed convection can initiate periodicity and asymmetry in the wake at lower Reynolds numbers than forced convection alone. For a given Reynolds number, the heating of the fluid in the channel is improved by mixed convection up to a certain Grashof number and deteriorates if the Grashof number is further increased.     

MIXED CONVECTION IN CAVITIES WITH A LOCALLY HEATED LOWER WALL AND MOVING SIDEWALLS

An optimal control algorithm for cryopreservation of cells using ultrarapid freezing technique is applied successfully in the present study to determine the strength of optimal laser heating based on the desired limited temperature distribution of the cell. The validity of this optimal control analysis utilizing the conjugate gradient method of minimization is examined using numerical experiments. Three different heating times are given, and the corresponding optimal control heat fluxes are determined. Results show that the optimal boundary heat fluxes can be obtained with any arbitrary initial guesses within a very short CPU time on a Pentium III 600-MHz PC.     

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.     

UNSTEADY FREE CONVECTION IN A VERTICAL CHANNEL WITH A BUILT-IN HEATED SQUARE CYLINDER

The cause of high operating temperatures experienced by grate blocks in a waste-to-energy power plant is investigated. A three-dimensional numerical analysis is performed to assess convection from the grate to the underfire air supply and conduction within the grate. A number of geometric complexities, including variable solid thickness, extended surfaces, sharp curvatures, and narrow passages, are accounted for via a finite element approach. The grate temperature is found to be very sensitive to the flow characteristics beneath the grates. Analysis of a modified grate structure was performed, showing a 14% reduction in maximum grate temperature.     

NATURAL CONVECTION IN A VERTICAL,ASYMMETRICALLY HEATED,PERMEABLE WALLED CHANNEL

Developing natural convection in an asymmetrically heated, open-ended vertical channel was studied both experimentally and numerically. A tightly stretched, perforated, plastic radiation shield was suspended parallel to an electrically heated aluminum plate to form a vertical channel. In order to model the heat transfer and fluid flow in the vertical channel, the unsteady, two-dimensional Navier-Stokes equations were solved using a primitive variable, finite-difference formulation. Flow through the perforated boundary was modeled using a modified form of Darcy's law. Radiative exchange between the boundaries and between the boundaries and the environment was included. The predicted mass flow was within 3% of that measured experimentally. Both the average plate temperature and the bulk exit channel air temperature were within 1·2°C of the measured values. However, the predicted average temperature of the radiation shield was 8°C higher than that measured.     

MIXED CONVECTION IN A CHANNEL WITH POROUS MULTIBLOCKS UNDER IMPOSED THERMAL MODULATION

This study is made of an enhancement of a mixed-convection heat transfer in a channel containing multiple porous blocks heated from below. The heat flux from the most upstream heater varies in a sinusoidal form, while other heaters have a constant heat flux. The Brinkman-Forchheimer-extended Darcy model and two-equation energy model are adopted to characterize the flow and temperature fields inside porous regions. The explicit effect of thermal modulation at the upstream heater is examined by acquiring comprehensive numerical solutions. The heat transfer enhancement is pronounced at the far downstream heaters when resonance is realized. The resonance frequency is close to the characteristic frequency of the system, which scales with the time for the main stream to travel from a heater to a neighboring heater. The evolutions of flow and temperature fields are exemplified to provide physical interpretations. The effects of pore density and of porous block height are reported. The benefit of heat transfer augmentation, as opposed to the increased friction factor, is assessed to justify the use of thermal modulation in the upstream heater.     

MIXED CONVECTION IN AN INCLINED CHANNEL WITH LOCALIZED HEAT SOURCES

Fully developed opposing mixed convection is numerically studied in an inclined channel that has discrete heating on the bottom and is insulated on the top. The numerical approach is based on the hypothesis that the solution is periodic according to the imposed wavelength of the heating elements. Considering that Ike heat produced by the heating elements is totally carried downstream, the temperature increment from one heating element to the other is defined on the basis of an energy balance. To verify the accuracy of the computational code, an analytical study of the extreme case with an entirely heated wall is investigated. Also, to validate that the solution of the problem is periodic with a wavelength corresponding to the imposed perturbation, a channel with entrance and exit sections containing four to six heating elements is simulated numerically. In the present study, the relative strength of the forced flow and buoyancy effects is examined for a broad range of Rayleigh numbers, Reynolds numbers, and inclination angles. Both overall and local recirculating flows are observed that are caused by buoyancy effects on the forced flow.     

EFFECTS OF BINARY MIXTURE CONDENSATION ON TURBULENT MIXED CONVECTION HEAT AND MASS TRANSFER IN A VERTICAL CHANNEL

Abstract

A numerical analysis was carried out to study the detailed heat and mass transfer processes between a condensation liquid film and mixed turbulent moist airflow. Results show that the condensation latent heat transfer is more important for a system with higher inlet relative humidity or lower inlet Reynolds number of a moist airstream. The heat and mass transfer coefficients are higher for a system with higher inlet relative humidity and inlet Reynolds number of moist air. In addition, the aiding-buoyancy forces cause diminution in heat and mass transfer results compared with the corresponding results of forced convection.     

MAGNETOHYDRODYNAMIC MIXED CONVECTION FROM A VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

Magnetohydrodynamic mixed convection flaw about a vertical flat plate embedded in a porous medium is considered. The effect of the magnetic field strength on the local Nusselt number and local wait shear stress is presented. The non-Darcian model including both the inertia and boundary effects is used. A particular transformation for the governing equations is adopted to cover the whole mixed convection regime within two finite limits. Appreciable effects of the magnetic field strength on the local Nusselt number as well as on the local wall shear stress in the mixed convection regime are found.     

CONJUGATE NATURAL CONVECTION FROM A HORIZONTAL CIRCULAR CYLINDER

ABSTRACT

Steady, laminar natural convection flow from a horizontal circular cylinder with a heated core region has been theoretically analyzed by taking account of the thermal conduction of the core region. The problem is conjugate, and the main focus of the study is to examine the effect of conduction in the core region on the natural convection flow from the cylinder. The governing equations were solved numerically using a finite difference technique. The effects of various parameters are presented in graphical form. Approximate solutions for the average boundary temperature at the surface of the cylinder and for the average Nusselt number are also found. In the parametric range investigated, both the theoretical and numerical results predict nearly the same values for the average boundary temperature at the surface of the cylinder and the same values for the average Nusselt number, showing the validity of the present analysis.     

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.     

ON THE PERIODIC CONDITIONS TO SIMULATE MIXED CONVECTION HEAT TRANSFER IN HORIZONTAL CHANNELS

Mixed convection heat transfer in open-ended channels with discrete heating from below is numerically studied when the convection cells remain attached to the heating elements. Two approaches an used: in method A, the computation domain covers the whole channel, while in method B, periodic conditions are imposed at the entrance and exit of a computation domain that is one wavelength long, Nu is calculated as functions of Ra (5 × 10³ ≤ Ra ≤ 20 × 10³) and of Pe (0.1 ≤ Pe ≤ 2.5). The results from two approaches show that method B can adequately be used to calculate heat transfer.