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.     

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.     

NATURAL CONVECTION IN OPEN CAVITIES AND SLOTS

The present work is concerned with natural convection from open cavities or heated plates attached with parallel vertical strips. The bottom of the cavity is heated, and the vertical walls are assumed adiabatic. Numerical results are presented for steady, laminar natural convection for the geometry described. Effects of Rayleigh numbers from 1 × 10 ³ to 1 × 10 ⁷ , inclination angles from 10^° to 90^°, and aspect ratios of 0.5, 1.0, and 2.0 are investigated for a fixed Prandtl number (0.7). It is found that the average Nusselt number is not very sensitive to the inclination angle. Flow becomes unstable at high Rayleigh numbers and at low inclination angles. Flow pattern and heat transfer results are presented and discussed.     

TRANSIENT NATURAL CONVECTION IN A CYLINDRICAL ENCLOSURE NONUNIFORMLY HEATED AT THE TOP WALL

Transient natural convection in a cylindrical enclosure heated nonumformly at the top wall is studied numerically. The primitive forms of the time-dependent governing equations are solved by a semi-implicit finite difference method. Grid-independent results are obtained by using uniform as well as nonuniform grids. The range of Rayleigh numbers considered is 70 to 7 × I0⁷, which includes both conduction-dominated and convection-dominated regimes. The effect of thermal boundary conditions is examined in detail. An extensive flow visualization study is conducted that employs a novel heat flow visualization technique based on the “ heatline” concept in addition to velocity vector, streamline, and isotherm plots. The flow visualization indicates that, in the convection-dominated regime, the unicellular motion degenerates into a multicellular motion, resulting in the stratification of the temperature field in the axial direction. The number of cells formed depends strongly on the Rayleigh number and the thermal boundary conditions employed. Heat transfer results are also reported by correlation of Nusselt and Rayleigh numbers.     

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.     

NUMERICAL ANALYSIS OF NATURAL CONVECTION IN CAVITIES WITH VARIABLE POROSITY

This work analyzes the effects of variable porosity on the heat transfer by natural convection, in a cavity with isothermal vertical walls and adiabatic horizontal ones and a porous medium inside. The hydrodynamic field in the porous medium is modelled according to the general model obtained by Brinkman's and Forchheimer's terms. An exponential variation of the porosity near the walls was considered. The equations in terms of the real variables were numerically solved by the finite-volume method, with a staggered variables arrangement. The pressure-velocity coupling was treated with the PRIME algorithm. The simulations involved both Darcian (Da = 10 -7 ) and non-Darcian flows (Da = 10 -6 ). In each case, the modified Rayleigh range (Ra m = Ra 2 Da) was from 10 to 1,000, and from 100 to 5,000, respectively. For the numerical simulation we considered Pr = 1, Rk = 1, A = 1, and k X = 0.36. The results are shown through streamlines and isotherms and velocity and temperatures profiles. This shows that the generalized method with variable porosity means an increase in the average Nusselt number. For physical validation, some experimental sets were simulated in which glass was the porous medium, and water, alcohol, and transformer oil were used as the fluids. The simulated results indicate that the adopted model reduces the discrepancy in the experimental results obtained with water and alcohol. We proposed a correlation to evaluate the average Nusselt number as a function of six parameters: Rayleigh number, Prandtl number, the dimensionless particle diameter, thermal conductivity ratio between solid and fluid phase, porosity, and the aspect ratio of the cavity.     

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.     

MIXED CONVECTION IN A RECTANGULAR ENCLOSURE WITH DISCRETE HEAT SOURCES

A numerical study is carried out on mixed convective heat transfer in an enclosure. The discrete heat sources are embedded on a vertical board, which is situated on the bottom wall of an enclosure. An external airflow enters the enclosure through an opening in one vertical wall and exits from another opening in the opposite wall. This study simulates a practical system, such as air-cooled electronic devices with heated elements. Emphasis is placed on the influence of the governing parameters, such as Reynolds number, Re, buoyancy parameter, Gr/Re², location of the heat sources, and the conductivity ratio, rk, on the thermal phenomenon in the enclosure. The coupled equations of the simulated model are solved numerically using the cubic spline collocation method. The computational results indicate that both the thermal field and the average Nusselt number (Nu) depend strongly on the governing parameters, position of the heat sources, as well as the property of the heat-source-embedded board.     

NATURAL CONVECTION IN A DIFFERENTIALLY HEATED SQUARE CAVITY WITH INTERNAL HEAT GENERATION

A high-resolution, finite-difference numerical study is reported on natural convection in a square cavity. The vertical sidewatts of the cavity are differentially heated, and a uniform internal heat generation is also present. Two principal parameters are considered, the internal Rayleigh number Ra_I, which represents the strength of the internal heat generation, and the external Rayleigh number Rag, which denotes the effect due to the differential heating of the side walls. The internal Rayleigh number varies in the range 10¹⁰ Ra_I ≤ 10⁷, while the external Rayleigh number is set at Ra_E = 5 x 10⁷ for most computations. As the relative strength of the internal heat generation increases, the flows near the tap portion of the heated sidewall are directed downward. When the effect of the internal heat generation is dominant, the thermal energy leaves the system for the surroundings over the top portion of the heated wall. Only in the bottom pari of the heated wall is heat transfer directed into the system. These numerical solutions are in qualitative agreement with the available experimental measurements.     

TRANSIENT NATURAL CONVECTION INSIDE POROUS CAVITIES: HYBRID NUMERICAL-ANALYTICAL SOLUTION AND MIXED SYMBOLIC-NUMERICAL COMPUTATION

A hybrid numerical-analytical solution for two-dimensional transient-free convection is presented and applied to a vertical porous cavity, based on application of the ideas in the generalized integral transform technique (GITT). The integral transformation process reduces the original coupled partial differential equations (PDEs), for stream function and temperature, into an infinite system of nonlinear ordinary differential equations (ODEs) for the transformed potentials, which is adaptively truncated and numerically solved through subroutine NDSolve from the Mathematica software system. All the analytical steps in the solution procedure are symbolically evaluated through the Mathematica package, mixing with the numerical computations and graphic representation.     

NATURAL CONVECTION AIR COOLING OF HEATED COMPONENTS MOUNTED ON A VERTICAL WALL

The present paper discusses a numerical study of natural-convection air cooling of single and multiple uniformly heated devices. A two-dimensional, conjugate, laminar-flow model is used. The solid and fluid physical properties are assumed constant (not varying with temperature). For the multicomponent cooling, the effects of component thickness, the spacing between components, nonpowered components, and highly powered components are studied to arrive at qualitative suggestions that may improve the overall cooling of a multicomponent system.     

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.     

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.     

BUOYANT CONVECTION IN A CAVITY WITH A BAFFLE UNDER TIME-PERIODIC WALL TEMPERATURE

A numerical study is made of buoyant convection at high Rayleigh number in a square cavity that contains a horizontal baffle at midheight. The horizontal walls of the cavity are insulated. At the cold left vertical wall, the nondimensional temperature is constant θ = 0, and at the hot right vertical wall, the wall temperature is time periodic, θ     

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.     

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.     

NATURAL CONVECTION IN TRAPEZOIDAL CAVITIES WITH BAFFLES MOUNTED ON THE UPPER INCLINED SURFACES

A numerical investigation has been undertaken to study the effects of mounting baffles to the upper inclined planes of trapezoidal cavities (representing a building or attic space). Two thermal boundary conditions are considered: (a) the vertical and upper surfaces are heated while the lower surface is cooled (summerlike conditions); (b) the lower surface is heated while the other surfaces are cooled (winterlike conditions). For each boundary condition, computations are performed for two baffle heights and two baffle locations. Rayleigh number (Ra) values range from 10³ to 5 x 10⁷ for summerlike conditions and from 10³ to 10⁶ for winterlike conditions. For both boundary conditions, results obtained with air as the working fluid reveal a decrease in heat transfer in the presence of baffles. In winterlike conditions, convection starts to dominate at an Ra much lower than that in summerlike conditions. The decrease in heat transfer becomes increasingly more significant as the baffle gets closer to the heated vertical wall for the bottom-cooled situation and as the baffle gets closer to the symmetry line for the bottom-heated case. In general, this decrease in heat transfer is higher with taller baffles. Average Nusselt number (Nu) correlations for both boundary conditions are presented.     

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.     

EVOLUTION TO CHAOTIC NATURAL CONVECTION IN A RECTANGULAR ENCLOSURE WITH MIXED BOUNDARY CONDITIONS

The purpose of this numerical study is to analyze the characteristics of transition from laminar to chaotic natural convection in a fluid-filled two-dimensional, unity aspect ratio rectangular cavity with mixed thermal boundary conditions. For a medium Prandtl number fluid ( Pr ) the numerical solution of the two-dimensional Navier-Stokes momentum and energy equation with Bousinessq approximation, it is found that there are finite Rayleigh numbers Ral Ra2, and Ra3 for the onset of single-, double-, and multiple-frequency oscillatory motion at different spatial locations in the enclosure. As Ra increases, the flow exhibits a change from steady convection to periodic to quasi-periodic flow, while no period doubting is observed. The onset of strong chaos appears when Ra = 57,000 Rac. This system does not revert to steady state convection for Rac as high as 285,000. As Ra increases, various measures of chaos, such as power spectrum, Poincare sections, phase portrait, and time series of various dynamical variable signals, all show an increasing degree of characteristics of chaos,     

NUMERICAL INVESTIGATION OF CONVECTION HEAT TRANSFER IN A HEATED ROOM

We describe numerical investigation of airflow and temperature field in a room with a convective heat source. The simulation involves using computational fluid dynamics (CFD) to validate different turbulence models, i.e., the standard k- k model and the low Reynolds number k- k model. The comparisons between computations and experiments show good and acceptable agreement. It can be concluded that the CFD simulations can capture the main flow features and provide satisfactory results. It can be seen that the thermal wall jet created by the heat source greatly influences airflow pattern and temperature field in the room. It can also be seen that the advanced turbulence model may produce better results than the standard one under a suitable mesh scheme.