Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side

A numerical study has been carried out in rectangular enclosures, which have a vertical active wall with all the other walls insulated. The equally divided active sidewall is heated and cooled with sinusoidal temperature profiles. Two cases have been considered: the first is the lower part is heated while the upper part is cooled and the second, the upper part is heated and lower part is cooled. Steady state heat transfer by laminar natural convection has been studied by numerically solving equations of mass, momentum and energy, to determine the thermal penetration in the enclosures and heat transfer as a function of Rayleigh number, the aspect ratio and the position of side heating with respect to side cooling. Rayleigh number was varied from 10³ to 10⁶ and the aspect ratio from 0.2 to 5, and the results are presented in the form of streamlines and isotherms, local and average Nusselt number, and heat penetration length. It is found that the penetration approaches to 100% at high Rayleigh numbers when the lower part is heated while the higher part is cooled. In the case of the higher part is heated and the lower part is cooled, the penetration is limited to 70% passing through maxima at Rayleigh number below 10⁶.     

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.     

Turbulent natural convection in an enclosure with localized heating from below

This study reports the results of a numerical investigation of turbulent natural convection in a square enclosure with localized heating from below and symmetrical cooling from the vertical side walls. The present study simulates the case of an accidental heat generation due to fire in a typical isolated building of a nuclear reactor or electronic components cabin. The source of fire is considered to be centrally located at the bottom wall with different heated widths, which is assumed to be either isothermal or with isoflux. For the purpose of the analysis, the source length is varied from 20 to 80% of the total width of the bottom wall. The top wall and the unheated portion of the bottom wall are considered to be adiabatic, whereas sidewalls are isothermal. Steady as well as transient forms of two-dimensional Reynolds–Averaged-Navier–Stokes equations and conservation equations of mass and energy, coupled with the Boussinesq approximation, are solved by the control volume based discretisation method employing the SIMPLE algorithm for pressure–velocity coupling. Turbulence is modeled using the standard k–ε model. Rayleigh number, Ra, based on the enclosure height is varied from 10⁸ to 10¹². Stream lines and isotherms are presented for various combinations of Ra and the heated width. A double cell flow pattern is observed with marginal loss in symmetry as Ra increases. The results are reported in the form of local and average Nusselt number on the heated floor. Correlations are developed to predict the heat transfer rates from the enclosure as a function of dimensionless heated width of the bottom wall and Ra, by least square linear regression analysis.     

Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure

In this paper, numerical simulations of laminar, steady, two-dimensional natural convection flows in a square enclosure with discrete heat sources on the left and bottom walls are presented using a finite-volume method. Two different orientated wall boundary conditions are designed to investigate the natural convection features. The computational results are expressed in the form of streamlines and isothermal lines for Rayleigh numbers ranging from 10² to 10⁷ in the cavity. In the course of study, a combination of third-order and exponential interpolating profile based on the convective boundedness criterion is proposed and tested against the partially heated cavity flow up to the highest Rayleigh number 10⁷. The effects of thermal strength and heating length on the hydrodynamic and thermal fields inside the enclosure are also presented. Numerical results indicate that the average Nusselt number increases as Rayleigh number increases for both cases. Moreover, it is seen that the effect of the heat transfer rate due to the heating strength on the left wall is different from the one on the bottom. For the heater size effect, it is observed that by increasing the length of heat source segment, the heat transfer rate is gradually increased for both cases.     

NATURAL CONVECTION OVER A ROTATING CYLINDRICAL HEAT SOURCE IN A RECTANGULAR ENCLOSURE

A numerical study of laminar two-dimensional natural convection heat transfer from a uniformly heated horizontal cylinder rotating about its center, and placed in an isothermal rectangular enclosure, is performed using a spectral element method. The physical aspects of the flow and its thermal behavior are studied for a wide range of pure natural convection to mixed convection at low and high rotational speeds of the cylinder. The computer program has been validated against experimental correlations available on pure natural convection of heated bodies in enclosures. The rotation of the cylinder has been found to enhance the heat transfer. At low ratios of Rayleigh number to the square of the rotational Reynolds number, Ra / Re_ω ², the maximum temperature on the cylinder surface is decreased by as much as 25–35% from similar cases with fixed cylinders. At moderate values of Ra/ Re_ω ², the thermal plume rising above the cylinder is shifted in the rotation direction and the angular shift decreases as Ra / Re_ω increases. The rotation produces more uniform temperature and shear stress distributions around the cylinder surface. At high Rayleigh numbers the increase in rotation reduces the cylinder mean Nusselt number by 2–10% as compared with the fixed cylinder.     

Numerical study of natural convection and acoustic waves using the lattice Boltzmann method

In this paper, the lattice Boltzmann method is used to study the acoustic waves propagation inside a differentially heated square enclosure filled with air. The waves are generated by a point sound source located at the center of this cavity. The main aim of this simulation is to simulate the interaction between the thermal convection and the propagation of these acoustic waves. The results have been validated with those obtained in the literature and show that the effect of natural convection on the acoustic waves propagation is almost negligible for low Rayleigh numbers (Ra ≤ 10⁴), which begins to appear when the Rayleigh number begins to become important (Ra ≥ 10⁵) and it becomes considerable for large Rayleigh numbers (Ra ≥ 10⁶) where the thermal convection is important.     

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.     

Lattice Boltzmann Simulation of Natural Convection in a Differentially Heated Square Enclosure Containing Heat Generating Low‐Prandtl Number Fluid

Lattice Boltzmann simulations were conducted for the free convective flow of a low‐Prandtl number (Pr = 0.0321) fluid with internal heat generation in a square enclosure having adiabatic top and bottom walls and isothermal side walls. The problem of free convection with volumetric heat source has represented itself in connection with advanced engineering applications, such as water‐cooled lithium–lead breeder blankets for nuclear fusion reactors and liquid metal sources of spallation neutrons for subcritical fission systems. A single relaxation time (SRT) thermal lattice Boltzmann method (LBM) was employed. While applying SRT, a D2Q9 model was used to simulate the flow field and temperature field. Results have been obtained for various Rayleigh numbers characterizing internal and external heating from 10³ to 10⁶. Flow and temperature fields in terms of stream function and isotherms in the enclosure were predicted for these cases. The temperature of the fluid in the enclosure was found higher than the heated wall temperature at high values of internal Rayleigh numbers. The internal heat generation affected the rate of heat transfer significantly as two convection loops are observed in the enclosure. The average Nusselt number at the heated and cold wall was determined for all the cases.     

Double dispersion,natural convection in an open end cavity simulation via Lattice Boltzmann Method

Double dispersion in an open end cavities are simulated using Lattice Boltzmann Method (LBM). The flow is driven by the buoyancy effect due to the heated vertical wall and species concentration at the heated wall of the cavity (closed end). The paper is intended to address the physics of flow, heat and mass transfers in open ended cavities and close end slots. Prandtl number (Pr) is fixed to 0.71 (air) for the thermal Rayleigh number (Ra_T) of 10⁴, 10⁵ and 10⁶. The results are presented for moderate Lewis number of 2, 4 and 8 and for a range of buoyancy ratio, N, (species to thermal). The species concentration induced buoyancy force either aids or opposes the thermally driven flow, which is determined by the value of buoyancy ratio (positive or negative, respectively). Interesting flow patterns were predicted for opposing buoyancy forces.     

Distribution of heat sources in vertical open channels with natural convection

In this paper we use the constructal method to determine the optimal distribution and sizes of discrete heat sources in a vertical open channel cooled by natural convection. Two classes of geometries are considered: (i) heat sources with fixed size and fixed heat flux, and (ii) single heat source with variable size and fixed total heat current. In both classes, the objective is the maximization of the global thermal conductance between the discretely heated wall and the cold fluid. This objective is equivalent to minimizing temperature of the hot spot that occurs at a point on the wall. The numerical results show that for low Rayleigh numbers (∼10²), the heat sources select as optimal location the inlet plane of the channel. For configuration (i), the optimal location changes as the Rayleigh number increases, and the last (downstream) heat source tends to migrate toward the exit plane, which results in a non-uniform distribution of heat sources on the wall. For configuration (ii) we also show that at low and moderate Rayleigh numbers (Ra_M ∼ 10² and 10³) the thermal performance is maximized when the heat source does not cover the entire wall. As the flow intensity increases, the optimal heat source size approaches the height of the wall. The importance to free the flow geometry to morph toward the configuration of minimal global resistance (maximal flow access) is also discussed.     

Numerical Investigation of Natural Convection in an Enclosure Filled with Porous Medium Under Magnetic Field

In this study, natural convection in an enclosure filled with a fluid-saturated porous medium in a strong magnetic field is investigated numerically. Two physical models are considered. One is heated from the bottom and cooled from the top (Model A), and the other is heated from the left side vertical wall and cooled from the opposite wall (Model B). An electric coil is set below this enclosure to generate a magnetic field. The Brinkman-Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for the fluid and solid are solved with the local thermal nonequilibrium (LTNE) model. The linkage between velocity and pressure is handled with the SIMPLE algorithm. Computations are performed for a range of Darcy number from 10^?5 to 10^?1, Rayleigh number from 10³ to 10⁵, and magnetic force parameter γ from 0 to 100. The results show that the magnetic force has significant effect on the flow field and heat transfer in the fluid-saturated porous medium.     

Mixed Convection in an Obstructed Open-Ended Cavity

Mixed convection in an obstructed cavity with heated horizontal walls is investigated in this work. Brinkman-Forchheimer-extended Darcy model is utilized to describe the flow characteristics within a porous medium for different angles of attack with respect to the forced convection. Numerical results are obtained for a wide range of Grashof numbers (10²–10⁹), Reynolds numbers (10²–10⁵), Darcy numbers (10^?6–10^?1), and aspect ratios (0.25–2). Effects of the pertinent physical parameters are investigated in terms of the flow and temperature fields, as well as Nusselt number distributions. The presented results show that the Darcy number plays a significant role on the flow and thermal fields and the Nusselt number distributions for different flow configurations. For an inclined flow, the vertical velocity component is substantially diminished within a narrow entrance section near the inlet boundary. It is shown that as the aspect ratio increases the thickness of the thermal boundary layer increases, resulting in a decrease in the heat transfer rate though the horizontal walls.     

Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with Linearly Heated Wall(s)

In this study, the lattice Boltzmann method is used in order to investigate the natural convection in a cavity with linearly heated wall(s). The bottom wall is heated uniformly and the vertical wall(s) are heated linearly, whereas the top wall is insulated. Investigation has been conducted for Rayleigh numbers of 10³ to 10⁵, while Prandtl number is varied from 0.7 to 10. The effects of an increase in Rayleigh number and Prandtl number on streamlines, isotherm counters, local Nusselt number and average Nusselt number are depicted. It has been observed that the average Nusselt number at the bottom wall augments with an increase in Prandtl number.     

Heat transfer in free convection-dominated melting of a phase change material in a horizontal annulus

Heat transfer during melting in enclosures is important in the design of heat exchangers using phase change materials (PCM) for latent heat thermal energy storage. In this paper, the finite element method is employed to simulate the convection-dominated melting of a PCM in a cylindrical-horizontal annulus heated isothermally from the inside wall. The effects of Rayleigh number on the melting rate as well as the evolution of the flow pattern are examined. Results of the numerical experiments reveal that an increases in Rayleigh number promotes heat transfer rate. Multiple cellular pattern is observed at high Rayleigh numbers (10⁶).     

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.     

Impingement heat transfer of a single thermal plume on the upper wall

We present numerical calculations of the generation, growth and impingement of a thermal plume in a two-dimensional buoyancy induced flow. Numerical values are obtained for the aspect ratios H/W=1/4, 3/8, 1/2, the Grashof numbers Gr=10⁴, 10⁵, and the Prandtl number Pr=170. Impingement heat transfer on the upper wall is evaluated at various times. Numerical results show that before a thermal plume impinges on the upper heated wall, the thermal conduction layer, which is the stable stratification, near the upper wall becomes thinner and the local heat transfer peaks. The local Nusselt number approaches the steady condition after the impingement of a thermal plume. Additionally, under certain conditions the stream function takes a symmetrical form of two ellipses.     

A numerical study of three-dimensional laminar mixed convection past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective flow over a three-dimensional cavity that lies at the bottom of a horizontal channel. The vertical walls of the cavity are isothermal and all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar and incompressible. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall over a wide range of the Grashof number (10³–10⁶) and two Reynolds numbers Re = 100 and 1000. The computed thermal and flow fields are displayed and discussed in terms of the velocity fields, streamlines, the temperature distribution and the averaged Nusselt number at the heated and cooled walls. It is found that the flow becomes stable at moderate Grashof number and exhibit a three-dimensional structure, while for both high Reynolds and Grashof numbers the mixed convection effects come into play, push the recirculating zone further upstream and the flow becomes unsteady with Kelvin–Helmholtz instabilities at the shear layer.     

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.     

TRANSIENT BUOYANCY-INDUCED FLOW THROUGH A HEATED,VERTICAL CHANNEL OF FINITE HEIGHT

A detailed numerical analysis is carried out to study the transient natural convection in a symmetrically heated vertical plate channel of finite height due to a step change in plate temperature. Both the inlet and exit effects are included in the analysis. In particular, a numerical scheme derived from the SIMPLER algorithm is employed to solve the governing differential equations. Emphasis is placed on the temporal evolution of the flow and thermal characteristics. Results are obtained for air with Ra varying from 10³ to 10⁶ and the aspect ratio from 5 to 10. The existence of multiple cells in the channel and in the region surrounding the top end during the transient stage is predicted. Over a certain period, temperature overshoot is noted, causing a dip in the time variation of the Nusselt number. Correlation equations are proposed for the average Nusselt number and the amount of air drawn into the channel at the steady state.     

Effect of nanofluid variable properties on natural convection in enclosures

In this work, the heat transfer enhancement in a differentially heated enclosure using variable thermal conductivity and variable viscosity of Al₂O₃–water and CuO–water nanofluids is investigated. The results are presented over a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 9%), and aspect ratios (½ ≤ A ≤ 2). For an enclosure with unity aspect ratio, the average Nusselt number of a Al₂O₃–water nanofluid at high Rayleigh numbers was reduced by increasing the volume fraction of nanoparticles above 5%. However, at low Rayleigh numbers, the average Nusselt number was slightly enhanced by increasing the volume fraction of nanoparticles. At high Rayleigh numbers, CuO–water nanofluids manifest a continuous decrease in Nusselt number as the volume fraction of nanoparticles is increased. However, the Nusselt number was not sensitive to the volume fraction at low Rayleigh numbers. The Nusselt number demonstrates to be sensitive to the aspect ratio. It was observed that enclosures, having high aspect ratios, experience more deterioration in the average Nusselt number when compared to enclosures having low aspect ratios. The variable thermal conductivity and variable viscosity models were compared to both the Maxwell-Garnett model and the Brinkman model. It was found that at high Rayleigh numbers the average Nusselt number was more sensitive to the viscosity models than to the thermal conductivity models.