Numerical study of heat transfer by natural convection and surface thermal radiation in an open cavity receiver

In this work the numerical results of natural convection and surface thermal radiation in an open cavity receiver considering large temperature differences and variable fluid properties are presented. Numerical calculations were conducted for Rayleigh number (Ra) values in the range of 10⁴–10⁶. The temperature difference between the hot wall and the bulk fluid (ΔT) was varied between 100 and 400 K, and was represented as a dimensionless temperature difference (φ) for the purpose of generalization of the trends observed. Noticeable differences are observed between the streamlines and temperature fields obtained for φ = 1.333 (ΔT = 400 K) and φ = 0.333 (ΔT = 100 K). The total average Nusselt number in the cavity increased by 79.8% (Ra = 10⁶) and 88.0% (Ra = 10⁴) as φ was varied from 0.333 to 1.333. Furthermore the results indicate that for large temperature differences (0.667 ? φ ? 1.333) the radiative heat transfer is more important that convective heat transfer.     

Computation of surface radiation and natural convection in a heated horticultural greenhouse

This study analyses the effects of the radiation exchange inside a horticultural greenhouse, under winter climatic conditions, according to the number of squared heating tubes used. These ones, hot and isothermal, are equidistant inside the greenhouse volume. The governing differential equations are discretized using a finite volume method and the coupling pressure–velocity problem is carried out by the SIMPLER algorithm. The algebraic systems obtained are solved by a conjugate gradient method. Results are reported in terms of isotherms, streamlines and average Nusselt number for Rayleigh number of 10³–10⁶. The contour lines show that the radiative effects are noted near the solid surfaces, and become increasingly important when the Rayleigh number increases. As a result, the rise in the value of Rayleigh number leads to an increase of the overall heat transfer within the greenhouse.     

Time-dependent natural convection fluid flow of stably stratified fluid in an asymmetrically heated vertical channel filled with an anisotropic porous material

This paper presents a theoretical analysis of the combined effects of anisotropic porous material and thermal stratification on the transient natural convection fluid flow in an asymmetrically heated vertical parallel channel. The solutions of the governing equations for the temperature and velocity fields are obtained using Laplace transform technique, Riemann sum approximation, and the D'Alembert method. The choice of the D'Alembert method is to provide a simple decoupling procedure for the coupled governing equations while still retaining their original orders. The research established that owing to the layering effect induced by the thermal stratification $(S)$, the temperature and the velocity distributions of the fluid are found to be attenuated with an increase in thermal stratification. It is also observed that the inclusion of anisotropic parameters in the transport equations aids in regulating the fluid velocity, temperature, Nusselt number, skin friction, and mass flow rate. In addition, by neglecting the anisotropic parameter and taking into account the adiabatic stratification of the fluid, the numerical values for the mass flow rate of the present research favorably compared with the numerical results obtained by Singh et al.     

Numerical analysis of natural convection in air in a vertical convergent channel with uniformly heated conductive walls

Natural convection in air in a convergent channel with the two principal flat plates at uniform heat flux with finite thickness and thermal conductivity was numerically investigated. Laminar, two-dimensional steady-state conditions were assumed. An extended computational domain was adopted, which allows to take into account the diffusion by both momentum and energy outside the channel. A comparison with experimental data was carried out. Stream function and temperature fields are presented. Average Nusselt numbers were evaluated and presented.Temperature profiles are strongly affected by the convergence angle at low Rayleigh numbers. At the lower minimum gap, streamlines and isotherms show a low pressure region in the channel due to a choked flow in its upper end. Numerical values of the Nusselt number are in good agreement with experimental results.     

Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

Numerical study on natural convection in a square enclosure containing a rectangular heated cylinder

In this paper, the natural convection in a square enclosure with a rectangular heated cylinder is investigated via the lattice Boltzmann method. A detailed study is conducted on the effect of the cylinder width and the Rayleigh number on the fluid flow and heat transfer. The flow structures and heat transfer patterns are classified into eight buoyant regimes, i.e., four steady regimes, two periodic regimes, one multiple periodic regime, and one chaos regime, two of which are reported for the first time.     

Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel

In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10³ ⩽ Ra ⩽ 10⁶ and 5 ⩽ L/b ⩽ 20.     

含加热圆管方腔内自然对流的数值研究

采用数值计算方法对含不同直径圆管以及相同直径圆管位置不同方腔内的层流自然对流进行了研究。以冷热壁面温度差为基准的瑞利数Rn为10^6,以圆管壁面热流密度为基准的Ra为10^8。计算结果表明,当圆管处于方腔中间位置时,随着圆管直径的增大,圆管表面局部努塞尔数呈减小趋势。当圆管直径不变时,由于在不同位置处浮力作用的强弱不同,随着圆管在方腔内位置的改变,方腔内流场结构和温度场分布也会发生变化。整个计算结果可为工程设计提供参考。     

Nusselt number for the natural convection and surface thermal radiation in a square tilted open cavity

In this communication, the numeric results of the heat transfer by natural convection and surface thermal radiation in a tilted 2D open cavity are presented. This study has importance in the thermal design of receivers for solar concentrators. The opposite wall to the aperture in the cavity holds a constant temperature of 500 K, while the temperature of the surrounding fluid interacting with the aperture is 300 K. The other walls are kept insulated. The results in the steady state are obtained for a Rayleigh range from 10⁴ to 10⁷ and for an inclination angles range of the cavity from 0° to 180°. The results show that the Nusselt numbers increase with the Rayleigh number except the convective Nusselt number for 180°, where it stays almost constant. The convective Nusselt number changes substantially with the inclination angle of the cavity, while the radiative Nusselt number is insensitive to the orientation change of the cavity.     

Entropy generation of convection heat transfer in an asymmetrically heated packed duct

An expression for the volumetric rate of entropy generation has been derived and displayed graphically to analyze the convection heat transfer for a fully established flow in a rectangular packed duct with L/H=16 and H/W=0.125. The top and bottom walls of the duct are heated by constant, asymmetric heat fluxes, while the other walls are insulated that is the L2 thermal boundary conditions. Entropy generation maps reveal the regions where excessive entropy generation occurs due to physical and geometric parameters for a specified task within the system.     

Experimental study of forced convection in asymmetrically heated sintered porous channels with/without periodic baffles

This study experimentally determined the local and average heat transfer characteristics in asymmetrically heated sintered porous channels with metallic baffles. The fluid medium was air. Measurements on the test specimen of four modes, without baffles (A), with periodic baffles on the top portion (B), with periodic baffles on the bottom portion (C) and with staggered periodic baffles on both sides (D), are performed. The effect of the average bead diameter was also examined (d = 0.704 and 1.163 mm). The data indicated that, the wall temperatures measured at baffles attached to the heated wall were slightly lower than those nearby, especially at high Reynolds numbers. In modes B and D, the heat transfer in the inlet region was weaker than that in modes A and C. Additionally, the heat transfer by forced convection in all modes increased as the bead diameter decreased. The effect of the bead diameter became stronger as the Reynolds number was increased. At Re > 2000, heat transfer was greatest in mode B and least in mode D, in which the heat transfer was even poorer than that without baffles. For a Re of around 1000, mode D was associated with an excellent heat transfer. In such a case, heat transfer enhancement was around 20 ∼ 30% in mode D, around 10 ∼ 20% in mode B and around 0 ∼ 12% in mode C.     

The effect of surface thermal radiation on entropy generation in an open cavity with natural convection

In this work, a numerical study on entropy generation in a square open cavity with natural convection and surface thermal radiation is presented. The overall continuity, momentum, and energy equations for the gas phase in the open cavity were solved numerically by means of the finite-volume method. Temperature-dependent fluid properties were considered. During the calculations, the values of the Rayleigh number (Ra) were set in the range of 10⁴–10⁶. The temperature difference between the hot wall and the bulk fluid (ΔT) was varied between 50 and 400 K, and was represented by a dimensionless temperature difference (φ) for the purpose of generalization of the present study. The results of this investigation indicate that surface thermal radiation increases the overall entropy generation rate between 33.52% and 560.87%, and thus cannot be neglected in the analysis of this type of system.     

Influence of surface radiation on the transition to unsteadiness for a natural convection flow in a differentially heated cavity

Abstract

The influence of surface radiation on the transition to the unsteady state in natural convection is studied numerically. The configuration of the differentially heated square cavity with adiabatic horizontal walls is chosen to generate an internal natural convection flow. It is known that radiative transfers reduce the temperature difference between the adiabatic walls, which consequently reduces the thermal stratification of the central zone and increases the velocity flow. Many studies have focused on the stationary regime, but few of them have investigated the transition to unsteady flow. For this purpose, the effect of the wall emissivity on the critical Rayleigh number and the associated critical frequency was studied for a given cavity length. The cavity length and mean temperature of isothermal walls are set for the whole study. The results show that all these values are between the values obtained without radiation and those obtained for perfectly conducting horizontal walls. The critical Rayleigh number decreases with emissivity while the associated frequency increases. Moreover, the symmetry of fluctuating properties of the flow is changed when the radiation is taken into account.     

Numerical simulation of natural convection heat transfer in a porous cavity heated from below using a non-Darcian and thermal non-equilibrium model

The present paper investigates the numerical simulation of steady laminar incompressible natural convection heat transfer in an enclosed cavity that is filled with a fluid-saturated porous medium. The bottom wall is subjected to a relatively higher temperature than the top wall while the vertical walls are considered to be insulated. The flow field is modeled upon incorporating different non-Darcian effects, such as the convective term, Brinkman effect and Forchhiemer quadratic inertial effect. Moreover the two-equation model is used to separately account for the local fluid and solid temperatures. The numerical solution is obtained through the application of the finite volume method. The appraisals of the sought objectives are performed upon identifying key dimensionless groups of parameters. These dimensionless groups along with their operating domains are: Rayleigh number 1 ⩽ Ra ⩽ 400, Darcy number 10⁻⁴ ⩽ Da ⩽ 10⁻³, effective fluid-to-solid thermal conductivity ratio 0.1 ⩽ κ ⩽ 1.0, and the modified Biot number 1 ⩽ χ ⩽ 100. The non-Darcian effects are first examined over a broad range of Rayleigh number. Next, the implications of the group of parameters on the flow circulation intensity, local thermal non-equilibrium (LTNE) and average Nusselt number are highlighted and pertinent observations are documented.     

Numerical simulation of nanostructured thermoelectric generator considering surface to surrounding convection

Thermoelectric systems (TE) can directly convert heat to electricity and vice-versa by using semiconductor materials. Therefore, coupling between heat transfer and electric field potential is important to predict the performance of thermoelectric generator (TEG) systems. This paper develops a general two-dimensional numerical model of a TEG system using nanostructured thermoelectric semiconductor materials. A TEG with p-type nanostructured material of Bismuth Antimony Telluride (BiSbTe) and n-type Bismuth Telluride (Bi₂Te₃) with 0.1 vol.% Silicon Carbide (SiC) nanoparticles is considered for performance evaluations. Coupled TE equations with temperature dependant transport properties are used after incorporating Fourier heat conduction, Joule heating, Seebeck effect, Peltier effect, and Thomson effect. The effects of temperature difference between the hot and cold junctions and surface to surrounding convective on different output parameters (e.g., thermal and electric fields, power generation, thermal efficiency, and current) are studied. Selected results obtained from current numerical analysis are compared with the results obtained from analytical model available in the literature. There is a good agreement between the numerical and analytical results. The numerical results show that as temperature difference increases output power and amount of current generated increase. Moreover, it is quite apparent that convective boundary condition deteriorates the performance of TEG.     

The simplest approach to forced convection in horizontal pipes exposed to natural convection and thermal radiation

By making use of a lumped formulation, the problem of laminar forced convection in horizontal pipes involving natural convection and radiation in the external medium has been analyzed with great success. Average values for both internal and external Nusselt numbers have been employed, leading to an expression for the mean bulk temperature that consists of a single exponential function accounting for the axial position and its effective average Nusselt number. Typical results for a combination of internal and external fluids are discussed at length and they are compared favorably with others available in numerically-oriented papers.