Analysis of Combined Natural Convection and Radiation Heat Transfer in a Partitioned Rectangular Enclosure with Semitransparent Walls
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In this paper, we present a two-dimensional numerical analysis of the conjugate natural convection and radiation heat transfer in a double-space enclosure with two semitransparent walls. Two kinds of boundary conditions are considered, the first being the isothermal process of the opaque wall, and the other the incidence of a constant radiation flux in the left semitransparent wall. The renormalization group k–ε model is adopted to simulate the turbulent flow in the enclosure. To compute the radiation heat transfer in a semitransparent medium, the discrete ordinates model is used. We compare the behaviors of enclosures with single and double semitransparent walls and determine the difference in the results obtained for semitransparent and opaque partitions. The results indicate that a semitransparent partition facilitates a reduction in the heat loss or obtains a higher temperature distribution. The transmittance of a semitransparent wall has a great effect on the thermal and flow characteristics in an enclosure. The change of wall temperature is found to be significant when the thermal conductivity values range from 0.05 to 0.5 W/(m·K), and to be small when ranging from 0.5 to 10 W/(m·K). These conclusions are helpful for green design and energy saving in solar buildings.
KeywordsNatural convection Enclosure Semitransparent wall Thermal conductivity Transmittance
List of Symbols
Heat flux (W/m2)
Mean temperature of left semitransparent wall (K)
Mean temperature of middle semitransparent wall (K)
Specific heat of fluid [J/(kg·K)]
Gravitational acceleration (m/s2)
Heat transfer coefficient [W/(m2·K)]
Radiation intensity (W/m2)
Thermal conductivity [W/(m·K)]
Thermal diffusivity (m2/s)
Thermal expansion coefficient of air (1/K)
Emissivity of semitransparent wall
Due to its prime importance in various industrial and natural processes, determining the natural convection with radiation inside a square cavity filled with different fluids is a classical scientific problem. The model most often used to study this problem is a rectangular enclosure with two vertical isothermal walls and two horizontal adiabatic walls . However, in terms of engineering applications, such as solar chimneys, double-skin facades, solar collectors, and Trombe walls, this simplified model cannot be correctly developed to investigate the flow and heat transfer characteristics , because the introduction of a semitransparent medium changes the enclosure characteristics. Compared to opaque materials, semitransparent materials allow a greater transmission of direct radiation. To use and understand the natural convection in buildings and systems, it is important to study the effect of a semitransparent medium on enclosures to provide references for practical applications.
Several theoretical and experimental studies have been conducted on enclosures with semitransparent walls. Moreno and Hernández  presented analytical solutions for a very simple room with glazing subjected to solar radiation, in which they identified the main physical mechanisms and the importance of the indoor temperature on the spectral and thermal parameters. Flores et al.  presented a study of the combined heat transfer in a cubic cavity containing a vertical semitransparent wall. From this parametric study, for a fixed absorbance of a solar-control coating, the contribution of the radiative heat transfer was found to be higher than that by convection, but both the convective and radiative heat transfers were determined to increase with an increase in the ambient temperature. Li et al.  investigated the effect of optical constants on the conjugate laminar natural convection and radiative heat transfer in a rectangular enclosure with one vertical semitransparent wall. It was found a marked effect of the optical constants of a semitransparent wall on the laminar natural convection in a rectangular enclosure. Wu and Lei  developed a transient heat balance model for predicting the thermal performance of a semitransparent water-wall system. A series of studies were conducted by Xamán et al. [7, 8, 9, 10, 11, 12, 13, 14, 15] regarding the heat transfer in a square cavity with a semitransparent wall. By performing numerical studies of the conjugate heat transfer in a square cavity with a semitransparent wall for laminar and turbulent flows, the authors obtained a set of correlations for the Nusselt number for both laminar and turbulent flows [7, 8]. The unsteady Reynolds-averaged Navier–Stokes (URANS) model together with a low-Reynolds-number turbulence k–ω model was solved using the finite-volume method . Using the glazing material available in the Mexican market, researchers have also investigated the thermal performance of a room with a double-glazed window [10, 11]. A thermal evaluation of a room with a double-glazed window both with/without a solar-control film made in Mexico was also presented [12, 13, 14]. Based on the results, we know that a room with a double-pane window with a solar-control coating is associated with a smaller heat flux than one with a window without a solar-control coating. The effect of the roofing material on a room with a semitransparent wall has also been analyzed .
Natural convection in a differentially heated, partitioned enclosure with an opaque partition wall occurs in various situations both in natural settings and in engineering applications. Recently, several works have outlined the heat transfer characteristics when using partitioned enclosures. Rabhi et al.  studied the effects of surface radiation and the number of partitions on the heat transfer and flow structures in an inclined rectangular enclosure, and found that the total heat transfer in the enclosure increased in the presence of a thermal radiation heat flux, and reduced significantly with an increasing number of partitions. Selimefendigil and Öztop  used the finite element method to investigate conjugate natural convection and conduction heat transfer in an inclined partitioned cavity filled with different nanofluids on different sides of the partition. Sun et al.  presented extensive numerical studies on fluid flow and heat transfer in inclined and fully divided CO2 enclosures with partitions on Mars. It was observed that three flow regimes formed in succession when the tilt angle increased, namely, Rayleigh–Bénard convection, transition convection, and single-cell convection. Sambou et al.  developed a one-dimensional analytical model of the coupled heat transfer (conduction, convection, radiation) in enclosures divided by multiple vertical diffusive partitions, and found that the thermal resistance could be improved by decreasing the thermal conductivity of the walls, decreasing the emissivity of the partitions faces, or using very thin partitions. Oztop et al.  performed numerical simulations of the conduction-combined forced and natural convection heat transfer and fluid flow in a 2D lid-driven square enclosure divided by a partition with a finite thickness and finite conductivity. It was observed there to be higher heat transfer for a higher Richardson number in an upward moving wall for all thermal conductivity ratios. Khatamifar et al.  studied the effects of partition thickness and position over a wide range of Rayleigh numbers, and found that the average Nusselt number increases with the Rayleigh number, but decreases with partition thickness. They also found that the partition position had a negligible effect on the average Nusselt number. Most previous studies of natural convection in partitioned enclosures have been concerned with cases where the partition wall is opaque. There is insufficient knowledge regarding enclosures with a semitransparent wall partition, as this may be a better model for many real situations.
There are also two significant points that must be emphasized in the study of rectangular enclosures. First, for most flows, the Rayleigh number often exceeds the critical values and the fluid flow becomes turbulent in many studies. However, many studies consider only laminar flows. Second, the contribution of thermal radiation is an important topic with respect to the heat transfer in enclosures. Radiation heat transfer depends on several parameters, such as the wall temperature, surface emissivity, and thermophysical properties of the internal medium. In studies of turbulent natural convection, the radiative mode of heat transfer is occasionally neglected because of the overwhelming number of computational resources it demands. However, the radiation heat transfer has a significant effect on the system and cannot be ignored, because this phenomenon occurs in numerous engineering applications. Recently, a few studies have addressed the combination of natural convection and radiation heat transfer in rectangular enclosures. Miroshnichenko et al. [22, 23, 24, 25] conducted a series of studies on transient turbulent natural convection combined with surface thermal radiation in a square cavity with a local heater. The Rayleigh number, thermal conductivity ratio, and internal surface emissivity have a significant effect on the temperature and stream function contours within the enclosure . In addition, they found that the presence of surface radiation leads to both an increase in the average total Nusselt number and intensive cooling of this type of system. A significant intensification of convective flow was also observed by an increase in the Rayleigh number [23, 24]. The results show that an increase in the cavity inclination angle leads to a reduction in the radiative Nusselt number . Turbulent natural convection in air-filled differentially heated cavities was numerically investigated using various RANS turbulence models and the discrete ordinates (DO) model . The result of this study shows that the shear stress transport k–ω model performs best overall and the standard k–ε model has the worst overall performance. Sharma et al.  conducted a numerical investigation of turbulent natural convection in a transparent fluid medium and its interaction with surface thermal radiation in an inclined differentially heated enclosure. Mao and Zhang  conducted a numerical simulation of the turbulent natural convection of compressible air in a tall cavity, and found that the k–ε model had high accuracy in predicting the velocity distribution, whereas the large eddy simulation model had good performance in predicting temperature distributions.
In this study, our main aim was to investigate the effect of semitransparent walls on the natural convection flow field and temperature distribution in a double-spaced rectangular enclosure. Computation fluid dynamics can be used to simulate this problem. To compute the radiation heat transfer in a semitransparent medium, the DO model is used. The comparison of the enclosures with single and double semitransparent walls is conducted, and the difference of semitransparent partition as well as opaque partition is analyzed. The impact of different transmittance combinations on the semitransparent wall is examined. In addition, the influence of different thermal conductivities in a semitransparent medium on the performance of the proposed enclosure is also detailed.
For two-dimensional steady flow and heat transfer of the presented physical model, the governing equations are listed as follows.
q1 (W/m2) (Case 1)
Tw (K) (Case 2)
150 × 130
180 × 160
240 × 220
In this study, we investigated the impact of a single factor on the enclosure. Thus, only the study object changes in the simulation and other factors are held constant. These constant values for the simulated parameters included the transmittance and thermal conductivity of the semitransparent wall, whose values were 0.8 and 0.5 W/(m·K), respectively.
We performed all calculations reported hereafter using the general-purpose commercial code FLUENT, based on the finite-volume method. The governing equations were discretized by the finite-volume method on a non-uniform staggered grid system using the SIMPLEC algorithm. PRESTO! scheme was used for the pressure discretization. The second-order upwind scheme was considered for the momentum and energy equations.
Results and Discussion
Effect of Single and Double Semitransparent Walls
Effect of Semitransparent and Opaque Partitions
Effect of Transmittance
The transmittance of a semitransparent wall has a significant effect on the thermal and flow characteristics in an enclosure. In this section, different combinations of transmittance in an enclosure with two semitransparent walls have been studied. The transmittance combination is expressed as (τleft, τmid).
Effect of Thermal Conductivity
The presence of a semitransparent partition has a significant impact on the flow field and temperature distribution, as compared to an enclosure without any partition. This result indicates that a semitransparent partition is beneficial for reducing heat loss, as shown in Case 1, and for obtaining a higher temperature distribution, as shown in Case 2.
From our comparison of an enclosure with either semitransparent or opaque walls, the results indicate that semitransparency allows radiation to pass through the material, thus enhancing the air temperature distribution in the enclosure.
The transmittance of a semitransparent wall has a great effect on the thermal and flow characteristics in an enclosure.
The change in wall temperature is significant, with thermal conductivity values ranging from 0.05 to 0.5 W/(m·K), and is slight with values ranging from 0.5 to 10 W/(m·K) for both cases. For Case 1, the heat flux also increases rapidly for λ values ranging from 0.05 to 0.5 W/(m·K) and tends to become constant as λ continues to increase.
This work was supported by the Shanghai Economic and Information Technology Committee Special Fund (CXY-2016-012). The simulation work was completed in cooperation with the High Performance Computing Center of Tianjin University, China.
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