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A finite-volume method (FVM) is used to address combined heat transfer, natural convection, and volumetric radiation with an isotropic scattering medium, in a tilted shallow enclosure. Numerical simulations are performed in the in-house fluid flow software GTEA. All the results obtained by the present FVM agree very well with the numerical solution...
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... physical model of the considered problem is displayed in Figure 1 with boundary conditions. It concerns a two-dimensional enclosure filled with a homogeneous, gray, absorbing, emitting, and isotropic scattering medium. ...
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... the effect of radiation decreases with the scattering albedo increasing. Figure 10 shows the dimensionless temperature profiles in the horizontal midplane, i.e., y=L ¼ 0.5, for five values of scattering albedo and for e 1,2 ¼ 1, e 3,4 ¼ 0, and e 1,2,3,4 ¼ 1. It can be observed that the difference between these profiles for x ¼ 0, 0.2 is very little. ...
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... for a higher value of x, the core of the cavity is more cold and a strong temperature gradient is noted near the hot boundary. A comparison of Figures 10a, b shows that the emissivity of the horizontal walls has a vanishingly small effect on the temperature profile for x ¼ 0, 0.2. However, when x increases from 0.5 to 1, the temperature of the core part is enhanced compared to e 1,2 ¼ 1, e 3,4 ¼ 0. ...
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... effects of the scattering albedo on the U-and V-velocity profiles at the midplanes x=W ¼ 0.5 and y=L ¼ 0.5, respectively, are displayed in Figures 11 and 12. Results show that for e 1,2,3,4 ¼ 1, both the horizontal and vertical velocities are slightly enhanced with respect to the one corresponding to e 1,2 ¼ 1, e 3,4 ¼ 0, whereas the effect of scattering albedo x decreases with an increase in the value of x. ...
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... the following section, the results are analyzed with particular interest on the influence of inclination angle a on the flow fields and heat transfer. We set the Ra number of 5 Â 10 6 , wall emissivity of e 1,2,3,4 ¼ 1, for four cases of s ¼ 0 and s ¼ 1, Figure 10. Temperature profiles at midplane y=L ¼ 0.5 with Pl ¼ 0.02, Ra ¼ 10 6 , AR ¼ 1, a ¼ 0 for x ¼ 0, 0.2, 0.5, 0.8, and 1: (a) e 1,2 ¼ 1, e 3,4 ¼ 0; (b) e 1,2,3,4 ¼ 1. ...
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... inclination angle is varied from À60 to 90 by an angle step equal to 30 . The results are summarized in Figures 13-16. ...
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... variations of the isotherm for inclination angle and scattering albedo are depicted in Figures 13a, b for negative angles and in Figures 13d, f for positive angles. At s ¼ 0, irrespective of how the angle a changes, the isotherms in the central part of the cavity are nearly perpendicular to the gravitation. ...
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... variations of the isotherm for inclination angle and scattering albedo are depicted in Figures 13a, b for negative angles and in Figures 13d, f for positive angles. At s ¼ 0, irrespective of how the angle a changes, the isotherms in the central part of the cavity are nearly perpendicular to the gravitation. ...
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... negative angles, the temperature gradient adjacent to the isothermal walls is relatively larger than in the cases of the positive angles. In Figures 13a, b, the structure of the isotherms is almost similar for x ¼ 0 and 0.5; moreover, the scattering alters significantly the thermal distributions in the range of x from 0.5 to 1. However, for positive tilt angles, thermal stratification exists and the isotherms are horizontal in the core area. ...
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... a transparent fluid (s ¼ 0), Figure 14a shows that the dimensionless temperature profile is symmetric for all tilt angles. The high gradient near the thermally active wall is produced at a ¼ 0 . ...
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... the temperature gradient slightly increases in the middle of the cavity for a pure scattering medium. From Figure 14a (s ¼ 0) and b (s ¼ 1, x ¼ 0), it is clear that the core region of the enclosure is more heated for the latter case (s ¼ 1, x ¼ 0). The effects of the parameter are almost similar to those in Figures 14a, b of ref [18]. ...
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... the other hand, the temperature profiles obtained at a ¼ 0 , À30 , and À60 are almost horizontal at the core region and there are little discrepancies among these results. By comparison cases with x ¼ 0.5 and 1 (Figures 14c, d), however, the effect of scattering albedo on the temperature profiles is dramatic, except for a ¼ 90 , where the effect is almost negligible. At a ¼ 0 , its effect has been presented for the case of Ra ¼ 10 6 (Figure 10b). ...
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... comparison cases with x ¼ 0.5 and 1 (Figures 14c, d), however, the effect of scattering albedo on the temperature profiles is dramatic, except for a ¼ 90 , where the effect is almost negligible. At a ¼ 0 , its effect has been presented for the case of Ra ¼ 10 6 (Figure 10b). Notice, at a ¼ À30 , the temperature gradients in the center part of the cavity are negative, presented in Figures 14a, d. ...
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... a ¼ 0 , its effect has been presented for the case of Ra ¼ 10 6 (Figure 10b). Notice, at a ¼ À30 , the temperature gradients in the center part of the cavity are negative, presented in Figures 14a, d. As for a ¼ À60 , it is evident that the temperature is largely lower in the center part of the cavity for the latter case. ...
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... of the mean convective, Nu conv , the radiative, Nu rad , and the total Nusselt numbers on the hot wall with respect to the tilt angle and the scattering albedo is discussed in Figure 15. It is found that the inclination angle and scattering albedo considerably change the heat transfer in the cavity. ...
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... of the mean radiative Nusselt number on the adiabatic walls with tilt angle range from À60 to 75 and scattering albedo of x ¼ 0, 0.5, and 1 is plotted in Figure 16. Regardless of scattering albedo, the maximum of the mean radiative Nusselt number on the bottom wall occurs at a ¼ 30 . ...
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... x ¼ 0, Nu rad along the top wall and the bottom wall is largely enhanced by an increase of tilt angles from À60 to À15 and 15 to 30 , and decreases as the tilt angles vary from À15 to 15 and 30 to 75 . For the case of x ¼ 0.5, Nu rad on the two adiabatic walls increases with the tilt angles ranging from Figure 17. Variation of mean radiative Nusselt number on the hot wall for aspect ratios AR ¼ 1, 2, 3, 4, and 5, and scattering albedo at a ¼ À15 . ...
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... mean radiative Nusselt number for enclosures tilted by À15 with five aspect ratios, AR ¼ 1, 2, 3, 4, and 5, and five scattering albedos, x ¼ 0, 0.2, 0.5, 0.8, and 1, are depicted in Figure 17. As it can be observed, the average Nu number Figure 18. ...
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... mean radiative Nusselt number for enclosures tilted by À15 with five aspect ratios, AR ¼ 1, 2, 3, 4, and 5, and five scattering albedos, x ¼ 0, 0.2, 0.5, 0.8, and 1, are depicted in Figure 17. As it can be observed, the average Nu number Figure 18. Isotherms for x ¼ 0, 0.2, 0.5, 0.8, and 1 at AR ¼ 5 tilted À15 . ...
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... for all values of scattering albedo, the radiative Nu number is considerably reduced by an increase of aspect ratio from 1 to 5. As an expected result, at a ¼ À15 , the highest and lowest values of heat transfer are obtained for x ¼ 0, AR ¼ 1 and x ¼ 1, AR ¼ 5, respectively. The influence of scattering albedo on the isotherm is presented in Figure 18, for the case of AR ¼ 5 tilted by À15 . The scattering albedo has a slight effect on the isotherm for x increasing from 0 to 0.8; however, its effect is quite obvious when x increases to 1. ...
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Citations
... Wang et al. [8] developed an iterative technique to solve the associated conduction-radiation heat transfer in semitransparent media. Using the finite-volume method, Fu et al. [9] considered natural convection coupled with radiation heat transfer in slanted square and shallow enclosures containing anisotropic scattering medium. Sans et al. [10] experimentally studied the associated conductive and radiative heat transfer in * Corresponding author. ...
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... On the other hand, the extinction coefficient had a significant impact on temperature distributions. It has been also observed that wall emissivity and scattering albedo have a significant influence on flow and temperature fields, also, heat transfer is decreased with increasing in scattering albedo (Mezrhab et al., 2006;Mondal and Mishra, 2008;Sun et al., 2011;Kumar and Eswaran, 2013;Fu et al., 2015;Parmananda et al., 2017). Karatas and Derbentli (2018) investigated the combined natural convection and radiation CHAPTER 1. INTRODUCTION 13 1.3. ...
The role of thermal radiation with collimated irradiation (the light rays travel in a single
direction) has strategic importance in many applications, like meteorology, environmental
science, and engineering, the influence of solar radiation on the oceanic movement, regu-
lating the productivity of aquatic ecosystems and altering their biological compositions,
preserving the water quality and bioactivities in water bodies, dynamics of clouds etc.
Further, solar cavity receivers get their energy mostly from collimated irradiation reflected
from the heliostat field. The solar energy entering through a semitransparent wall (glass
window) has a significant impact on the heat transport characteristics inside a room,
affecting the heating, ventilation, and air conditioning (HVAC) systems. In such conditions, induced natural convection plays an important role. This kind of phenomenon has
captivated researchers’ attention, thus, leading to the investigation of complex fluid flow
and heat transfer mechanisms in basic geometries such as squares, rectangles, cylinders,
hexahedrons etc. In such a scenario, study of all modes of heat transfer, i.e., conduction,
convection and radiation are vital. Further, the qualitative and quantitative analysis of
radiation heat transfer (diffuse+collimated beam) is required in order to understand its
effects on the fluid flow and also on heat transfer.
Foremost, the collimated feature has been developed in the OpenFOAM framework - an
open-source software. This feature is first validated against the analytical and numeri-
cal work from the literature. Then the collimated beam feature is combined with fluid
flow and heat transfer libraries. The new application is named as LaminarBoussinesq-
CollimatedFoam. It has the flexibility to simulate pure natural convection, combined
diffuse/collimated beam radiation with natural convection in two- and three-dimensional
geometries.
Further, the LaminarBoussinesqCollimatedFoam is employed for the combined natural convection with volumetric radiation in a two-dimensional cavity with convective bottom heating (h=50 W/m 2 K, T=305 K) and cooled (T=296 K) from sides have been investigated, numerically. The influence of various optical thicknesses of the medium for the diffuse radiation scenario on flow and heat transfer has been analyzed. The results reveal that diffuse radiation has little effect on the dynamics of two rolls inside the cavity
for present problem. Also, the average total Nusselt number decreases with an increase
in the optical thickness on the bottom as well as on the side walls. Further, a small
semitransparent window has been created on the left wall of the above geometry and a
collimated irradiation of value 1000 W/m 2 at an azimuthal angle 135^0 is applied on this
semitransparent window. Now, the numerical simulations have been carried for the com-
bined diffuse and collimated beam radiation with natural convection for the scenario of
iiibottom heating with symmetrical cooling. The results showed, that the collimated beam
irradiation changes the dynamics of two rolls significantly and also the heat transfer
characteristics. This further changes with the optical thickness of the medium. The left
side roll is bigger than the right side roll for collimated beam in a transparent medium,
whereas, a reverse trend is seen for the collimated beam for the non-zero optical thickness
of the medium. The size of the left roll increases with the increase of optical thickness
of the medium. The heat transfer reversal happens at the zone of a collimated beam
incident on the bottom wall for transparent medium, whereas, this does not happen for
the participating medium.
The above study is further extended to investigate the effects of two thermal adiabatic
boundary conditions that arise on the semitransparent window (wall made of glass ma-
terial) owing to the fact that whether semitransparent window allows the energy to leave
the system by radiation mode of heat transfer or not on the fluid flow and heat trans-
fer phenomena. It is assumed that the energy does not leave by the conduction mode of
heat transfer, due to the low thermal conductivity of semitransparent material. This does
mean that the semitransparent window may behave as only conductive adiabatic (q c = 0)
or combined conductive and radiative adiabatic (q c +q r = 0). In this case, the left vertical
wall has been divided into upper and lower parts in the ratio 4:6. The upper section is a
semitransparent window, while the lower section is an isothermal wall. The effects of the
above two boundary conditions on the fluid flow and the heat transfer characteristics in-
side the cavity have been studied for a range of irradiation values 0−1000 W/m 2 , Rayleigh
numbers of 10^4 −10^7 and Prandtl numbers of 0.71−50. Furthermore, the study of effect of the semitransparent window’s aspect ratio i.e., height ratio (h r ) and window width ratio
(w r ) has been performed. The other parameters like flow parameter (Ra = 10 5 ), fluid
parameter (P r = 0.71), thermal parameter conduction-radiation parameter (N = 1.5),
Irradiation (G = 1000 W/m 2 ), Angle of incidence (ϕ = 135 0 ) and geometrical parameter
(A r =1) and the wall conditions have been kept constant. The localized heating of the
fluid is also seen for the case of large height ratio of the semitransparent window. The
conduction, radiation and total Nusselt numbers are also greatly affected.
Finally, the three-dimensional numerical simulations have been carried for the coupled
natural convection with diffuse and collimated beam irradiation in a cubic cavity. This
study has been performed in two stages: First, the effect of diffuse radiation on the natural
convection has been performed. Second, a square semitransparent window is created on
the left wall of the cavity and a collimated beam is irradiated on this window at the polar
and azimuthal angles of 90 0 and 135 0 , respectively. The influences of transparent(τ =
0) and the participating (τ = 2.5 and 10) media are examined. The results reveal a quadrantal symmetry of fluid flow and heat transfer for various optical thicknesses and the
ivcavity contains four conical vortices where each vortex is occupied in tetrahedron space in case of without collimated beam radiation. Moreover, the Q-criteria reveals the formation of a mushroom-like fluid-structure inside the cavity. However, with the inclusion of collimated beam irradiation, the quadrantal symmetry breaks and a bilaterally symmetric nature is established about the plane of the collimated beam. The flow structure becomes much more complex and has been explained by critical flow theory. In addition, the heat transfer characteristic also changes in accordance with the dynamics of vortices inside the cavity. The Q-criterion reveals the existence of a non-regular fluid structure inside the cavity.
... Furthermore, natural convection coupled with radiation in an emitting, absorbing, and scattering medium was investigated for various aspect ratios (Fu et al., 2015) with various parameters such as Planck numbers, wall emissivity, scattering albedo, and extinction coefficient (Mondal and Mishra, 2008), and these parameters significantly influenced the heat transfer characteristics inside the cavity. The numerical works of Mezrhab et al. (2006), Sun et al. (2011), Kumar and Eswaran (2013) and Parmananda et al. (2017) showed that the radiation exchange homogenised the temperature field inside the cavity. ...
The effect of the semitransparent window's aspect ratio, i.e., the height ratio (hr) and window width ratio (wr) and Planck numbers on the interaction of the collimated beam with natural convection has been investigated numerically. The cavity is convectively heated from the bottom, and a semitransparent window is created on the left wall, and a collimated beam is irradiated on the window at an azimuthal angle (ϕ) of 135 •. The dynamics of two vortices inside the cavity change considerably by combination of window's aspect ratio and Planck number (P l) of the medium. The thermal plume flickers depending on the situation of the dynamics of two vortices inside the cavity. The localised heating of the fluid happens mostly for the large height ratio of the semitransparent window. The conduction, radiation, and total Nusselt numbers are also greatly affected by the aspect ratio and Planck number of the medium.
... The extinction coefficient had a pronounced effect on the temperature distributions. A coupled numerical investigation on natural convection with volumetric radiation with gray and isotropic scattering medium in two-dimensional rectangular cavity were analysed for Planck numbers, scattering albedo of the medium for various tilt angles and the aspect ratios of the cavity in [14]. They observed that emissivity of the horizontal wall and the scattering albedo have significant effect on the flow and temperature patterns. ...
The effects of the semitransparent winodw's aspect ratio on the interaction of the collimated beam with natural convection have been investigated numerically in the present work. The combination of geometrical parameters of the semitransparent window, i.e., height ratio () and window width ratio () and Planck numbers of the medium have been considered. The other parameters, like flow parameter (Ra), fluid parameter (Pr=0.71), thermal parameter (N), Irradiation (G=1000 ), Angle of incidence () and geometrical parameter of the geometry (=1) and the wall conditions have been kept constant. A collimated beam is irradiated with irradiation value (G=1000 ) on the semitransparent window at an azimuthal angle (. The cavity is convectively heated from the bottom with heat transfer coefficient 50 and free stream temperature 305 K. A semitransparent window is created on the left wall and isothermal conditions (T=296 K) is applied on the semitransparent, left and right vertical walls, wherein adiabatic conditions are applied on upper wall of the cavity. The dynamics of two vortices inside the cavity change considerably by combinations these semitransparent window's aspect ratio and Planck number (Pl) of the medium. The left vortex breaks into two parts and remains confined in upper and lower left corners for some combination of aspect ratios and Planck numbers of the medium. The thermal plume flickers depending on the situation of dynamics of two vortices inside the cavity. The localized hating of the fluid happens mostly for large height ratio of semitransparent window. The conduction; radiation and total Nusselt number are also greatly affected by the semitransparent window's aspect ratio and the Planck number of the medium.
Two-dimensional simulations of natural convection driven by the absorption of nonuniform concentrated solar radiation in a molten binary salt-filled enclosure inclined at 0 ≤ ϕ ≤ 60 are presented. The enclosure is volumetrically heated from the top boundary and accommodates a black rigid, heat-conducting plate of finite thickness at the lower boundary, which aids in the generation of natural convective mixing at the lower boundary. The governing equations that account for the depth-dependent absorption of radiation are solved using the finite-element method. Numerical results reveal that increasing the inclination angles decreases the natural convection and higher Rayleigh promotes natural convection.
