Abstract
The present research work focuses on numerical simulation of combined natural convection and radiation inside a square enclosure with a vertical partition having different heights. The distance of the partition is varied from the hot wall for establishing the results. The left wall is considered to be the hot, the right wall as the cold and the horizontal top and bottom walls are considered to be adiabatic. The analysis is done in both the laminar and in the turbulent range for the Rayleigh number in range of 103 to 1010. The partition is considered to have a fixed thickness which is taken to be L/20. Also, it is assumed to be adiabatic. Air is taken as the working medium. It has been concluded from the results that an increase in radiative Nusselt number is much higher than that of convective Nusselt number for turbulent flow regime. It was found to be 379% as the Rayleigh number increases from 108 to 1010. Also, the increase in NuT is almost 352% when Ra is increased from 108 to 1010. However, as the partition height is increased the value of NuT decreases to 15 and 28% for Ra 105 and 1010 respectively.
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1 Introduction
The study of natural convection and radiation inside cavities with different orientations and boundary conditions has been a topic of interest for the past decades by the thermal engineering researchers. The heat transfer and fluid flow are the major factors studied in these researches. However, often in these studies the combined effect of natural convection and radiation is not considered. So, in this research work the combined effect of natural convection and radiation is studied in both the laminar and turbulent range. Bahlaoui et al. [1] in their research work present the results of mixed convection and radiation inside a cavity which is heated from below and consists of a vertical adiabatic partition on this horizontal heated surface. The results are shown with the help of streamline and isotherm contours. Han and Baek [2] in their paper studied the phenomenon of heat transfer and fluid flow by considering three cases, in the first case only natural convection is considered, in the second case convection along with surface radiation is considered and in the third case convection with surface/gas radiation is considered. Both the partitions were considered to be adiabatic. The results obtained showed that the surface radiation had greater effect than the gas radiation on the heat transfer phenomenon. Again, the result is presented with the help of streamlines and temperature contours along with the calculation of Nusselt number. Zemani et al. [3] carried out a numerical simulation inside a cavity having hot and cold vertical walls with a partition placed parallel to the horizontal walls on the hot wall. The Rayleigh number was considered between 106 and 3.7 × 109. Finite volume method was used to solve the governing equations. Time evolutions and temperature contours were presented to demonstrate the ongoing simulation along with the calculation of Nusselt number. Also, the results show that the presence of partition highly abrupt the fluid flow and heat transfer inside the cavity. Nakhi and Chamka [4] in their research work presented the results of laminar natural convection inside a square enclosure consisting of an inclined partition attached to the vertical hot wall while the rest of the three sides of the cavity were cooled from outside. Brown and Solvason [5] performed an experimental study of the phenomenon of natural convection inside rectangular openings with two cases, in the first case considering a vertical partition and in the second case considering a horizontal partition. The Grashof number for the present study was considered between 106 and 108. The results were presented in the form of Nusselt number calculated from the study. Nagaraja [6] in his research work carried out a numerical simulation of natural convection in a square enclosure with partition. The Rayleigh number for the present study is considered in the laminar range i.e., 103 to 106. Similar to the other studies, the results in this also are presented in the form of streamline, isotherm contours and the Nusselt number. From the above studies we can see that most of the studies are done either in laminar region or in turbulent region. In the present study, the numerical computation is done both in the laminar region and in the turbulent region. Also, the cavity considered for the analysis consists of a vertical partition.
2 Physical Model and Problem Description
In the present study, a square cavity is considered with vertical walls as hot and cold walls while the horizontal walls are assumed to be adiabatic as shown in Fig. 1. The vertical partition considered in the present research work is assumed to be adiabatic. Air is taken as the working fluid having a Prandtl number of 0.71 and also the Boussinesq approximation is adopted. All other physical parameters are assumed to be constant. The present study is carried out for Rayleigh number 103, 105, 108 and 1010 resulting in the analysis in both the laminar and turbulent regions. In order to study the effect of partition height, the length of partition is varied as L, 3L/4, L/2 and L/4 as in Cases 1, 2, 3 and 4 respectively. Likewise, the partition distance is varied as L/4, L/2 and 3L/4 respectively as in Cases a, b and c.
3 Solution Methodology
The numerical simulation for the present study is done using ANSYS FLUENT 2022R1 which is a finite volume-based solver. The pressure velocity coupling is done using Coupled algorithm. Also, the pressure interpolation is done by Second order scheme. For solving momentum and energy equation Second order Upwind is used. The surface emissivity value for all the general cases is considered to be 1 and Discrete Ordinate is used as the radiation model. SST K-Ω model is adopted as the turbulence model after detailed model sensitivity analysis beyond 80 × 80.
4 Grid Sensitivity Test
The grid sensitivity analysis has been carried out for Ra 105 for case 1b. Grid sizes 80 × 80, 100 × 100, 120 × 120 and 140 × 140 have been chosen for the analysis. Table 1 shows that the changes in the Nu values are almost negligible. Therefore, 100 × 100 has been chosen for further analysis for all the cases. Also, the test is done for turbulent flow in the enclosure.
5 Results and Discussion
5.1 Effect of Rayleigh Number
Heat transfer and fluid flow characteristics in the enclosure are studied in both the laminar and turbulent regimes. The variation of total Nusselt number with Rayleigh number is depicted in Fig. 2. It can be seen that as the Rayleigh number is increased from 103 to 105 i.e., in the laminar range the total Nusselt number increases to a value of around 202%. Again, when the Rayleigh number is increased from 108 to 1010 i.e., in the turbulent range the percentage increase in total Nusselt number is 343%. Thus, we can see that as the Rayleigh number is increased either in the laminar or in the turbulent region, the value of NuT increases with it in the direct proportion.
5.2 Effect of Partition Height
In the research work in order to study the effect of partition height on the overall heat transfer and fluid flow, different cases of partition height are considered. In case 1 the height of the partition is taken as L, in case 2 it is taken as 3L/4, in case it is considered as L/2 and for the 4th case it is taken as L/4. It is observed that as the partition height is increased from L/4 to L, the value of total Nusselt number decreases to 15% for Rayleigh number 105 and 28% for Rayleigh number 1010 as shown in Fig. 3. Thus, it leads us to the observation that both the stature of partition and NuT are inversely proportional to each other.
5.3 Combined Radiation and Natural Convection
The study of natural convection and radiation is done inside a square cavity with a vertical partition. All these analyses are done both in the laminar and turbulent range for Rayleigh number 103 to 1010 and as such the results are presented in the form of isotherm and streamline contours as shown in Figs. 4, 5, 6 and 7 respectively. For all the Rayleigh number and for all the considered cases the value of surface emissivity is taken as 1 i.e., ε = 1. In the laminar range i.e., for Ra = 103 and 105 it can be observed from the streamline contours for Case ‘a’ when the partition is close to the hot wall, that the fluid flow is in the clockwise direction with the fluid rising from the bottom of right side of the partition, rising above than after coming in contact with the top adiabatic wall flows along the left wall in the downward direction thus forming uniform flow of the fluid. When the partition is present at the center, the fluid flows on both the side of the partition as in Case ‘b’. While when the partition is present near the cold wall in Case ‘c’ the fluid flow occurs on the right side of the partition. Also, from the temperature contours for Ra 103 we can observe the contours are almost parallel to the vertical walls. However, for Ra 105 the isotherms are observed to be disrupted. Similarity is breaking and unsymmetrical flow behavior is seen along the vertical sides.
The streamline and isotherm contours for turbulent range are shown in Figs. 6 and 7 for Rayleigh number 108 and 1010 respectively. For all the cases of partition height and distance it can be observed that the fluid flows very close to the enclosure walls and the partition wall in the clockwise direction. The isotherm contours for Ra 108 are almost parallel to the horizontal walls but as the Ra number is increased to 1010 the contours get disturbed.
Figure 8 shows the variation of NuC, NuR and NuT with Rayleigh number. It can be observed that there is a slight variation in NuC as the Ra varies from 103 to 105 however beyond that the change is significant to a value of almost 290% as Ra changes from 108 to 1010. For NuR the percentage change from 108 to 1010 is extremely high similar to a value of 379%. Also, it can be observed that the value of NuR is greater than the value of NuC. The increase in NuC and NuR results in the increase of NuT with the increase in Rayleigh number.
6 Conclusion
This paper presents the interaction of natural convection and surface radiation in partitioned enclosure for laminar and turbulent flow regimes. More than 70 cases were analyzed and the following systematic inference from the investigation were addressed. It can be concluded from the study that the increment in radiative Nusselt number is much higher than that of convective Nusselt number for higher Rayleigh number. When Ra number increases from 108 to 1010 the percentage increase in NuC and NuR are observed to be almost 290% and 379% respectively. Thus, radiation plays a major role in net heat transfer from the enclosure. It has been observed from the decrease in the values of about 15% and 28% for Ra 105 and 1010 as the partition height is increased from L/4 to L respectively. Hence, this leads to the conclusion that as the partition stature is decreased, the heat transfer and fluid flow increase thus resulting in an increase in the NuT.
References
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Ali, M., Sharma, A.K. (2024). Investigation of Laminar and Turbulent Natural Convection Combined with Radiation in a Square Enclosure with a Vertical Partition. In: Siddiqui, M.A., Hasan, N., Tariq, A. (eds) Advances in Heat Transfer and Fluid Dynamics. AHTFD 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-7213-5_21
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DOI: https://doi.org/10.1007/978-981-99-7213-5_21
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