# Numerical Study on Mixed Convection Flow and Energy Transfer in an Inclined Channel Cavity: Effect of Baffle Size

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Methods

_{B}is attached at the top wall and its length varies inside the cavity. The gravitational force acts downwards.

## 3. Numerical Method

^{−6}. The Trapezoidal rule is used to compute the physical quantities of transport rate along the surface. The more detailed numerical procedure is found in [18,19].

## 4. Results and Discussion

^{5}, and the Reynolds numbers are chosen as $31.6\le Re\le 3162$. The Prandtl number value used is 0.71. The length of the baffle is used as ${L}_{B}=0,0.25,0.5,0.75$. The inclination angle is chosen as $0\le \varphi \le 90$.

_{B}≤ 0.25. The drag force behaves nonlinearly with the Ri number for all inclination angles when L

_{B}= 0.75. It reduces sharply until Ri = 1 and then it grows when increasing the value of Ri for all inclinations. However, it diminishes sharply until Ri = 10 for the non-inclined case. The variation in drag force among the inclination angle is not significant in the forced convective regime when L

_{B}≤ 0.5. Figure 7a–d portray the average temperature for various values of Ri, inclination and sizes of the baffle. The average temperature performs non-linearly with the Ri number for all inclined cases when L

_{B}≤ 0.5. The average temperature enhances with the Richardson number for the case of L

_{B}= 0.75. However, there is no significant variation in the average temperature among the inclinations for L

_{B}= 0.75. The average temperature is high at Ri = 100.

_{B}= 0 and L

_{B}= 0.25. The increment in heat transport is observed in the occurrence of a baffle in the forced convective regime for all tilting angles except at a Ri = 0.01 and $\varphi =90\xb0$. The mixed convection regime provides a decrement in energy transportation for all inclined channel cavity cases. Figure 10b clearly shows that an increment in thermal energy transportation is observed in all cases of Ri and inclination angles, except Ri = 100 and $\varphi =0\xb0$. The energy transfer increases by around 80% at Ri = 0.1 and $\varphi =90\xb0$ with ${L}_{B}$ = 0.25 compared to the absence of a baffle. Figure 10c undoubtedly indicates that there is no decrement in energy transfer with ${L}_{B}$ = 0.75 compared with the absence of a baffle. The highest amount of heat transport is about 450% with L

_{B}= 0.75 at Ri = 0.1 and $\varphi =90\xb0$. Further, it is concluded from these figures that the increment of energy transportation grows when increasing the size of the baffle.

## 5. Conclusions

- ○
- The recirculating eddies beside the baffle become weak or disappear when increasing the inclination angle of the channel cavity.
- ○
- The energy transfer enriches when enhancing the baffle size since the stream further induces the inner part of the cavity with the existence of the partition, resulting in an enormous energy transference within the cavity.
- ○
- The average thermal energy transportation reduces steadily until the Ri = 1 and then it rises for all inclination angles and lengths of the baffle. When comparing the inclination angles, no constant angle provides a higher heat transport inside the channel cavity.
- ○
- The increment of energy transference enhances when increasing the size of the baffle. The highest quantity of heat transport is found to be about 450% with the occurrence of a baffle.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- You, X.; Li, S. Fully Developed Opposing Mixed Convection Flow in the Inclined Channel Filled with a Hybrid Nanofluid. Nanomaterials
**2021**, 11, 1107. [Google Scholar] [CrossRef] [PubMed] - Borrelli, A.; Giantesio, G.; Patria, M.C. Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection. Fluids
**2021**, 6, 154. [Google Scholar] [CrossRef] - Khan, S.I.U.; Alzahrani, E.; Khan, U.; Zeb, N.; Zeb, A. On Mixed Convection Squeezing Flow of Nanofluids. Energies
**2020**, 13, 3138. [Google Scholar] [CrossRef] - Mohamed, A.B.; Hdidi, W.; Tlili, I. Evaporation of Water/Alumina Nanofluid Film by Mixed Convection Inside Heated Vertical Channel. Appl. Sci.
**2020**, 10, 2380. [Google Scholar] [CrossRef] [Green Version] - Armaghani, T.; Ismael, M.A.; Chamkha, A.J.; Pop, I. Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel. Energies
**2019**, 12, 1150. [Google Scholar] [CrossRef] [Green Version] - Ozgen, F.; Varol, Y. Numerical Study of Mixed Convection in a Channel Filled with a Porous Medium. Appl. Sci.
**2019**, 9, 211. [Google Scholar] [CrossRef] [Green Version] - Carozza, A. Numerical Study on Mixed Convection in Ventilated Cavities with Different Aspect Ratios. Fluids
**2018**, 3, 11. [Google Scholar] [CrossRef] [Green Version] - Sivasankaran, S.; Sivakumar, V.; Hussein, A.K. Numerical study on mixed convection in a lid-driven cavity with discrete heating. Int. Comm. Heat Mass Transf.
**2013**, 46, 112–125. [Google Scholar] [CrossRef] - Roy, M.; Roy, S.; Basak, T. Role of various moving walls on energy transfer rates via heat flow visualization during mixed convection in square cavities. Energy
**2015**, 82, 1–22. [Google Scholar] [CrossRef] - Sivasankaran, S.; Niranjan, H.; Bhuvaneswari, M. Chemical reaction, radiation and slip effects on MHD mixed convection stagnation-point flow in a porous medium with convective boundary condition. Int. J. Numer. Methods Heat Fluid Flow
**2017**, 27, 454–470. [Google Scholar] [CrossRef] - Manca, O.; Nardini, S.; Khanafer, K.; Vafai, K. Effect of heated wall position on mixed convection in a channel with an open cavity. Numer. Heat Transfer A
**2003**, 43, 259–282. [Google Scholar] [CrossRef] - Leong, J.C.; Brown, N.M.; Lai, F.C. Mixed convection from an open cavity in a horizontal channel. Int. Comm. Heat Mass Transf.
**2005**, 32, 583–592. [Google Scholar] [CrossRef] - Rahman, M.M.; Öztop, H.F.; Saidur, R.; Mekhilef, S.; Al-Salem, K. Finite element solution of MHD mixed convection in a channel with a fully or partially heated cavity. Comput. Fluids
**2013**, 79, 53–64. [Google Scholar] [CrossRef] - Rahman, M.M.; Parvin, S.; Saidur, R.; Rahim, N.A. Magneto-hydrodynamic mixed convection in a horizontal channel with an open cavity. Int. Comm. Heat Mass Transf.
**2011**, 38, 184–193. [Google Scholar] [CrossRef] - Sharma, A.K.; Mahapatra, P.S.; Manna, N.K.; Ghosh, K. Mixed convection heat transfer in a grooved channel in the presence of a baffle. Numer. Heat Transf. Part A
**2015**, 67, 1097–1118. [Google Scholar] [CrossRef] - Janagi, K.; Sivasankaran, S.; Bhuvaneswari, M.; Eswaramurthi, M. Numerical study on free convection of cold water in a square porous cavity with sinusoidal wall temperature. Int. J. Numer. Methods Heat Fluid Flow
**2017**, 27, 1000–1014. [Google Scholar] [CrossRef] - Cheong, H.T.; Sivasankaran, S.; Bhuvaneswari, M. Natural convection in a wavy porous cavity with sinusoidal heating and internal heat generation. Int. J. Numer. Methods Heat Fluid Flow
**2017**, 27, 287–309. [Google Scholar] [CrossRef] - Sivasankaran, S.; Bhuvaneswari, M. Natural convection in a porous cavity with sinusoidal heating on both sidewalls. Numeri. Heat Transf. A
**2013**, 63, 14–30. [Google Scholar] [CrossRef] - Bhuvaneswari, M.; Sivasankaran, S.; Kim, Y.J. Magneto-convection in an enclosure with sinusoidal temperature distributions on both sidewalls. Numer. Heat Transf. A
**2011**, 59, 167–184. [Google Scholar] [CrossRef] - Li, Q.; Wang, J.; Wang, J.; Baleta, J.; Min, C.; Sundén, B. Effects of gravity and variable thermal properties on nanofluid convective heat transfer using connected and unconnected walls. Energy Convers. Manag.
**2018**, 171, 1440–1448. [Google Scholar] [CrossRef] - Bhardwaj, S.; Dalal, A.; Pati, S. Influence of wavy wall and non-uniform heating on natural convection heat transfer and entropy generation inside porous complex enclosure. Energy
**2015**, 79, 467–481. [Google Scholar] [CrossRef] - Sivasankaran, S.; Cheong, H.T.; Bhuvaneswari, M.; Ganesan, P. Effect of moving wall direction on mixed convection in an inclined lid-driven square cavity with sinusoidal heating. Numer. Heat Transf. A
**2016**, 69, 630–642. [Google Scholar] [CrossRef] - Cheong, H.T.; Siri, Z.; Sivasankaran, S. Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition. Int. Comm. Heat Mass Transf.
**2013**, 45, 75–85. [Google Scholar] [CrossRef] - Sivakumar, V.; Sivasankaran, S. Mixed convection in an inclined lid-driven cavity with non-uniform heating on both sidewalls. J. Appl. Mech. Tech. Phy.
**2014**, 55, 634–649. [Google Scholar] [CrossRef] - Hadidi, N.; Bennacer, R.; Ould-amer, Y. Two-dimensional thermosolutal natural convective heat and mass transfer in a bi-layered and inclined porous enclosure. Energy
**2015**, 93, 2582–2592. [Google Scholar] [CrossRef] - Wang, H.; Chen, J.; Dai, P.; Zhang, F.; Li, Q. Simulation and Experimental Study of the Influence of the Baffles on Solar Chimney Power Plant System. Processes
**2021**, 9, 902. [Google Scholar] [CrossRef] - Thao, P.B.; Truyen, D.C.; Phu, N.M. CFD Analysis and Taguchi-Based Optimization of the Thermohydraulic Performance of a Solar Air Heater Duct Baffled on a Back Plate. Appl. Sci.
**2021**, 11, 4645. [Google Scholar] [CrossRef] - Alazwari, M.A.; Safaei, M.R. Combination Effect of Baffle Arrangement and Hybrid Nanofluid on Thermal Performance of a Shell and Tube Heat Exchanger Using 3-D Homogeneous Mixture Model. Mathematics
**2021**, 9, 881. [Google Scholar] [CrossRef] - Yu, L.; Xue, M.; Zhu, A. Numerical Investigation of Sloshing in Rectangular Tank with Permeable Baffle. J. Mar. Sci. Eng.
**2020**, 8, 671. [Google Scholar] [CrossRef] - Mahapatra, S.K.; Sarkar, A. Numerical simulation of opposing mixed convection in differentially heated square enclosure with partition. Int. J. Therm. Sci.
**2007**, 46, 970–979. [Google Scholar] [CrossRef] - Ilis, G.G.; Mobedi, M.; Oztop, H.F. Heat transfer reduction due to a ceiling-mounted barrier in an enclosure with natural convection. Heat Transf. Eng.
**2011**, 32, 429–438. [Google Scholar] [CrossRef] [Green Version] - Khatamifar, M.; Lin, W.; Armfield, S.W.; Holmes, D.; Kirkpatrick, M.P. Conjugate natural convection heat transfer in a partitioned differentially-heated square cavity. Int. Comm. Heat Mass Transf.
**2017**, 81, 92–103. [Google Scholar] [CrossRef]

**Figure 10.**Comparison of the average Nu for different lengths of baffle and various inclination angles and Richardson numbers with ${L}_{B}$ = 0.

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**MDPI and ACS Style**

Sivasankaran, S.; Janagi, K.
Numerical Study on Mixed Convection Flow and Energy Transfer in an Inclined Channel Cavity: Effect of Baffle Size. *Math. Comput. Appl.* **2022**, *27*, 9.
https://doi.org/10.3390/mca27010009

**AMA Style**

Sivasankaran S, Janagi K.
Numerical Study on Mixed Convection Flow and Energy Transfer in an Inclined Channel Cavity: Effect of Baffle Size. *Mathematical and Computational Applications*. 2022; 27(1):9.
https://doi.org/10.3390/mca27010009

**Chicago/Turabian Style**

Sivasankaran, Sivanandam, and Kandasamy Janagi.
2022. "Numerical Study on Mixed Convection Flow and Energy Transfer in an Inclined Channel Cavity: Effect of Baffle Size" *Mathematical and Computational Applications* 27, no. 1: 9.
https://doi.org/10.3390/mca27010009