Abstract
Natural convective flow and heat transfer around a locally heated circular cylinder kept in a rectangular enclosure are investigated. At first, a problem valid for a rectangular domain is formulated and then an analytical coordinate transformation is introduced to map the rectangular domain to the physical domain considered here. Based on the coordinate transformation, a set of governing equations is obtained which is further simulated by imposing appropriate conditions on the walls of the cavity and the inner solid bodies. Numerical solutions are validated through comparison of the present results with the available published data. It is found that streamlines and isotherms are greatly influenced by the width (w) and breadth (b) of the heat source and the Rayleigh number (
References
[1] G. Batchelor, Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Q. Appl. Math.12 (1954), 209–233.10.1090/qam/64563Search in Google Scholar
[2] Y. Jaluria and Natural Convection Heat, Mass Transfer, Pergamon Press, Oxford, UK, 1980. 209–235.Search in Google Scholar
[3] G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer. Methods Fluids3 (1983), 249–264.10.1002/fld.1650030305Search in Google Scholar
[4] S. Ostrach, Natural convection in enclosures, J. Heat Transf.110 (1988), 1175–1190.10.1016/S0065-2717(08)70039-XSearch in Google Scholar
[5] M. Sankar and Y. Do, Numerical simulation of free convection heat transfer in a vertical annular cavity with discrete heating, Int. Commun. Heat Mass Transf.37 (2010), 600–606.10.1016/j.icheatmasstransfer.2010.02.009Search in Google Scholar
[6] K. Khanafer, A. Al-Amiri and J. Bull, Laminar natural convection heat transfer in a differentially heated cavity with a thin porous fin attached to the hot wall, Int. J. Heat Mass Transf.87 (2015), 59–70.10.1016/j.ijheatmasstransfer.2015.03.077Search in Google Scholar
[7] Z. Boulahia, A. Wakif and R. Sehaqui, Numerical investigation of mixed convection heat transfer of nanofluid in a lid driven square cavity with three triangular heating blocks, Int. J. Comput. Appl.143 (2016), 37–45.10.5120/ijca2016910227Search in Google Scholar
[8] A. Wakif, Z. Boulahia, S. R. Mishra, M. M. Rashidi and R. Sehaqui, Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno’s mathematical model, Eur. Phys. J. Plus133 (2018), 181.10.1140/epjp/i2018-12037-7Search in Google Scholar
[9] A. Wakif, A. Chamkha, T. Thumma, I. L. Animasaun and R. Sehaqui, Thermal radiation and surface roughness effects on the thermo-magneto-hydrodynamic stability of alumina–copper oxide hybrid nanofluids utilizing the generalized Buongiorno’s nanofluid model, J. Therm. Anal. Calorim. (2020), DOI: 10.1007/s10973-020-09488-z.Search in Google Scholar
[10] A. Sohankar, C. Norberg and L. Davidson, Low Reynolds number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition, Int. J. Numer. Methods Fluids26 (1998), 39–56.10.1002/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-PSearch in Google Scholar
[11] O. Posdziech and R. Grundmann, A systematic approach to the numerical calculation of fundamental quantities of the twodimensional flow over a circular cylinder, J. Fluids Struct.23 (2007), 479–499.10.1016/j.jfluidstructs.2006.09.004Search in Google Scholar
[12] S. Sarkar, A. Dalal and G. Biswas, Unsteady wake dynamics and heat transfer in forced and mixed convection past a circular cylinder in cross flow for high Prandtl numbers, Int. J. Heat Mass Transf.54 (2011), 3536–3551.10.1016/j.ijheatmasstransfer.2011.03.032Search in Google Scholar
[13] L. Carassale, A. Freda and M. Marrè-Brunenghi, Experimental investigation on the aerodynamic behaviour of square cylinders with rounded corners, J. Fluids Struct.44 (2014), 195–204.10.1016/j.jfluidstructs.2013.10.010Search in Google Scholar
[14] A. Minaei, M. Ashjaee and M. Goharkhah, Experimental and numerical study of mixed and natural convection in an enclosure with a discrete heat source and ventilation ports, Heat Transf. Eng.35 (2014), no. 1, 63–73.10.1080/01457632.2013.810455Search in Google Scholar
[15] M. A. Mansour, S. E. Ahmed and A. M. Rashad, MHD natural convection in a square enclosure using nanofluid with the influence of thermal boundary conditions, J. Appl. Fluid Mech.. 9 (2016), no. 5, 2515–2525.10.18869/acadpub.jafm.68.236.24409Search in Google Scholar
[16] S. E. Ahmed and A. M. Rashad, Natural convection of micropolar nanofluids in a rectangular enclosure saturated with anisotropic porous media, J. Porous Media19 (2016), no. 8, 737–750.10.1615/JPorMedia.v19.i8.60Search in Google Scholar
[17] A. M. Rashad, R. S. R. Gorla, M. A. Mansour and S. E. Ahmed, Magnetohydrodynamic effect on natural convection in a cavity filled with a porous medium saturated with nanofluid, J. Porous Media20 (2017), no. 4, 363–379.10.1615/JPorMedia.v20.i4.50Search in Google Scholar
[18] A. F. Al-Mudhaf, A. M. Rashad, S. E. Ahmed, A. J. Chamkha and S. M. M. EL-Kabeir, Soret and Dufour effects on unsteady double diffusive natural convection in porous trapezoidal enclosures, Int. J. Mech. Sci. (2018), DOI: 10.1016/j.ijmecsci.2018.02.049.Search in Google Scholar
[19] Z. Abdel-Nour, A. Aissa, F. Mebarek-Oudina, A. M. Rashad, H. M. Ali, M. Sahnoun, et al., Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation, J. Therm. Anal. Calorim. (2020), DOI: 10.1007/s10973-020-09690-z.Search in Google Scholar
[20] G. S. Barozzi and M. A. Corticelli, Natural convection in cavities containing internal sources, Heat Mass Transf.36 (2000), 473–480.10.1007/s002310000119Search in Google Scholar
[21] T. -H. Chen and L. -Y. Chen, Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure, Int. J. Therm. Sci.46 (2007), 1219–1231.10.1016/j.ijthermalsci.2006.11.021Search in Google Scholar
[22] G. V. Kuznetsov and M. A. Sheremet, Conjugate heat transfer in an enclosure under the condition of internal mass transfer and in the presence of the local heat source, Int. J. Heat Mass Transf.52 (2009), 1–8.10.1016/j.ijheatmasstransfer.2008.06.034Search in Google Scholar
[23] T. H. Hsu and S. G. Wang, Mixed convection in a rectangular enclosure with discrete heat sources, Numer. Heat Transf., Part A, Appl.38 (2000), no. 6, 627–652.10.1080/104077800750021170Search in Google Scholar
[24] S. M. Aminossadati and B. Ghasemi, Natural convection of water–CuO nanofluid in a cavity with two pairs of heat source–sink, Int. Commun. Heat Mass Transf.38 (2011), 672–678.10.1016/j.icheatmasstransfer.2011.03.013Search in Google Scholar
[25] M. Sankar, B. Kim, J. M. Lopez and Y. Do, Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus, Int. J. Heat Mass Transf.55 (2012), 4116–4128.10.1016/j.ijheatmasstransfer.2012.03.053Search in Google Scholar
[26] S. G. Martyushev and M. A. Sheremet, Numerical analysis of conjugate natural convection and surface radiation in an enclosure with local heat source, Comput. Therm. Sci., 5 no. 1, (2013), 11–25.10.1615/ComputThermalScien.2012006040Search in Google Scholar
[27] H. F. Öztop, P. Estellé, W. -M. Yan, K. Al-Salem, J. Orfi and O. Mahian, A brief review of natural convection in enclosures under localized heating with and without nanofluids, Int. Commun. Heat Mass Transf.60 (2015), 37–44.10.1016/j.icheatmasstransfer.2014.11.001Search in Google Scholar
[28] M. Mirzaie and E. Lakzian, Natural convection of Cu–water nanofluid near water density inversion in horizontal annulus with different arrangements of discrete heat source-Sink pair, Adv. Powder Technol.27 (2016), no. 4, 1337–1346.10.1016/j.apt.2016.04.028Search in Google Scholar
[29] N. S. Bondareva and M. A. Sheremet, Effect of inclined magnetic field on natural convection melting in a square cavity with a local heat source, J. Magn. Magn. Mater.419 (2016), 476–484.10.1016/j.jmmm.2016.06.050Search in Google Scholar
[30] N. Gibanov and M. Sheremet, Unsteady natural convection in a cubical cavity with a triangular heat source, Int. J. Numer. Methods Heat Fluid Flow 27 (2017), 1795–1813.10.1108/HFF-06-2016-0234Search in Google Scholar
[31] A. Doostali and M. Rezazadeh, Numerical study of natural convection in a cavity with discrete heat sources, Eur. Phys. J. Plus133 (2018). 511.10.1140/epjp/i2018-12323-4Search in Google Scholar
[32] N. C. Roy, Md. A. Hossain and R. S. R. Gorla, Natural convection in a cavity with trapezoidal heat sources mounted on a square cylinder, SN Appl. Sci. 2 (2020) Art. No. 143.10.1007/s42452-019-1927-9Search in Google Scholar
[33] C. Shu and Y. D. Zhu, Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder, Int. J. Numer. Methods Fluids38 (2002), 429–445.10.1002/fld.226Search in Google Scholar
[34] V. Prasad, F. C. Lai and F. A. Kulacki, Mixed convection in horizontal porous layers heated from below, J. Heat Transf.110 (1988), no. 2, 395–402.10.1115/1.3250498Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research Articles
- A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations
- A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining
- The Ideal Gas in Slow Time
- Natural Convection Around a Locally Heated Circular Cylinder Placed in a Rectangular Enclosure
- Exergy-Based Ecological Optimization of an Irreversible Quantum Carnot Heat Pump with Spin-1/2 Systems
- Polydisperse Colloids Two-Moment Diffusion Model Through Irreversible Thermodynamics Considerations
- Open-Circuit Voltage Comes from Non-Equilibrium Thermodynamics
Articles in the same Issue
- Frontmatter
- Research Articles
- A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations
- A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining
- The Ideal Gas in Slow Time
- Natural Convection Around a Locally Heated Circular Cylinder Placed in a Rectangular Enclosure
- Exergy-Based Ecological Optimization of an Irreversible Quantum Carnot Heat Pump with Spin-1/2 Systems
- Polydisperse Colloids Two-Moment Diffusion Model Through Irreversible Thermodynamics Considerations
- Open-Circuit Voltage Comes from Non-Equilibrium Thermodynamics