Abstract
Natural convection in a triangular enclosure subject to non-uniform cooling at the inclined surfaces and uniform heating at the base is investigated numerically. The numerical simulations of the unsteady flows over a range of Rayleigh numbers and aspect ratios are carried out using the Finite Volume Method. Since the upper surface is cooled and the bottom surface is heated, the air flow in the enclosure is potentially unstable to Rayleigh--Benard instability. Based on the numerical results, the transient flow development in the enclosure is classified into three distinct stages: an early stage, a transitional stage, and a steady stage. In addition, the flow inside the enclosure strongly depends on the governing parameters; Rayleigh number and aspect ratio. The asymmetric behaviour of the flow about the geometric centre line is discussed in detailed. The heat transfer through the roof and the ceiling as a form of Nusselt number is also reported. References O. M. Kamiyo, D. Angeli, G. S. Barozzi, M. W. Collins, V. O. S. Olunloyo, S. O. Talabi, A comprehensive review of natural convection in triangular enclosures, Applied Mechanics Reviews , 63 , 060801. doi:10.1115/1.4004290 S. C. Saha, M. M. K. Khan, A review of natural convection and heat transfer in attic-shaped space, Energy and Buildings , 43 , 2564--2571. doi:10.1016/j.enbuild.2011.06.020 V. A. Akinsete, T. A. Coleman, Heat transfer by steady laminar free convection in triangular enclosures, Int. J. Heat Mass Trans. , 25 , 1982, 991--998. doi:10.1016/0017-9310(82)90074-6 E. M. del Campo, M. Sen, E. Ramos, Analysis of laminar natural convection in a triangular enclosure, Numer. Heat Transfer , 13 , 1988, 353--372. doi:10.1080/10407788808913618 H. Asan, L. Namli, Numerical simulation of buoyant flow in a roof of triangular cross-section under winter day boundary conditions, Energy and Buildings 33 , 2001, 753--757. doi:10.1016/S0378-7788(01)00063-9 D. Poulikakos, A. Bejan, The fluid dynamics of an attic space, J. Fluid Mech. 131 , 1983, 251--269. doi:10.1017/S0022112083001317 C. Lei, S. W. Armfield, J. C. Patterson, Unsteady natural convection in a water-filled isosceles triangular enclosure heated from below, Int. J. Heat Mass Trans. 51 , 2008, 2637--2650. doi:10.1016/j.ijheatmasstransfer.2007.09.036 S. C. Saha, J. C. Patterson, C. Lei, Natural convection in attic-shaped spaces subject to sudden and ramp heating boundary conditions, Heat Mass Transfer , 46 , 2010, 1432--1181. doi:10.1007/s00231-010-0607-5 S. C. Saha, Unsteady natural convection in a triangular enclosure under isothermal heating, Energy and Buildings , 43 , 2011a, 695-703. doi:10.1016/j.enbuild.2010.11.014 S. C. Saha, Scaling of free convection heat transfer in a triangular cavity for $Pr > 1$, Energy and Buildings , 43 , 2011b, 2908--2917. doi:10.1016/j.enbuild.2011.07.016 G. A. Holtzman, R. W. Hill, K. S. Bal, Laminar natural convection in isosceles triangular enclosures heated from below and symmetrically cooled from above, J. Heat Transfer , 122 , 2000, 485--491. doi:10.1115/1.1288707 S. C. Saha, J. C. Patterson, C. Lei, Natural convection and heat transfer in attics subject to periodic thermal forcing, Int. J. Thermal Sciences , 49 , 2010, 1899--1910. doi:10.1016/j.ijthermalsci.2010.05.010
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