Natural Convection In Triangular Enclosure Research Articles

Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation

The flow and heat transfer due to natural convection in a triangular enclosure filled with a fluid saturated porous medium with a circular body in presence of heat generation has been numerically analyzed. The bottom wall of the enclosure is heated at a constant temperature while the left and right inclined wall of the cavity is maintained at cold temperature. The cavity contains a circular body which is insulated. The governing equations are solved numerically subject to suitable boundary conditions by Galerkin’s weighted residuals scheme of finite element method. Results are presented by streamlines, isotherms, mean Nusselt numbers for the variant parameters such as heat generation (λ) and radius of the circular body (R). Prandtl number (Pr) and Rayleigh number (Ra) are considered unchanged. It is found that these parameters have significant effect on the flow and temperature fields inside the cavity.

Natural convection in a triangular enclosure due to non-uniform cooling on top

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

Investigation of natural convection in triangular enclosure filled with porous medi saturated with water near 4 °C

Analysis of natural convection in right-angle triangular enclosure filled with saturated cold water which has a density maximum around of 3.98 °C is performed numerically. The bottom and vertical wall of triangular enclosure is isothermal while inclined wall is adiabatic. But temperature of bottom wall is higher than that of vertical wall. Non-Boussinesq and Darcy models are used in mathematical formulations of governing equations. The calculations were performed for different Ra number as (50 ⩽ Ra ⩽ 1000) and ratio of height to base of enclosure (0.25 ⩽ AR ⩽ 1.0). It is observed that heat transfer decreases with the effects of density inversion and it decreases with increasing of aspect ratio. It is an interesting result that effects of aspect ratio becomes insignificant for Ra ⩾ 1000 .

Unsteady natural convection in a triangular enclosure induced by absorption of radiation – a revisit by improved scaling analysis

The present study is concerned with radiation-induced natural convection in a water-filled triangular enclosure with a sloping bottom, which is directly relevant to buoyancy-driven flows in littoral regions. An improved scaling analysis is carried out to reveal more detailed features of the flow than a previously reported analysis. Two critical functions of the Rayleigh number with respect to the horizontal position are derived from the scaling for identifying the distinctness and stability of the thermal boundary layer. Four flow scenarios are possible, depending on the bottom slope and the maximum water depth. For each flow scenario, the flow domain may be composed of multiple subregions with distinct thermal and flow features, depending on the Rayleigh number. The dividing points between neighbouring subregions are determined by comparisons of the critical functions of the Rayleigh number with the global Rayleigh number. Position-dependent scales have been established to quantify the flow properties in different subregions. The different flow regimes for the case with relatively large bottom slopes and shallow waters are examined in detail. The present scaling results are verified by numerical simulations.

Finite element analysis of natural convection in a triangular enclosure: Effects of various thermal boundary conditions

The phenomena of natural convection in a right-angled triangular enclosure is studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier–Stokes and energy balance equations. The detailed study is carried out in two cases depending on various thermal boundary conditions: (a) Vertical wall is uniformly or linearly heated while inclined wall is cold isothermal. (b) Inclined wall is uniformly or linearly heated while vertical wall is cold isothermal. In all the cases horizontal bottom wall is adiabatic and the aspect ratio of the lengths of base and height is considered to be one. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Rayleigh number Ra ( 10 3 ⩽ Ra ⩽ 10 5 ) and Prandtl number Pr ( 0.07 ⩽ Pr ⩽ 1000 ) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It has been found that at low Rayleigh numbers ( Ra ⩽ 10 4 ) , the isotherms are almost parallel near the bottom portion of the triangular enclosure while at Ra = 10 5 , the isotherms are more distorted. This is because the heat transfer is primarily due to conduction for lower values of Rayleigh number. As Rayleigh number increases, there is a change from conduction dominant region to convection dominant region, and the critical Rayleigh number corresponding to on-set of convection is obtained. It has been shown that the average Nusselt number for vertical wall is 2 times that of the inclined wall as the bottom wall is adiabatic and that verifies the thermal equilibrium of the system for all case studies.