Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature

• Published in: International journal of numerical methods for heat & fluid flow 2018-01, Vol.28 (1), p.103-117
• Main Authors: K, Kalidasan, Velkennedy, R, Taler, Jan, Taler, Dawid, Oclon, Pawel, P, Rajesh Kanna
• Format: Article
• Language: English
• Subjects: Adiabatic flow; Aerodynamics; Air; Alternating direction implicit methods; Amplitude; Boundary conditions; Buoyancy; Civil engineering; Computational fluid dynamics; Computer simulation; Contours; Convection; Cooling; Direction; Enclosures; Energy; Energy equation; Engineering schools; Fluid flow; Fluid mechanics; Fluids; Free convection; Heat; Heat transfer; Heating; Hydrodynamics; Investigations; Isotherms; Laminar flow; Low temperature; Mathematical models; Mechanical engineering; Momentum; Parameters; Rayleigh number; Shape; Stream functions; Stream functions (fluids); Streamlines; Velocity; Vorticity; Wall temperature
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/HFF-03-2017-0125

Purpose This study aims to perform a numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature under laminar flow conditions. The geometry of the enclosure contains two isothermal blocks placed equidistant along the streamwise direction. The top wall is assumed to be cold (low temperature). The bottom wall temperature is either kept as constant or sinusoidally varied with time. The vertical walls are considered as adiabatic. The flow is diagonally upwards and assisted by the buoyancy force. The inlet is positioned at the bottom of the left wall, and the outlet is placed at the top of the right wall. The parameters considered in this paper are Rayleigh number (104-106), Prantdl number (0.71), amplitude of temperature oscillation (0-0.5) and the period (0.2). The effects of these parameters on heat transfer and fluid flow inside the open cavity are studied. The periodic results of fluid flow are illustrated with streamlines and the heat transfer is represented by isotherms and time-averaged Nusselt number. By virtue of increasing buoyancy, the heat transfer accelerates with an increase in the Rayleigh number. Also, the heat transfer is intensive with an increase in the bottom wall temperature. Design/methodology/approach The momentum and energy equations are solved simultaneously. The energy equation (3) is initially solved using the alternating direction implicit (ADI) method. The results of the energy equation are updated into the vorticity equation. The unsteady vorticity transport equation is also solved using the ADI method. Dimensionless time step equal to 0.01 is used for high Ra (105 and 106) and 0.001 is used for low Ra (104). Convergence criteria of 10−5 is used during the vorticity, stream function and temperature calculations, as the sum of error should be very small. Findings Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature is performed under laminar flow condition. The effect of the isothermal blocks on the heat transfer is analyzed for different Rayleigh numbers and the following conclusions are arrived. The hydrodynamic blockage effect is subdued by the isothermal heating of square blocks. Based on the streamline diagrams, it is found that the formation of vortices is greatly influenced by the Rayleigh number when all the walls are exposed to a constant wall temperature. The influence of amplitud