# Simulation of Natural Convection Heat Transfer in a 2-D Trapezoidal Enclosure

• K. Venkatadri Department of Mathematics, VEMU Institute of Technology, P.Kothakota-517112, India
• S. Abdul Gaffar Department of Information Technology, Mathematics Section, Salalah College of Technology, Salalah, Oman
• Ramachandra Prasad V. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore – 6322014, India
• B. Md. Hidayathulla Khan Department of Mathematics, Sir Vishveshwaraiah Institute of Science and Technology, Madanapalle- 517325, India
• O. Anwar Beg Magnetohydrodynamics, Biological Propulsion and Energy Research, Aeronautical and Mechanical Engineering Division, University of Salford, M5 4WT, UK
Keywords: Natural convection, Trapezoidal enclosure, Finite difference method, Incompressible flow, explicit time integration

### Abstract

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energyrelated applications, in case of proper design of enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 103 ≤ Ra ≤ 105 and Prandtl number (Pr = 0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra = 104 ). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported.

Published
2019-12-31
How to Cite
Venkatadri, K., Gaffar, S., Prasad V., R., Hidayathulla Khan, B. M., & Anwar Beg, O. (2019). Simulation of Natural Convection Heat Transfer in a 2-D Trapezoidal Enclosure. International Journal of Automotive and Mechanical Engineering, 16(4), 7375-7390. https://doi.org/10.15282/ijame.16.4.2019.13.0547
Section
Articles