Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top
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ORIGINAL CONTRIBUTION
Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top Saddam Hossain Mullick1
•
Amit Kumar1
•
Pranab Kumar Kundu2
Received: 11 May 2020 / Accepted: 1 September 2020 The Institution of Engineers (India) 2020
Abstract The prime objective of the present numerical study is to analyse buoyancy-driven thermal flow behaviour inside an enclosure with the application of nonlinear heating from top surface which is commonly essential in glass industries. A fluid-filled square cavity with sinusoidal heating from top surface, adiabatic bottom wall and constant temperature side walls is considered here. The thermal flow behaviour has been numerically observed with the help of relevant parameters like stream functions, isotherms and Nusselt number. For the present investigation, Rayleigh number (Ra), Prandtl number (Pr) and heating frequency of the wall (x) are varied from 103 to 106, 0.7 to 7 and 0.5 to 2, respectively. It has been noticed from the investigation that flow dynamics drastically alter with Ra, x and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by x and Pr. Keywords Free convection Buoyancy Rayleigh number Pr number Sinusoidal heating List cp g H k Nu
of symbols Specific heat at constant pressure (J kg-1 K-1) Gravitational acceleration (ms-2) Height of the enclosure (m) Thermal conductivity (W m-1 K-1) Nusselt number
& Pranab Kumar Kundu [email protected]; [email protected] 1
Mechanical Engineering Department, National Institute of Technology Sikkim, Ravangla 737139, South Sikkim, India
2
Mechanical Engineering Department, Motilal Nehru National Institute of Technology Allahabad, Prayagraj 211004, India
Pr P p Ra T TC U u V v X x Y y
Prandtl number Non-dimensional pressure component Pressure component (Pa) Rayleigh number Temperature of the fluid (K) Temperature of side wall (K) Dimensionless velocity component along X Velocity component along x (ms-1) Dimensionless velocity component along Y Velocity component along y (ms-1) Dimensionless distance along x Distance along x (m) Dimensionless distance along y Distance along y (m)
Greek letters a Thermal diffusivity (m2 s-1) b Volumetric expansion coefficient (K-1) q Kinetic viscosity (m2 s-1) t Density of fluid (kg m-3) h Dimensionless temperature x Heating frequency of the top wall
Introduction The problem of buoyancy-driven thermal flow behaviour inside enclosure has received attention of researchers as it has a great advantage of no external power requirement to circulate the flow and has wide range of engineering applications such as high sensitive chemical reactor, cooling of electronic devices, crude oil production, etc. [1–4]. A good volume of studies is available in which free convection inside enclosure has been investigated thoroughly to understand the flow characteristics where
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J. Inst. Eng. India Ser. C
buoyancy is induced from below [5, 6] and from side walls [7]. Bhattac
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