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Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top

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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 (ω) 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, ω and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by ω and Pr.

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Abbreviations

\(c_{p}\) :

Specific heat at constant pressure (J kg−1 K−1)

\(g\) :

Gravitational acceleration (ms−2)

\(H\) :

Height of the enclosure (m)

\(k\) :

Thermal conductivity (W m−1 K−1)

Nu:

Nusselt number

\(\Pr\) :

Prandtl number

\(P\) :

Non-dimensional pressure component

\(p\) :

Pressure component (Pa)

\(\text{Ra}\) :

Rayleigh number

\(T\) :

Temperature of the fluid (K)

\(T_{C}\) :

Temperature of side wall (K)

\(U\) :

Dimensionless velocity component along X

\(u\) :

Velocity component along x (ms−1)

\(V\) :

Dimensionless velocity component along Y

\(v\) :

Velocity component along y (ms−1)

\(X\) :

Dimensionless distance along x

\(x\) :

Distance along x (m)

\(Y\) :

Dimensionless distance along y

\(y\) :

Distance along y (m)

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\beta\) :

Volumetric expansion coefficient (K−1)

\(\rho\) :

Kinetic viscosity (m2 s−1)

\(\upsilon\) :

Density of fluid (kg m−3)

\(\theta\) :

Dimensionless temperature

\(\omega\) :

Heating frequency of the top wall

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Authors and Affiliations

  1. Mechanical Engineering Department, National Institute of Technology Sikkim, Ravangla, 737139, South Sikkim, India

    Saddam Hossain Mullick & Amit Kumar

  2. Mechanical Engineering Department, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004, India

    Pranab Kumar Kundu

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  1. Saddam Hossain Mullick
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  2. Amit Kumar
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Correspondence to Pranab Kumar Kundu.

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Mullick, S.H., Kumar, A. & Kundu, P.K. Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top. J. Inst. Eng. India Ser. C 101, 1043–1050 (2020). https://doi.org/10.1007/s40032-020-00618-y

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  • DOI: https://doi.org/10.1007/s40032-020-00618-y

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