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Buoyancy-driven fluid and energy flow in protruded heater enclosure

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Abstract

Flow structures and thermal aspects of buoyancy-driven flow occurring in the presence of protruded heater inside a square enclosure are investigated under different thermal boundary conditions of the enclosure for two common fluids (of Prandtl numbers Pr = 0.71 and 6.9) at various Rayleigh numbers (Ra = 103–106) numerically. The study is conducted considering a single heater as well as a set of two identical heaters located symmetrically on the bottom wall of the enclosure. Results reveals that the heat transfer, energy flow and fluid flow are markedly dependent on the heater aspect ratio, Ra, Pr and thermal boundary condition. Although with the single heater symmetric trends of fluid and heat flow are observed, the strong asymmetric flow features are found in case of the double heaters for Pr = 6.9 at higher Ra. Some interesting energy and fluid flow patterns are evolved depending upon the values of heater aspect ratio, interspatial heater distance and enclosure’s boundary condition. The visualization of mass and energy transports are properly appreciated using streamfunction and heatfunction. Total fluid flow inside the enclosure is analyzed by applying a novel approach based on streamfunctions of thermally induced vortices, which is also used to formulate a new streamfunction based symmetry indicator. It is seen that, with the increase in heater height although the total flow decreases, a consistent trend of increasing heat transfer is observed. The nature of steady-state solutions for the cavity is also analyzed by gradually increasing and decreasing Ra. Symmetry breaking bifurcation has been identified for Pr = 6.9. The bifurcation characteristics changes from supercritical to subcritical bifurcation depending upon thermal boundary conditions of the enclosure.

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Abbreviations

A :

Heater aspect ratio

d :

Distance between two heaters

D :

Dimensionless interspatial distance

g :

Acceleration due to gravity

h :

Heater height

H :

Dimensionless heater height

\(I_{\theta }\) :

Symmetry indicator based on \(\theta\)

\(I_{\psi }\) :

Symmetry indicator based on \(\psi\)

L :

Length/height of the enclosure

\({\text{Nu}}\) :

Nusselt number

p :

Pressure

P :

Dimensionless pressure

Pr :

Prandtl number

\(q_{i}\) :

Dimensionless total heat inflow

\(q_{o}\) :

Dimensionless total heat outflow

Ra :

Rayleigh number

SSC:

Side-side cold condition

STSC:

Side-top-side cold condition

T :

Temperature

u, v :

Velocity components

U, V:

Dimensionless velocity components

w :

Heater width

X, Y :

Dimensionless Cartesian coordinates

\(\alpha\) :

Thermal diffusivity

\(\beta\) :

Volumetric expansion coefficient

\(\theta\) :

Dimensionless temperature

\(\nu\) :

Kinematic viscosity

\(\varPi\) :

Dimensionless heat function

\(\rho\) :

Fluid density

\(\tau\) :

Dimensionless time

\(\varPsi\) :

Dimensionless streamfunction

1H, 2H :

One heater, two heaters

1HE :

Single heater enclosure

2HE :

Double heater enclosure

a :

Ambient

avg :

Average

c, h :

Cold wall, hot wall

max :

Maximum

min :

Minimum

tot :

Total

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Acknowledgments

The present authors would like to thank anonymous reviewers for their comments and valuable suggestions, which have improved the quality of this manuscript. The authors also wish to acknowledge helpful discussions with Prof. Dipankar Sanyal and Prof. Achintya Mukhopadhyay, Department of Mechanical Engineering, Jadavpur University.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700 032, India

    Nirmalendu Biswas & Nirmal Kumar Manna

  2. Department of Mechanical and Industrial Engineering, UIC, Chicago, IL, USA

    Pallab Sinha Mahapatra

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  1. Nirmalendu Biswas
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  2. Pallab Sinha Mahapatra
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  3. Nirmal Kumar Manna
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Correspondence to Nirmal Kumar Manna.

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Biswas, N., Mahapatra, P.S. & Manna, N.K. Buoyancy-driven fluid and energy flow in protruded heater enclosure. Meccanica 51, 2159–2184 (2016). https://doi.org/10.1007/s11012-016-0366-6

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