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Analysis of geometrical shape impact on thermal management of practical fluids using square and circular cavities

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Abstract

The heating or cooling performance of convective thermal systems is critically dependent upon their geometrical shapes/configurations apart from other controlling aspects. Here, an effort is made to address the shape impact on thermal performance, using square and circular systems under the classical differentially heating configuration. The comparison of systems’ performance is made by applying the constraints of identical fluid volume, heating and cooling surfaces, and cavity inclinations for both systems. The study covers mostly used practical working fluids namely air, water, and a water-based nanofluid. For such a type of thermal system analysis, the numerical approach is chosen appropriately to generate a huge volume of the solved results. The Prandtl number, Rayleigh number, the nanofluid concentration, and cavity orientation are used as the system parameters, and the study reveals a strong impact of the cavities’ shapes. In general, the thermal performance and evolved circulation (due to the differential heating) are found superior with the circular cavity over its equivalent square cavity configuration. The analysis confirms that the geometric modification is a better choice for achieving superior heat transfer; the heat transfer enhancement could be up to \(\sim 22.21{\%}\) (when the cavity is horizontal), 24.11% (with inclined cavity) with air as a working medium. There is a further enhancement on heat transfer with the modified circular cavity up to 2.76% (with horizontal cavity), 15.19% (with inclined cavity) using nanofluid. The heat flow dynamics from the heating side to the cooling side are also explored using the Bejan’s heatlines. The outcome of this study will help the designer to model the thermal device considering various controlling aspects from an appropriate thermal management point of view.

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Availability of data

The data that support the findings of this study are available from the corresponding author upon request.

Abbreviations

\(C_{P}\) :

Specific heat of fluid (J \(\hbox {kg}^{-1}\, \hbox {K}^{-1})\)

g :

Acceleration due to gravity (m \(\hbox {s}^{-2})\)

H :

Cavity height/length scale (m)

k :

Thermal conductivity (W \(\hbox {m}^{-1}\, \hbox {K}^{-1})\)

Ha:

Hartmann number

Nu:

Average Nusselt number

P :

Dimensionless pressure

Pr:

Prandtl number

Ra:

Rayleigh number

T :

Temperature (K)

u,v :

Velocity components (m \(\hbox {s}^{-1})\)

U, V :

Dimensionless velocity components

x, y :

Cartesian coordinates (m)

X, Y :

Dimensionless coordinates

\(\alpha \) :

Thermal diffusivity (\(\hbox {m}^{2}\, \hbox {s}^{-1})\)

\(\beta \) :

Thermal expansion coefficient (\(\hbox {K}^{-1})\)

\(\theta \) :

Dimensionless temperature

\(\mu \) :

Dynamic viscosity(Nm \(\hbox {s}^{-2})\)

\(\nu \) :

Kinematic viscosity (\(\hbox {m}^{2}\, \hbox {s}^{-1})\)

\(\rho \) :

Density (kg \(\hbox {m}^{-3})\)

\(\zeta \) :

Nanoparticle volume fraction

\(\psi \) :

Dimensionless stream function

c :

Cold

f :

Base fluid

h :

Hot

max :

Maximum

min :

Maximum

r :

Property ratio

s :

Solid

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Authors and Affiliations

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

    Abhinav Saha, Nirmal K. Manna & Koushik Ghosh

  2. Department of Power Engineering, Jadavpur University, Salt Lake, Kolkata, India

    Nirmalendu Biswas

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  1. Abhinav Saha
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  2. Nirmal K. Manna
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  3. Koushik Ghosh
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  4. Nirmalendu Biswas
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Correspondence to Nirmalendu Biswas.

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Saha, A., Manna, N.K., Ghosh, K. et al. Analysis of geometrical shape impact on thermal management of practical fluids using square and circular cavities. Eur. Phys. J. Spec. Top. 231, 2509–2537 (2022). https://doi.org/10.1140/epjs/s11734-022-00593-8

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