Numerical study of natural convection around a square cylinder within a square enclosure for different orientations


To attain the goal of sustainable development of resources, a study was conducted around a heated square cylinder placed inside a relatively cooler square enclosure. The temperature difference between the enclosure and cylinder is governed by different Rayleigh numbers (104, 105 and 106). For each case, analysis was done to know how the change in orientation of cylinder about its central axis affects the heat flow and flow characteristics. The problem is analyzed using ANSYS fluent and the plots are built-in Tecplot. The study also hopes to provide necessary analysis on flow characteristics by swotting through the Nusselt number, Skin friction coefficient, and pressure coefficient of each case. To further enrich the study, analysis on its vorticity, velocity magnitude, and drag is done. By comparing a square at the different rotation of 0°, 15°, 30°, 45°, 60°, and 75°, we inferred that 45° angle of rotation provides the most optimum and efficient means of heat transfer higher Rayleigh number. This is caused due to effective formation of the recirculation system around, which is formed due to an increase in velocity and skin friction drag around the cylinder and inside the enclosure.

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T h :

Temperature of cylinder walls (k)

T c :

Temperature at walls (k)

H :

Side of the square enclosure (m)

L :

Side of the square cylinder

θ :

Rotation angle

Nu :

Nusselt number

Ra :

Rayleigh number

k :

Thermal conductivity \(\left( {\frac{{{\rm W}}}{{{\rm K}}\,{{\rm m}}}} \right)\)

β :

Thermal expansion coefficient (K−1)

T :

Surface temperature (K)

T :

Bulk mean temperature (K)

α :

Thermal diffusivity (m2 s−1)

v :

Kinetic viscosity (m2 s−1)

h :

Convective heat transfer coefficient (w K m−2)

k :

Thermal conductivity (w  K m−1)

C f :

Coefficient of skin friction

τ w :

Shear stress (N  m−2)

ρ :

Density (kg  m−3)

C p :

Pressure coefficient

p :

Static pressure (N  m−2)

p :

Free stream pressure (N  m−2)

V :

Free stream velocity (m  s−1)

p ο :

Stagnation pressure (N  m−2)

V :

Velocity (m  s−1)


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We would like to thank the Product Development lab authorities and SRM Institute of Science and Technology for providing us with the resources to make this possible.

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Correspondence to Rajendran Senthil Kumar.

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Savio, R.R., Shaik, S. & Kumar, R.S. Numerical study of natural convection around a square cylinder within a square enclosure for different orientations. J Therm Anal Calorim (2021).

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  • Natural convection
  • Square enclosure
  • Square cylinder
  • CFD
  • Fluid flow