# Natural convection heat transfer and entropy generation from a heated cylinder of different geometry in an enclosure with non-uniform temperature distribution on the walls

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## Abstract

A numerical investigation has been performed to visualize the natural convective heat transfer and nature of entropy generation from a heated cylinder of two separate geometries (circular and square) situated within a square enclosure subjected to non-uniform temperature distributions on the left vertical and bottom walls. The flow inside the enclosure is steady, incompressible and laminar and the working fluid is Newtonian with constant Prandtl number (*Pr* = 0.71). The results are discussed in terms of the distribution of streamlines and isotherms, surface-averaged Nusselt number and entropy generation, for a different combination of Rayleigh number (10^{3} to 10^{6}) and dimensionless wavelength of sinusoidal temperature distribution (\(0.1 \le \lambda \le 0.7\)). It reveals that sinusoidal temperature with higher wavelength enhances the heat transfer. Moreover, the highest value of Nusselt number is obtained in case of enclosure embraces the circular cylinder. Further, the thermal entropy generation is observed to be minimum for sinusoidal temperature distribution with a wavelength of 0.7 irrespective of Rayleigh number. In addition to this, the geometrical configuration of the cylinder has a negligible effect on the variation of fluid friction and thermal irreversibility at higher Rayleigh number. Finally, the circular shape of the embedded cylinder is found to be optimal since it results in maximum heat transfer with least entropy generation.

## Keywords

Natural convection Entropy generation Sinusoidal temperature distribution Embedded cylinder## List of symbols

*d*Diameter or side length of the embedded cylinder (m)

*D*Dimensionless diameter or side length of the embedded cylinder (=

*d*/*L*)- g
Gravitational acceleration (m s

^{−2})*h*Heat transfer coefficient (W m

^{−2}K^{−1})*k*Thermal conductivity (W m

^{−1}K^{−1})*L*Side length of the square enclosure (m)

*Nu*_{φ}Local Nusselt number (–)

- \(\overline{Nu}\)
Surface average Nusselt number

*N*_{θ,T}Dimensionless volumetric thermal entropy generation (–)

*N*_{Ψ,T}Dimensionless volumetric viscous entropy generation (–)

*p*Pressure (Pa)

*P*^{*}Dimensionless pressure

*Pr*Prandtl number

*Ra*Rayleigh number

*Be*Bejan number

*T*_{c}Temperature of cold wall (K)

*T*_{h}Maximum temperature (K)

*u*,*v*Velocity components in

*x*and*y*directions (m s^{−1})*U*^{*},*V*^{*}Dimensionless velocity components in

*X*and*Y*directions*x*,*y*Cartesian coordinates (m)

*X*^{*},*Y*^{*}Cartesian coordinates in dimensionless form

## Greek symbols

- \(\alpha\)
Thermal diffusivity (m

^{2}s^{−1})- \(\beta\)
Coefficient of thermal expansion (K

^{−1})*θ*Dimensionless temperature

*λ*Dimensionless wavelength

*µ*Dynamic viscosity (N s m

^{−2})*ν*Kinematic viscosity (m

^{2}s^{−1})*ρ*Fluid density (kg m

^{−3})*χ*Wavelength (m)

## Notes

## References

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