# Multi-objective optimization of the heat transmission and fluid forces around a rounded cornered square cylinder

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## Abstract

The unsteady fluid stream and warmth transmission nearby a square cylinder with sharp and rounded cornered edges are numerically examined, and then the roundness of the corner is predicted and optimized for the minimum fluid forces and maximum heat transmission rate. The roundness of the cylinder corner is changing 0.5*D* (circle) to 0.71*D* (square); *D* is the depth of the cylinder. The fluid flow and the heat transmission features around the sharp and curved cornered square cylinder are evaluated with the streamline, isotherm patterns, pressure coefficient, drag and lift coefficients, local Nusselt number (*Nu*_{local}) and average Nusselt number (*Nu*_{avg}) at different *Re* and for several roundness values. These characteristics are predicted by the gene expression programming, and then the multi-objective genetic algorithm is utilized for the optimization. A number of combinations of values of corners have been found in the form of Pareto-optimal solution to compromise the minimum fluid forces with maximum heat transfer rate.

## Keywords

Sharp and rounded corner Fluid flow and heat transfer Multi-objective optimization NSGA## List of symbols

*B*Blockage ratio (

*D*/*H*)*C*_{p}Specific heat of the fluid (J/kg K)

*D*Width of the square cylinder (m)

*h*Local convective heat transfer coefficient (W/m

^{2}K)*H*Height of the domain (m)

*k*Thermal conductivity of the fluid (W/m K)

*L*_{d}Downstream face distance of the inlet from the cylinder center (m)

*L*_{u}Upstream face distance of the inlet from the cylinder center (m)

*N*_{i}Actual value

*P*_{i}Predicted value

*Re*Reynolds number (\(= \frac{{\rho U_{\infty } D}}{\mu }\)) (dimensionless)

*t*Time (dimensionless)

*U*_{∞}Free stream velocity (m/s)

*x*,*y*Cartesian coordinates

*p*_{∞}Free stream pressure

*R*Radius of corner (m)

*r*Radius of corner (dimensionless,

*R*/*D*)*u*,*v*Velocity components in

*x*and*y*directions (m/s)

## Greek symbols

*μ*Viscosity of the fluid (Pa s)

*ρ*Density

*θ*Dimensionless temperature (\(= \frac{{\bar{T} - T_{\infty } }}{{T_{\text{w}} - T_{\infty } }}\))

## Subscript

- ∞
Free stream

- w
Cylinder surface

*i*Number of data

## Superscript

- –
Dimensional variable

## Notes

### Compliance with ethical standards

### Conflict of interest

There is no conflict of interest.

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