# Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements

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## Abstract

Buoyancy-driven convective heat transfer from a semi-circular cylinder for various confinements has been studied using numerical simulations for wide ranges of parameters, Reynolds numbers (1 ≤ *Re* ≤ 50), Richardson numbers (0 ≤ *Ri* ≤ 2), Prandtl numbers (0.7 ≤ *Pr* ≤ 50) and confinement ratios (0.2 ≤ *β* ≤ 0.8). A hot semi-circular cylinder is symmetrically kept in a 2D rectangular confinement. The circular side of the cylinder faces the upstream flow and the fluid flows against gravity in the channel. The governing equations are numerically solved using FLUENT and the results obtained are presented in the form of isotherms, streamlines, pressure coefficients, drag coefficients, Nusselt numbers, etc. The highest value of pressure coefficient increases with blockage ratio for all cases. The drag coefficient decreases with *Re* and shows complex phenomena with change in *Ri* and blockage ratio of the channel. Pressure drag has contributed more as compared with viscous drag in all cases. The curved surface showed more heat transfer than the flat surface of the semi-circular cylinder. The value of *β* also has great influence at large value of Peclect numbers (= 2500). Overall average heat transfer in terms of average Nusselt number is a function of *Ri*, *Re*, *Pr* and *β*.

## Keywords

Channel flow mixed convection semi-circular cylinder CFD## Nomenclature

*C*_{D}drag coefficient at the surface of semi-circular cylinder (dimensionless)

*C*_{DF}friction (viscous) drag coefficient at the surface of semi-circular cylinder (dimensionless)

*C*_{DP}pressure drag coefficient at the surface of semi-circular cylinder (dimensionless)

*c*_{p}specific heat capacity of the fluid (J/kg K)

*C*_{P}pressure coefficient at the surface of semi-circular cylinder (dimensionless)

*D*diameter of semi-circular cylinder (m)

*F*_{D}drag force per unit length of semi-circular cylinder (N/m)

*F*_{DP}pressure drag force per unit length of semi-circular cylinder (N/m)

*F*_{DF}friction (viscous) drag force per unit length of semi-circular cylinder (N/m)

*g*gravitational acceleration (m/s

^{2})*h*_{avg}average heat transfer coefficient at surface of semi-circular cylinder (W/m

^{2}K)*Gr*Grashof number [=

*gβ*_{V}Δ*T D*^{3}*ρ*^{2}/*µ*^{2}] (dimensionless)*k*thermal conductivity of the fluid (W/m K)

*L*gap between two adiabatic confining walls (m)

*M*,*N*distance (m)

*n*_{s}unit vector normal to cylinder surface

*P*pressure (Pa)

*Pe*Peclet number [=

*Re.Pr*] (dimensionless)*P*_{s}static pressure at cylinder surface (Pa)

*P*_{∞}fluid pressure at inlet section (Pa)

*Pr*Prandtl number [=

*c*_{p}*µ*/*k*] (dimensionless)*Re*Reynolds number [=

*DV*_{∞}*ρ*/*µ*] (dimensionless)*S*surface area of cylinder (m

^{2})*T*_{w}wall temperature of the cylinder (K)

*T*fluid absolute temperature (K)

*T*_{∞}fluid temperature at the inlet section (K)

*U*fluid velocity in

*X*-direction (m/s)*V*fluid velocity in

*Y*-direction (m/s)*V*_{max}maximum velocity at inlet of confinement (m/s)

*V*_{∞}average velocity at inlet of confinement (m/s)

*X*,*Y*Cartesian co-ordinates (m)

## Greek symbols

*β*blockage ratio of confinement [=

*D*/*L*] (dimensionless)*β*_{V}coefficient of thermal volumetric expansion of fluid (K

^{−1})*θ*fluid temperature (dimensionless)

*ρ*fluid density (kg/m

^{3})*ρ*_{∞}fluid density at temperature of

*T*_{∞}(kg/m^{3})*µ*dynamic viscosity of fluid (kg/m s)

*δ*size of grid element at surface of semi-circular cylinder (m)

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