**Cylinder Correlation: **

In this section we study the mass transfer around cylinder, for this reason we put a cylinder of hight $H$ and diameter $D$ such that $H=D$ and we perform simulations for constant Schimit number $Sc=100$ and Reynold number $Re \in [0,1]$ . We vary the angle $\alpha$ of the cylindre as explained in the figure below and we calculate the flux for $\alpha \in [0,90]$ in order to see the effect of the angle on the mass transfer and in order to find a correlation similar to Ranz-Marshall correlation for the cylinder.

** **

** The angle $\alpha$ between the cylinder axis and the vertical**

** Geometry Mesh**

As proposed by some papers , the correlation in convection-diffusion phenomena can be written according to the power law:

$$ Sh=A+BRe^nSc^m$$

Where the constants can be detrmined from the fitting of the data . From pure diffusion A can be determined because at velocity equal to zero there is no convection and $Re=0$ and so the second term vanishes , from pure diffusion we have obtained A=2.48 . The other constants will be detrmined from the fitting .

**Velocity profile-Re=0.4**

** ****Concentration profile-Re=0.4,Pe=40**

** **** The calculated Sherwood number for diffirent angles with the basic fitting .**

The above figure shows the Sherwood number variation for different angels $\alpha$ in a laminar flow , the flux decreases when $\alpha$ increases untill it reaches a minimum at $\alpha=90$. At $\alpha=0$ the calculated values have a basic fitting $Sh=Sh_0+Re^{0.4}Sc^{0.46}$ where $Sh_0=2.48$ and has been determined from pure diffusion.