# Sherwood Number

on . Posted in Dimensionless Numbers

Sherwood number, abbreviated as Sh, a dimensionless number, is used in fluid dynamics and heat/mass transfer to describe the rate of mass transfer in a fluid flow over a surface.  It's often used in contexts where there is a transfer of material, such as heat or mass, between a fluid and a solid surface.  The Sherwood number is analogous to the Nusselt number (for heat transfer) and the Reynolds number (for fluid flow).  It characterizes the relative importance of convective transport (fluid movement) to diffusive transport (molecular diffusion) of a substance in the fluid and can be applied to various scenarios, including mass transfer of gases, liquids, or particles.

The Sherwood number can vary depending on the specific scenario and the nature of the mass transfer process.  For example, in the context of heat transfer, it can represent the ratio of convective heat transfer to conductive heat transfer.  In the context of mass transfer, it characterizes the ratio of convective mass transfer to diffusive mass transfer.

The Sherwood number is particularly relevant in applications involving chemical engineering, environmental engineering, and various industrial processes where understanding and optimizing mass transfer rates are important.  It's used to analyze and predict how quickly a substance is transported through a fluid medium across a solid surface.

## Sherwood Number formula

$$\large{ Sh = \frac{ K \; l_c }{ D } }$$     (Sherwood Number)

$$\large{ K = \frac{ Sh \; D }{ l_c } }$$

$$\large{ l_c = \frac{ Sh \; D }{ K } }$$

$$\large{ D = \frac{ K \; l_c }{ Sh } }$$

### Solve for Sh

 mass transfer coefficient, K characteristic length, lc diffusion coefficient, D

### Solve for K

 Sherwood number, Sh diffusion coefficient, D characteristic length, lc

### Solve for lc

 Sherwood number, Sh diffusion coefficient, D mass transfer coefficient, K

### Solve for D

 mass transfer coefficient, K characteristic length, lc Sherwood number, Sh

Symbol English Metric
$$\large{ Sh }$$ = Sherwood number $$\large{dimensionless}$$
$$\large{ K }$$ = mass transfer coefficient $$\large{dimensionless}$$
$$\large{ l_c }$$ = characteristic length $$\large{ft}$$ $$\large{m}$$
$$\large{ D }$$ = diffusion coefficient $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$

Tags: Flow Mass Fluid