# Mass transfer coefficient from a numerical model

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In summary, the conversation discusses the relationship between Sherwood number and Reynolds number in a channel with different laminar velocity profiles. The focus is to find the relation between the mass transfer coefficient, which is dependent on the mass transport and concentration gradient, and the average velocity of the fluid. The concentration gradient can be determined by taking the difference between the concentration at the wall and the first layer of liquid in steady state. The question is raised on how to determine the mass transport of the species and whether it is sufficient to use the proportional relationship between the mass transfer coefficient and the average concentration gradient. The conversation also mentions a negative power relation between average velocity and the mass transfer coefficient, which is unexpected.
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TL;DR Summary
A numerical model has been made to obtain the relation between Sh and Re for different velocity profiles. How can Sh be expressed though, since the mass transport is not able to be expressed, or can it be left out? Without it, a negative power exponential relation is found.
Dear all,

For an assignment, I am trying to find the relationship between the Sherwood number and the Reynolds number in a channel for different laminar velocity profiles, where there is a concentration of a species at both the top and bottom wall which is transported to the fluid. For this, I solve a convection-diffusion problem. Now what it basically comes down to is find the relation between the mass transfer coefficient (the relevant parameter in the Sherwood number) and the average velocity of the fluid (the relevant parameter in the Reynolds number). However, the mass transfer coefficient depends on the mass transport and the concentration gradient, the driving force. The concentration gradient can be obtained by taking the difference between the concentration of the wall and the first layer of the liquid in steady state. My question is now, how do I determine the mass transport of the species exactly? Or would it be sufficient to just take: k (the mass transfer coefficient) = proportional to 1/average concentration gradient? This is what I took for now, but if I plot this, I get a negative power relation between average velocity and k. I would expect to find a positive power relation between 0 and 1. Could anybody help me with this? Thanks in advance!

The mass transfer coefficient is based on the difference between the concentration at the wall and the mixing cup average concentration: $$D\left(\frac{\partial C}{\partial z}\right)_{wall}=k(C_{wall}-\bar{C})$$For laminar flow, this is also going to be a function of distance along the channel.

MexChemE

## What is a mass transfer coefficient?

A mass transfer coefficient is a parameter that describes the rate at which a substance is transferred from one phase to another, such as from a gas to a liquid or from a liquid to a solid. It is typically expressed in units of mass per unit time per unit area.

## How is the mass transfer coefficient calculated from a numerical model?

The mass transfer coefficient can be calculated from a numerical model by solving equations that describe the physical processes involved in the transfer of mass. These equations take into account factors such as the properties of the substances involved, the flow conditions, and the geometry of the system.

## What factors can affect the mass transfer coefficient?

The mass transfer coefficient can be affected by a variety of factors, including the physical properties of the substances involved (such as their diffusivity and solubility), the temperature and pressure of the system, the flow rate and turbulence of the fluids, and the geometry of the system.

## Why is the mass transfer coefficient important in numerical modeling?

The mass transfer coefficient is an important parameter in numerical modeling because it helps to predict the rate at which a substance will be transferred between phases in a given system. This information is crucial for understanding and optimizing processes in fields such as chemical engineering, environmental science, and biotechnology.

## How can the accuracy of the mass transfer coefficient from a numerical model be validated?

The accuracy of the mass transfer coefficient from a numerical model can be validated by comparing the model's predictions to experimental data. This can involve conducting controlled experiments in a laboratory setting or collecting data from real-world systems. Additionally, sensitivity analyses can be performed to determine the impact of different factors on the calculated mass transfer coefficient.

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