# Heat and mass transfer empirical equations

• bill nye scienceguy!
In summary, when you want to identify the governing equation for a process, you first gather all the relevant data and then try to fit a curve to it.

#### bill nye scienceguy!

I guess this question applies to deriving empirical equations from any data set but in my engineering studies I've wondered this when working with heat and mass transfer.

When you do an experiment and want to identify the governing equation for the process, is it simply a case of bringing together all the variables you think appropriate and then trying to make an arrangement of them fit the curve on your graph?

It crosses my mind now as I'm working out the performance ratio of a multi-stage flash distillation plant and wondering how the hell someone derived this equation with 9 different terms, 7 different variables and 2 constants!

When you do an experiment and want to identify the governing equation for the process, is it simply a case of bringing together all the variables you think appropriate and then trying to make an arrangement of them fit the curve on your graph?

generally, yes, that's a good description. I have no idea how the specific equation you describe was developed, but likely it did not happen all at once...likely someone took a stab at it and someone else improved it...and it was gradually developed. It's analogous to fitting a straight line to a bunch of data points via a least squares fit...maybe that's accurate enough maybe not...for Hubble, as an example, that seemed to do the trick developing H0, the Hubble constant.

What you describe is also pretty much what Einstein did developing GR...he started from the famous insight, his equivalence principle, and so was able to derive a number of answers from the acceleration analogy to gravity...he had a number of different formulations and apparently discarded one by one them based on his understanding of how well they would match his anticipated behavior for the phenomena...In his case he did not even know how to do the math at first, his former teacher researched and found Riemannian geometry for Einstein...and Einstein leaned on other earlier formulations as well, like those of Lorentz and fitzgerald...

Another example is developing a feedback equation for some electrical system...a trick is to correlate the transfer function of the circuit with poles and zeros...one can then plot the results and get a visual representation of behavior...but before that mathematical trick was learned, it must have taken incredible trial and error and intuition to design a circuit with desired characteristics.

Today, I'm sure there must be some numerical analysis techniques that are computerized that can do a lot of what you suggest quickly and efficiently.

## 1. What are heat and mass transfer empirical equations?

Empirical equations are mathematical equations that have been derived from experimental data to describe the relationship between heat and mass transfer variables, such as temperature, pressure, and concentration. These equations are often used in engineering and scientific applications to predict the heat and mass transfer rates in different systems.

## 2. How are heat and mass transfer empirical equations different from theoretical equations?

Theoretical equations are based on fundamental principles and laws, such as conservation of energy and mass, and can be derived from first principles. Empirical equations, on the other hand, are based on experimental data and do not have a theoretical basis. They are often used when theoretical equations are not available or when the system is too complex to be described by theoretical models.

## 3. What are the limitations of heat and mass transfer empirical equations?

Empirical equations are based on experimental data and may not accurately describe the behavior of a system outside of the range of data used to derive the equation. They also do not take into account all the factors that may affect heat and mass transfer, such as fluid properties, geometry, and turbulence. Therefore, they should be used with caution and validated with experimental data for each specific application.

## 4. How are heat and mass transfer coefficients calculated using empirical equations?

The heat and mass transfer coefficients are calculated by using the empirical equations in conjunction with experimental data for the specific system. The data is used to determine the constants and parameters in the equation, which are then used to calculate the coefficients. These coefficients represent the rate of heat or mass transfer between the two mediums in the system.

## 5. What are some common examples of heat and mass transfer empirical equations?

Some common examples of heat and mass transfer empirical equations include the Nusselt number and Sherwood number correlations, which are used to calculate the heat and mass transfer coefficients in convection and diffusion processes, respectively. The Chilton-Colburn analogy is another example, which relates the heat and mass transfer coefficients in a system with similar fluid properties.