# Clothes Dryer Modeling: Mass & Heat Transfer

• Eng27
In summary: The second equation is for the temperature of the air. The temperature will drop and the humidity in the air will increase because of the evaporation of water from the clothes.
Eng27
The other day I started what I thought would be an easy project of modeling what happens in a clothes dryer but I quickly realized I have no idea what equations to use for mass and heat transfer between the inlet air and the clothes in the dryer. I'm assuming they both depend on the reynolds number of the ventilation air and obviously its heat/humidity but how those factors interact with fabric is something I don't know how to even approximate. And the reynolds number would probably change drastically from when it enters the tumbler to when it runs into the tumbling cloths to when it exits through the exhaust. I tried looking up heat and mass transfer coefficients for fabric in turbulent air and got nothing. Any idea for a good model, close approximation, or even a table with some useful heat/mass transfer coefficients would be super helpful.

Eng27 said:
The other day I started what I thought would be an easy project of modeling what happens in a clothes dryer but I quickly realized I have no idea what equations to use for mass and heat transfer between the inlet air and the clothes in the dryer. I'm assuming they both depend on the reynolds number of the ventilation air and obviously its heat/humidity but how those factors interact with fabric is something I don't know how to even approximate. And the reynolds number would probably change drastically from when it enters the tumbler to when it runs into the tumbling cloths to when it exits through the exhaust. I tried looking up heat and mass transfer coefficients for fabric in turbulent air and got nothing. Any idea for a good model, close approximation, or even a table with some useful heat/mass transfer coefficients would be super helpful.

Welcome to the PF.

Reynolds number? Try starting first with a more simplified model to get some initial results that are close, then add more complicated modeling into get more accurate results. What equations can you start with for evaporation as a function of temperature?

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I've already made an initial model with results that are somewhat close to real-world expectations... but definitely not to the point where it's a reliable model. The only equation I've found for evaporation rate is the following which is intended to calculate evaporation rate of water from a standing pool with a flow of air across the surface of a constant velocity:

O=.0000881+.0000776*v;
m=((O*(P1-P2))/Y)*A; %water evaporated in kg/s

where:
P1-P2 = difference in vapor pressure between the water and passing air (in Pa)
v=velocity of the air (m/s)
Y=2501; heat of vaporization (in kJ/kg)
A=Area (m^2) of water exposed to the air

I've used this equation in the model but I'm getting results that don't match experimental data. And the area term is pretty hard to estimate in a tumbling dryer situation.

As for the heat transfer, I'm just using the basic equation:
Q=h*A*(T1-T2)
but without a good way to determine h, I've just been inputing numbers until the results of my model start approaching experimental data. The problematic A term is also in this equation.

All of which goes to show that the clothes dryer was designed neither by scientists nor engineers.

You may be ahead of me already... but what value have you assumed for velocity? I am guessing the velocity of the clothes during the tumble exceeds the velocity of the air flow through the drum by a significant amount.

I don't know if some of the equations you are using for your model are particularly apt for a clothes dryer.

The dryer blows warm air onto the clothes to increase evaporation and remove the moisture from the fibers. Hopefully, the warm air is also drier and has the capacity to accept more moisture content. If you time dry on a warm humid day versus a cold dry day, your clothes may not come out of the machine fully dry on the hot day.

The tumbling action serves not only to increase air flow over the wet clothes, but it also helps to expose more of the area of the clothes to the warmer air circulating in the machine, otherwise, without tumbling, the clothes would stick together and only those clothes on top would get dried.

Such a simple machine, but devilishly complex to model.

Eng27
Have a look at Wet-bulb temperature form wkii, the well known source of information
http://en.wikipedia.org/wiki/Wet-bulb_temperature

There are 2 equations that you can use or modify to suit your purpose, plus an explanation.

Basically the clothes are a source of water that has air of a water content blowing over them. From the first eqaution the water from the clothes evaporates into the air and the temperature of the clothes will drop, and the moisture content of the air will increase. Obviously that is not the case but you could use that as one of your models to see how it turns out.

The second equation has a conductive heat transfer from the air to the clothes. With this the moisture content of the air increases and the temperature of the clothes also increases via conduction. From that one gets the Tsat = Twet-bulb, which would be the temperature of the more humid air coming out of the exit tube.

You can also look up adiabatic saturation temperature and see how that is calculated.

Here is a more involved pdf that someone put out there on wet bulb and adaibatic saturation temperatures, though that uses the Reynolds, Prandtl, Nusselt, Lewis, Schmidt, and Sherwood ( that's a new one for me ) numbers and has a few nifty equations, if you really want to be courageous in addapting that to your clothes dryer.

good luck!

Thanks everyone for the responses, the initial equations I could find were obviously not meant for this type of model and I appreciate the help.

Chet,
These sources look like they should hold the solution to this problem, thanks! They're both a little daunting but hopefully once I get further in, things will start falling into place. I'm going to try one more simplified model using the experimental data I have to estimate mass/heat transfer rates but once I get a good base model set up the equations in these sources should be able to fill any holes.

As for using just the mass/heat transfer involved with a wet-bulb setup, this seems like a good setup for an initial model. But down the line I don't think it takes into account the complexity of what happens at the surface of the fabric. It also wouldn't take the velocity of the air into account which is known to have a sizable effect on the evaporation rate and wouldn't explain the slow-down of evaporation once the clothes get closer to their dry point.

Here's another idea. You could try a best case model (to give you the minimum possible drying time and/or air usage). Assume that the air and clothes in the dryer are well mixed, and that the exit air is at the same temperature as the clothes and at 100% humidity at that temperature. Then you could do a simple transient heat and mass balance on the clothes, and a heat and mass balance on the air (which could be treated as treated as quasi steady state). This is basically the same as assuming that the heat transfer coefficient between the clothes and the air, and the mass transfer coefficient between the clothes and the air are very high, and that the air in the dryer is well-mixed. This model would at least give you some numbers to play with, and would give you a first order picture of what the effect of changes in inlet air humidity, inlet air temperature, clothes mass, clothes initial temperature, and clothes initial water content would have.

Chet

## 1. What is clothes dryer modeling and why is it important?

Clothes dryer modeling is the process of using mathematical equations and computer simulations to study the mass and heat transfer that occurs during the drying process. It is important because it allows for a better understanding of how different factors, such as load size and dryer settings, affect the drying performance and energy efficiency of the dryer.

## 2. What are the key factors that affect the mass and heat transfer in a clothes dryer?

The key factors that affect mass and heat transfer in a clothes dryer include the air temperature, humidity, air flow rate, and the physical properties of the clothes being dried. These factors can impact the drying time, energy consumption, and overall drying efficiency of the dryer.

## 3. How do scientists model the mass and heat transfer in a clothes dryer?

Scientists use a combination of experimental data and mathematical equations to model the mass and heat transfer in a clothes dryer. These equations take into account the variables mentioned in the previous question, as well as the geometry of the dryer and the materials used in its construction.

## 4. What are the challenges in modeling mass and heat transfer in a clothes dryer?

One of the main challenges in modeling mass and heat transfer in a clothes dryer is accurately representing the complex interactions between the air, clothes, and dryer components. Additionally, the physical properties of clothes, such as fabric type and moisture content, can vary greatly and can be difficult to measure, making it challenging to create accurate models.

## 5. How can clothes dryer modeling help improve dryer design and efficiency?

Clothes dryer modeling can help improve dryer design and efficiency by providing insights into how different factors and settings affect the drying performance. This information can be used to optimize dryer design and settings, leading to shorter drying times, reduced energy consumption, and improved overall efficiency.

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