# Mathematical model of fabric drying

#### seaside20

http://i.imgur.com/NArldL3.jpg

Problem:

Fabric is moving with given velocity on a surface heated by condensing vapor and air flows across fabric with given velocity. Air state, velocities, dimensions of fabric, temperatures of surface and air are given, also initial mass of fabric per m2 and initial moisture content of fabric are given.
For start I have to calculate how are temperature and moisture content changing along the fabric.

My try: I need to set the mass and energy balance. I calculated thermal transmittance of air (via Reynolds and Nusselt) and heat flux transfered to air.

This heat flux = heat flux of condensing vapor - heat flux used for drying fabric (evaporate water from it). qX-q(X+dX)=0 where X is moisture content and q is kg of dry fabric/sec

I don't think this is correct so I'm asking for your help.

#### studiot

A nice modelling problem.

I don't see a control volume in your picture.

I assume that the airflow over the fabric is dry.
So we can assume a certain volume of dry air at a certain temperature passes through a control volume and becomes saturated before exiting the control volume to be replaced by further dry air.
It may be that the exiting air is not fully dry inwhi h case exit conitions as well as entry conditions will be required.

It is not clear what you mean by "heated by condensing vapour".
Does this vapour or its condensate mix with the drying air or the fabric?

That would not make sense so I assume not.
In which case all you need from this sub process is the heat exhanged.

#### seaside20

Airflow over the fabric is not dry. The temperature and relative humidity are given which I used to calculate moisture content and enthalpy of air.

The biggest problem for me is that the temperature and moisture content are probably changing along x and y axis since the heated surface is moving also.

The condensate doesn't mix with the drying air or the fabric since it is in a bucket.