Fouling Factor in Heat Exchanger

Overall Heat Transfer Co-efficient

Reference - Heat Transfer A Basic Approach - M. Necati Ozisik
               Heat Transfer - J.P.Holman
all these pictures are taken from my notes. i don't have much time to write these equations in illustrator or other softwares. so, please forgive me if my handwriting is too bad to read. 

Heat Exchangers

Heat is a form of energy which we need to exchange for usual and unusual reasons. And, that is why heat exchangers have been created. Heat exchangers are devices that facilitate heat transfer between two or more bodies. Heat exchanger is very different from condensers and boilers. Heat exchangers are just devices which facilitate heat transfer and this heat transfer can be done to condensate or to boil a fluid. So, in short the purpose of a heat exchanger is to transfer heat from a hot body to a cold body but it doesn't mean that it is a condenser or it's cooling something. 

High Vapor Velocity Effect on Condensation Film Theory

According to Nusselt's assumption on condensation film theory, the vapor will be stagnant at the interface and there will be no frictional drag between the condensate and the vapor. However, it is not valid when the vapor velocity is large compared to the condensate velocity. Vapor causes the film thickness to increase. It happens when the vapor flows upward. The film thickness decreases when the vapor flows downward. Thus the heat transfer co-efficient increases.
Carpenter and Colburn correlated the data for condensation with high vapor velocity and got the following equation,

here,
hm = heat transfer co-efficient
Gm= mean mass velocity of vapor
f= frictional co-efficient

  

Blackbody Is not Actually Black

When we read blackbody, we usually think of a body which is completely black. But, it is not necessary that a body needs to be black to be a blackbody. Actually, in physics we have learned that the body which absorbs all incident rays of all wavelengths from all direction is called blackbody. Or, a body which radiates all kinds of rays of all wavelengths to all directions is called blackbody. However, the most important thing is the energy difference between a blackbody and a body which is staying around that blackbody. For example, we can consider sun as a blackbody with respect to earth.

outer surface of sun by NASA

The whole phenomena is called blackbody radiation. Fundamental quantity that specifies the magnitude of the radiation energy emitted by a blackbody at a certain wavelength at any fixed temperature is called spectral blackbody radiation intensity.


I know, saying things about a blackbody under condensation is funny, but i just can't finish my equations. I will upload my next post on condensation heat transfer again. 

Nusselt’s Theory of Film Condensation on Vertical Surface

In the above figure the condensation of vapor on a vertical plate has been shown. X- Axial co-ordinate which is measured downwards along the plate and y is the co-ordinate measured upward along the plate. The problem was first analyzed by Nusselt and there are several assumptions. These assumptions are,

-         

             Uniform plate temperature will be less than the saturation temperature of the vapor.

-          Vapor exerts no drag force on the condensate. 

-          Flow of the condensate is laminar.

-          Flow velocity is very low.

-          Properties of fluid are constant.

-          Liquid temperature distribution is linear because of pure conduction heat transfer across the condensate layer.

These assumptions are absolutely necessary to complete the analysis.  

Heat Flow While Condensation

Condensers and Boilers constitute an important and widely used type of heat exchanger with unique characteristics of heat transfer. Well, the analysis of heat transfer during condensing and boiling states is very complicated. To understand this phenomena we should start with the very basic steps.

If a vapor strikes a surface that is at a temperature below saturation temperature, the vapor will immediately converts into its liquid form. This incident is called condensation.

Thus we get filmwise condensation and dropwise condensation. When condensation takes place over a surface which is continuously being cooled by some cooling system and the condensed liquid is being removed by the motion produced by gravity then a thin layer of continuous liquid covers the whole condensing surface. This incident is called filmwise condensation.

Again, when condensation takes place over a surface and the condensed liquid is broken into droplets then it is called dropwise condensation.
Dropwise condensation usually occurs on those surfaces which are non-wettable or contains a good amount of impurities such as dust, oil, etc.
Heat transfer rate is between surface and vapor is very high for dropwise condensation because the film of condensed liquid produced in filmwise condensation process acts as a barrier. Thus dropwise condensation offers much less resistance to heat flow on the vapor side than the filmwise condensation.

Heat Flow Facts:

The motion of condensate is laminar and heat is transferred from vapor to liquid interface by conduction unless the velocity of vapor is very high or the liquid film thickness is very large. 

The rate of heat flow depends on the thickness of condensate. And, this thickness is dependent on the rate at which vapor is condensed and the rate at which vapor is removed. 

On the vertical surface the film thickness increases continuously from top to bottom.