If hot water flowing through pipe is to be cooled by air forced convection with known mass flow rate and cross sectional area, then which boundary condition is to be used?
Since temp of water in pipe goes on decreasing, the constant wall temp boundary condition cannot be used i guess.
Does heat transfer coefficient boundary condition imply constant heat flux boundary condition?
Hi Gaurav,
By "heat transfer coefficient boundary", my impression is that you meant a convective condition at your interface. Some textbooks call this a third-type boundary condition. This condition is used when you have a fixed fluid condition around your object and therefore a constant convective heat transfer coefficient. This does sound appropriate for your case, but it does not mean that heat flux is constant. Your boundary condition at the outside of the pipe is:
h (Tpipe - Tair) = -k dTpipe/dr_pipe
The heat flux to air depends on h, your temperature difference between the pipe surface and the air, and the local gradient of temperature at the pipe surface. As your fluid temperature decreases, the pipe temperature decreases as well, meaning less heat transfer to the surrounding air stream.
Indeed the simplest boundary condition between a wall at Tw and a flow at Tf is the approximation of Newton, stating that the heat flux F (heat transport per unit time and surface area) from the wall to the fluid is proportional to the temperature difference (Tw-Tf)between the wall and the fluid:
F=h(Tw-Tf)
where h is the so called heat transfer coefficient. This coefficient can be estimated but often empirical relations are used. In some cases (high temperature differences Tw-Tf) Tf is not the bulk fluid temperature, but rather a "film" temperature. This relationship should be used on both the water side and the air side. In addition to this the wall resistance to heat flux can be significant, unless one uses a metallic wall (in glass for example). Hence you have 3 contributions to the resistance to heat transport (water-wall, wall internal, wall-air). In transient cases you may have to take into account the heat capacity of the wall.
The book of Adrian Bejan on heat transfer or on heat exchangers is most useful:
http://k204.ru/books/English/Heat_transfer_handbook_.pdf
Thankyou sir,
but then why temperature variation profile ( wall and fluid) along the length is not available for convective boundary condition unlike in other 2 cases
I do not understand your statement.
Basically one can use different boundary conditions depending on the accuracy of the model. In a model assuming a uniform temperature in the water and a uniform temperature of the air, one usually uses the Newton approximation. Depending on the wall properties one should also calculate the temperature profile in the wall (transversal or longitudinal). As stated earlier the book of Bejan provides excellent detailed discussion, you should read the book. There is no simple answer to your question.
Hi Gaurav,
You should look at the derivation of the heat exchanger equations - this will give you one idea of how to account for the change in water temperature as it goes down the pipe. If your pipe wall is relatively thin (thin enough to be pseudo-steady) then looking at the lumped capacitance model will also be relevant - any undergrad heat transfer textbook will have this analysis.
Derrick
In addition to the respected answered offered, you should care about the flow regime and being fully-developed or developing flow, since calculating the convective heat transfer coefficient strongly depends on the correlations you are using.
- Badges
- Science topic
- Similar topics
- Engineering
- Modeling