
[Sponsors] 
Is CovectionDiffusion the right equation for my problem? 

LinkBack  Thread Tools  Search this Thread  Display Modes 
January 12, 2020, 08:56 
Is CovectionDiffusion the right equation for my problem?

#1 
New Member
Muhammad Usama
Join Date: Sep 2017
Posts: 6
Rep Power: 4 
I have a simple internal pipe flow. The walls are made of water (if that makes sense) and I know the walls's temperature at the top and at the bottom. I also know the inlet temperature of the air, but I want to know the outlet temperature of the air  I also want the temperature profile of the whole wall, knowing temperatures at every point.
Which equation should I be solving, I have a feeling it should be ConvectionDiffusion equation. Here, I've made a simple illustration to explain my problem. (PLEASE HELP ) https://drive.google.com/open?id=1hy...On8bnMn9JEi8sb 

January 12, 2020, 11:08 

#2 
Senior Member

I have doubts on the configuration, as even in deep space without gravity you wouldn't be able to keep "water walls" still with the air flowing along, not to mention how you could blow air between them and not move the water.
However, it can be done simply by treating the "walls" as solid (as in more regular scenarios) but using the water properties. But I'm not sure if this actually represents what you have in mind... and, in any case, you have to solve the NS equations, not a simple convection diffusion one 

January 12, 2020, 14:46 

#3 
New Member
Muhammad Usama
Join Date: Sep 2017
Posts: 6
Rep Power: 4 
Well I actually just want to develop a mathematical model for the evaporation phenomena for a simplistic cooling tower in which I have the freedom to change input air Temperature and input water Temperature.
My methodology is to solve Convection Diffusion equation for the water using FDM, this would simply give me a temperature profile of the water along the length of the tower. I will then use this temperature profile in a formula for convection that is designed to give output temperature of air flowing inside a pipe, if you have the temperature of the internal walls of the pipe and the temperature of the air inlet. I intend to use the Convection Diffusion equation to get the temperature of internal walls. Finally, I should be left with a mathematical model that gives you the temperature profile of air inside a cooling tower assuming that all the water thrown from the top gets evaporated just when it reaches the bottom. Why would I need to solve the NS equations? Is there a mistake or shortcoming in my methodology? I'm a total beginner so my questions may sound naive. Sorry :/ 

January 12, 2020, 16:24 

#4  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 5,005
Rep Power: 53 
Quote:
The convective part of the temperature equation requires the velocity field of the water. Are you considering that the velocity field is already known? Generally, temperature can be solved after the velocityt field in case of incompressible flows but some case requires to take into account the buoyancy effect. 

January 13, 2020, 03:01 

#5 
New Member
Muhammad Usama
Join Date: Sep 2017
Posts: 6
Rep Power: 4 
Yes, I'm considering constant velocity of both water and air in the cooling tower and I've confirmed that experimentally, it's a very reasonable assumption.
But does the temperature equation take into account the changes in latent heat as water evaporates? and by temperature equation, you mean the energy governing (NS) equation, right? Thanks 

January 13, 2020, 03:06 

#6  
New Member
Muhammad Usama
Join Date: Sep 2017
Posts: 6
Rep Power: 4 
Quote:
But does the temperature equation take into account the changes in latent heat as water evaporates? and by temperature equation, you mean the energy governing (NS) equation, right? Thanks 

January 13, 2020, 04:24 

#7 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 5,005
Rep Power: 53 
Yes, the internal energy equation is that for solving the temperature field.
Be aware that a uniform velocity field is a vere very rude assumption. 

January 13, 2020, 04:29 

#8 
New Member
Muhammad Usama
Join Date: Sep 2017
Posts: 6
Rep Power: 4 
In the energy equation, how do I incorporate temperature change due to phase change process? In my case, water temperature drops as it loses heat of vaporization and water vapors leave the bulk water surface. But air also loses temperature as a temperature difference is created between water and air due to phase change.


January 13, 2020, 06:23 

#9  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 5,005
Rep Power: 53 
Quote:
you have to look for multiphase flow problems, a very different and more complex NSE problem than the simple linear convectiondiffusion equation 

Tags 
convection, diffusion, fdm, heat and mass transfer 
Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
mass flow in is not equal to mass flow out  saii  CFX  12  March 19, 2018 06:21 
Adding diffusion term to interFoam transport equation  Gearb0x  OpenFOAM Programming & Development  2  August 30, 2017 08:51 
Setting the height of the stream in the free channel  kevinmccartin  CFX  10  July 9, 2015 22:36 
Problem in discretising the governing equation.  sahilkala50  Main CFD Forum  2  September 4, 2013 06:45 
problem on energy and flow equation solving separately  preetam69  FLUENT  2  July 30, 2013 22:08 