Convection heat transfer, Fluent vs Calculations

[eaboujaoudeh]

Hi all

I've been calculating heat convection off a horizontal heated plate to still cool air around it. Since the plate has a size of 50m2 the GrPr number is turbulent i there's no equation in my book to calculate heat transfer by convection for GrPr > 10^11, so i used the equation of GrPr at 10^11, and got that the heat transfer from the plate to the surrounding is 1700W. On fluent 6.1 I'm getting 600W...which one to believe?

Elie

 

[desA]

Decrease your element size on Fluent a few times, until the solution stops changing. What do you have now?

 

[eaboujaoudeh]

the solution on Fluent is stable, i have 410000+ meshed volumes, the pc would explode if i add more. the answer is constantly 600W ! and i think it has reached convergence.

 

[desA]

the solution on Fluent is stable, i have 410000+ meshed volumes, the pc would explode if i add more. the answer is constantly 600W ! and i think it has reached convergence.

Mesh convergence, or solution convergence?

Your equation geometry vs the Fluent model geometry will be important.

 

[eaboujaoudeh]

well solution convergence. the equation geometry? the setting is normal convection over a horizontal plate. there's no integration and the like, just 1 simple derived formula. My setting is a pool inside a closed fixed temp room. I've taken the pool as a plate to be able to find the Heat transfer coefficient of air, this coeff is independant of the surface in contact with air. since i need to heat the pool to a fixed temperature, so taking the pool as a plate shouldn't be a bad idea ! (its like taking an intermediate plate between the pool and air and finding the total resistance then setting the plate's thickness to zero). so i don't know where i did wrong !

 

[desA]

I see where you are going.

Is your airflow blowing over the surface of the pool & picking up its heat that way?

In terms of getting the heat transfer from a surface up into a fluid volume, the element shape & size immediate to the surface is crucial, as the temperature & velocity gradients at the surface are the ones used in calculating the final heat-transfer. Take a lot of care in this area - perhaps rather increase mesh density in this region, & decrease further out in the volume as you move away from the surface - a trade. This may be part of the reason for the discrepancy.

This is what I meant by mesh convergence - try adjusting this & watch to see if the heat-transfer changes with mesh change. Keep on refining near to the surface until the answer converges to an asymptote. I hope this helps.

desA

 

[eaboujaoudeh]

i already did that. i installed boundary layers next to the area close to the pool but how do u check mesh convergence? Btw, before on the plate i put plate thickness of 2m which is the depth of the pool. in the next trial which I'm doing now i removed the thickness, the heat transfer rocketed to 6000W ! I'm losing my mind

 

[desA]

Mesh convergence is a way of getting a comfort-level of your solution value.

Basically, as I said, decrease & keep on refining your mesh - on the airside - closest to the surface in both x-y dimension & especially *thickness* - & plot your solution as you go. You may need to do a few runs before you see a trend emerging.

The water thickness is less important for now as it conducts heat much better than the water-air interface. Take a lot of care at the water-air interface.

Go back to your textbooks on convective heat-transfer & look at the way the convection relationships were derived. All rely on a temperature profile & temperature gradient AT the surface. This will make, or break your solution accuracy in your Fluent model if the elements are too thick.

desA

 

[eaboujaoudeh]

if water thickness is not that important,(which i know) but how did it change the answer from 600W-->5900W? i will remesh my volume, mayb try one without a boundary layer even though i think bdry layer is very important in such natural convection. btw. do u believe that the empirical equation might be somewhat correct even though it was designed for a different Gr.Pr number?

 

[desA]

It would be useful if you try to see how the equation was derived, as many of these convection-type equations start off actually being derived from first principles on an assumed temperature & velocity profile. This ends up in an ODE which is solved via separation of variables & ultimately infinite series. The resulting value is then tweeked slightly from experimental values.

Get hold of Crawford's convection book.

The reason for your change with your water calculation probably has to do with a small versus large volume. What I meant was that you can treat the water as a lumped condition applied to the fluid-air interface - in the form of a boundary condition. Then you model in Fluent only the airside.

It is useful to try a hand computation on this first - which you've probably done - then figure out how to model in the effect of the water heat-transfer as a boundary-condition applied to the water-air interface. You save elements, computation time. A body of water will not support meaningful changes of temperature across its width without trying to compensate, but this will mean a huge model & then, honestly, I'd do a simple hand computation.

 

[eaboujaoudeh]

now I've realized something. when i put thickness to the water plate it changes temperature, while if i put a no thickness plate it maintains its temperature, propably that was the difference between the heat transfer fluxes. I've tried the method u told me, unfortunately i can't trust my hand calculations using the wrong formula which wasn't designed for my case. i will try to see Crawford's convection book, but i don't have high hopes about finding it. anyway u guessed the next step, i have to compensate later by designing a heat exchanger that would harness heat to heat the pool:) which i have to do by hand then check it on Fluent. thnx for your help i'll try to check the origins of the formula like u said, mayb i'll find a clue.

 

[eaboujaoudeh]

wow, I'm getting 2000W ! very close to the 1713 i got by hand ! i think I'm pretty close now..i'll take that as my answer. thnx man

 

[desA]

My pleasure - 2000W is close-enough. You now have a design factor-of-safety of slightly more than 10%.

Well done.

 

[rlamadri]

hi, could you please tell me, in which option yo can see the convection coefficient.

thanks