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What exactly is h in externalWallHeatFluxTemperature BC?

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Old   January 16, 2015, 09:24
Default What exactly is h in externalWallHeatFluxTemperature BC?
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Petr Furmanek
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Hi all!

Maybe it is a stupid question, but after looking into the code I'm still a bit confused about true meaning of h in the externalWallHeatFluxTemperature. If I assume the following boundary problem

internal fluid -> wall -> environment

there are two heat transfer coefficients coming into play -
alpha_1 between the internal fluid and the wall and
alpha_2 between the wall and the environment.

So which one of these is h?
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Old   January 17, 2015, 05:39
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Alexey Matveichev
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Hi,

If you take a look at the sources, here's the way heat flux is calculated:

Code:
        case fixedHeatTransferCoeff:
        {
            scalar totalSolidRes = 0.0;
            if (thicknessLayers_.size() > 0)
            {
                forAll (thicknessLayers_, iLayer)
                {
                    const scalar l = thicknessLayers_[iLayer];
                    if (kappaLayers_[iLayer] > 0.0)
                    {
                        totalSolidRes += l/kappaLayers_[iLayer];
                    }
                }
            }
            q = (Ta_ - Tp)*(1.0/h_ + totalSolidRes);
            break;
        }
Ta_ is ambient temperature, Tp is temperature on the patch. Now, assuming you neglected additional thermal resistance, h can be calculated as

1/h = 1/h_{flud->wall} + 1/h_{wall} + 1/h_{wall->external}
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Old   January 17, 2015, 16:51
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Petr Furmanek
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Hi Alexey,

thanks for the reply. I'm using OF v 2.3.x with a little bit different code

Code:
            if (thicknessLayers_.size() > 0)
            {
                forAll (thicknessLayers_, iLayer)
                {
                    const scalar l = thicknessLayers_[iLayer];
                    if (kappaLayers_[iLayer] > 0.0)
                    {
                        totalSolidRes += l/kappaLayers_[iLayer];
                    }
                }
            }
            hp = 1.0/(1.0/h_ + totalSolidRes);
and then

Code:
    else if (mode_ == fixedHeatTransferCoeff)
    {
        Qr /= Tp;
        refGrad() =  0.0;
        refValue() =  hp*Ta_/(hp - Qr);
        valueFraction() =
            (hp - Qr)/((hp - Qr) + kappa(Tp)*patch().deltaCoeffs());
    }
where Qr is radiative heat flux. You're right that from theory the overall hp value is
Quote:
1/hp = 1/h_{fluid->wall} + 1/h_{wall} + 1/h_{wall->external}
I wasn't sure if there is something neglected in the code or not... So if it isn't then apparently

1/h_{wall} = totalSolidRes

so I presume

1/h_ = 1/h_{fluid->wall} + 1/h_{wall->external}

I suppose I have to estimate the 1/h_{fluid->wall} for example from



as mentioned in https://en.wikipedia.org/wiki/Heat_transfer_coefficient

and then do a similar thing for 1/h_{wall->external} to get the h_ for input of the boundary condition...
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Old   January 18, 2015, 05:05
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Petr Furmanek
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After looking into code of mixedFvPatchScalarField and fluidThermo I think I got it. The h_ is the outer heat transfer coefficient - the 1/h_{wall->external}.

Heat transfer from internal fluid -> wall is solved using the kappa() field, inside the wall with the use of totalSolidRes which leaves the h_{wall->external} to be set by the user.
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Old   January 18, 2015, 09:35
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Alex
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Exactly Petr, h is the external heat transfer coefficient, the value of the solid resistance is calculated if you provide values of the kappa layers and thickness layers, otherwise it's neglected.

Regards,

Alex
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