CFD Online Discussion Forums - heat transfer equation of parcel

Dear All

Could you please write mathematical formulation of heat transfer equation for a droplet?

It is interpreted as follows in src/lagrangian/intermediate/parcels/Templates/ThermoParcel.C

Code:

template<class ParcelType>

template<class TrackData>

Foam::scalar Foam::ThermoParcel<ParcelType>::calcHeatTransfer

(

    TrackData& td,

    const scalar dt,

    const label cellI,

    const scalar Re,

    const scalar Pr,

    const scalar kappa,

    const scalar NCpW,

    const scalar Sh,

    scalar& dhsTrans,

    scalar& Sph

)

{

    if (!td.cloud().heatTransfer().active())

    {

        return T_;

    }



    const scalar d = this->d();

    const scalar rho = this->rho();



    // Calc heat transfer coefficient

    scalar htc = td.cloud().heatTransfer().htc(d, Re, Pr, kappa, NCpW);



    if (mag(htc) < ROOTVSMALL && !td.cloud().radiation())

    {

        return

            max

            (

                T_ + dt*Sh/(this->volume(d)*rho*Cp_),

                td.cloud().constProps().TMin()

            );

    }



    htc = max(htc, ROOTVSMALL);

    const scalar As = this->areaS(d);



    scalar ap = Tc_ + Sh/As/htc;

    scalar bp = 6.0*(Sh/As + htc*(Tc_ - T_));

    if (td.cloud().radiation())

    {

        tetIndices tetIs = this->currentTetIndices();

        const scalar Gc = td.GInterp().interpolate(this->position(), tetIs);

        const scalar sigma = physicoChemical::sigma.value();

        const scalar epsilon = td.cloud().constProps().epsilon0();



        ap = (ap + epsilon*Gc/(4.0*htc))/(1.0 + epsilon*sigma*pow3(T_)/htc);

        bp += 6.0*(epsilon*(Gc/4.0 - sigma*pow4(T_)));

    }

    bp /= rho*d*Cp_*(ap - T_) + ROOTVSMALL;



    // Integrate to find the new parcel temperature

    IntegrationScheme<scalar>::integrationResult Tres =

        td.cloud().TIntegrator().integrate(T_, dt, ap*bp, bp);



    scalar Tnew =

        min

        (

            max

            (

                Tres.value(),

                td.cloud().constProps().TMin()

            ),

            td.cloud().constProps().TMax()

        );



    Sph = dt*htc*As;



    dhsTrans += Sph*(Tres.average() - Tc_);



    return Tnew;

}