# heat transfer equation of parcel

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 March 6, 2015, 07:12 heat transfer equation of parcel #1 Member   Neilson Whit Join Date: Aug 2011 Location: Japan Posts: 57 Rep Power: 7 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 template Foam::scalar Foam::ThermoParcel::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::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; }```

 June 23, 2016, 04:24 #2 New Member   Amir Join Date: Feb 2012 Posts: 11 Rep Power: 6 Dear Neilson, Have you found any mathematics formulation for parcel energy balance or any reference that the model is written based on? Regards,

 November 24, 2016, 10:49 #3 Member   Chris Cloney Join Date: Jun 2016 Location: Halifax, Canada Posts: 33 Rep Power: 2 One note here is that Spu, Sh, Sph, and dhstrans are all passed in as zeros to the calcHeatTransfer function. That starts to get you close to something that looks like the textbook equations, but I am still working on it.

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