{
    volScalarField k1
    (
        "k1",
        alpha1*(thermo1.alpha()/rho1 + sqr(Ct)*nut2*thermo1.CpByCpv()/Prt)
    );

    volScalarField k2
    (
        "k2",
        alpha2*(thermo2.alpha()/rho2 + nut2*thermo2.CpByCpv()/Prt)
    );

    volScalarField& he1 = thermo1.he();
    volScalarField& he2 = thermo2.he();

    volScalarField Cpv1(thermo1.Cpv());
    volScalarField Cpv2(thermo2.Cpv());

    fvScalarMatrix he1Eqn
    (
        fvm::ddt(alpha1, he1)
      + fvm::div(alphaPhi1, he1)

        // Compressibity correction
      - fvm::Sp(fvc::ddt(alpha1) + fvc::div(alphaPhi1), he1)

      - fvm::laplacian(k1, he1)
     ==
        heatTransferCoeff*(thermo2.T() - thermo1.T())/rho1
      + heatTransferCoeff*he1/Cpv1/rho1
      - fvm::Sp(heatTransferCoeff/Cpv1/rho1, he1)
      + alpha1*(dpdt/rho1 - (fvc::ddt(K1) + fvc::div(phi1, K1)))
    );

    fvScalarMatrix he2Eqn
    (
        fvm::ddt(alpha2, he2)
      + fvm::div(alphaPhi2, he2)

        // Compressibity correction
      - fvm::Sp(fvc::ddt(alpha2) + fvc::div(alphaPhi2), he2)

      - fvm::laplacian(k2, he2)
     ==
        heatTransferCoeff*(thermo1.T() - thermo2.T())/rho2
      + heatTransferCoeff*he2/Cpv2/rho2
      - fvm::Sp(heatTransferCoeff/Cpv2/rho2, he2)
      + alpha2*(dpdt/rho2 - (fvc::ddt(K2) + fvc::div(phi2, K2)))
    );

    he1Eqn.relax();
    he1Eqn.solve();

    he2Eqn.relax();
    he2Eqn.solve();

    thermo1.correct();
    thermo2.correct();
}