/* * The thermal conductivity is computed from the following mixture rule: * \f[ * \lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right) * \f] * * It's used to compute the flux of energy due to a thermal gradient * * \f[ * j_T = - \lambda \nabla T * \f] * * The flux of energy has units of energy (kg m2 /s2) per second per area. * * The units of lambda are W / m K which is equivalent to kg m / s^3 K. * * @return Returns the mixture thermal conductivity, with units of W/m/K */ doublereal MixTransport::thermalConductivity() { int k; update_T(); update_C(); if (!m_spcond_ok) updateCond_T(); if (!m_condmix_ok) { doublereal sum1 = 0.0, sum2 = 0.0; for (k = 0; k < m_nsp; k++) { sum1 += m_molefracs[k] * m_cond[k]; sum2 += m_molefracs[k] / m_cond[k]; } m_lambda = 0.5*(sum1 + 1.0/sum2); m_condmix_ok = true; } return m_lambda; }
doublereal AqueousTransport::thermalConductivity() { update_T(); update_C(); if (!m_spcond_ok) { updateCond_T(); } if (!m_condmix_ok) { doublereal sum1 = 0.0, sum2 = 0.0; for (size_t k = 0; k < m_nsp; k++) { sum1 += m_molefracs[k] * m_cond[k]; sum2 += m_molefracs[k] / m_cond[k]; } m_lambda = 0.5*(sum1 + 1.0/sum2); } return m_lambda; }
/* * The thermal is computed using the general mixture rules * specified in the variable compositionDepType_. * * Solvent-only: * \f[ * \lambda = \lambda_0 * \f] * Mixture-average: * \f[ * \lambda = \sum_k {\lambda_k X_k} * \f] * * Here \f$ \lambda_k \f$ is the thermal conductivity of pure species \e k. * * @see updateCond_T(); */ doublereal SimpleTransport::thermalConductivity() { update_T(); update_C(); if (!m_cond_temp_ok) { updateCond_T(); } if (!m_cond_mix_ok) { if (compositionDepType_ == 0) { m_lambda = m_condSpecies[0]; } else if (compositionDepType_ == 1) { m_lambda = 0.0; for (size_t k = 0; k < m_nsp; k++) { m_lambda += m_condSpecies[k] * m_molefracs[k]; } } m_cond_mix_ok = true; } return m_lambda; }