/*
* 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;
}
