Heat Flow in homogeneous multi-phase fluid flow
| (1) | (\rho \,c_{pt})_m \frac{\partial T}{\partial t} - \ \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \eta_{s \alpha} \ \frac{\partial p_\alpha}{\partial t} + \bigg( \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \mathbf{u}_\alpha \bigg) \ \nabla T - \nabla (\lambda_t \nabla T) = \frac{\delta E_H}{ \delta V \delta t} |
Heat Flow in single-phase fluid flow
| (2) | \rho \, c_p \, \frac{\partial T}{\partial t} - {\bf \nabla}\, \left( \lambda \, {\bf \nabla} T \right) + \rho \, c_p \, {\bf u} \, {\bf \nabla} T - \rho \ c_p \ \eta_s \ \frac{\partial p}{\partial t} = \frac{\delta E_H}{ \delta V \delta t} |
Heat Flow in stabilised single-phase fluid flow
| (3) | \rho \, c_p \, \frac{\partial T}{\partial t} - {\bf \nabla}\, \left( \lambda \, {\bf \nabla} T \right) + \rho \, c_p \, {\bf u} \, {\bf \nabla} T = \frac{\delta Q}{ \delta V \delta t} |
The heat flow in a restricted volume is also influenced by the heat exchange with other fluids or solids at the contact surface:
| (4) | j_q |_1 = j_q |_2 |
where j_q |_1 and j_q |_2 are a heat flux at contacting surfaces.
See also
Physics / Thermodynamics / Heat Transfer / Heat flow
[ Heat Flux ]