Theory

Schematic overview

The fluid and bed phase are discretised in N and M nodes respectively. All bed material within the same fluid node is assumed to have the same temperature distribution.

Governing equations

OpenTerrace solves partial differential equations for both phases.

$${ϵ}_f{\rho }_f{c}_{p,f}\frac{\partial T}{\partial t}=-{\rho }_f{c}_{p,f}u\frac{\partial T}{\partial x}+\frac{\partial }{\partial x}\left(k_f\frac{\partial T}{\partial x}\right)+S$$

$${ϵ}_b{\rho }_b{c}_{p,b}\frac{\partial T}{\partial t}=\frac{\partial }{\partial x}\left(k_b\frac{\partial T}{\partial x}\right)+S$$

The source term S contains effects such as coupling between the phases or heat loss to surroundings.