# Problem

Develop continuity, momentum, energy, and water species equations and boundary conditions capable of describing this process and calculate the outlet air temperature and moisture content of the particles as a function of time for 10 min of the drying process.

© Springer International Publishing AG 2017

H. Arastoopour et al., *Computational Transport Phenomena of Fluid-Particle Systems, *Mechanical Engineering Series, DOI 10.1007/978-3-319-45490-0_5

# Solution

In addition to the conservation equations (i.e., mass, momentum, and species) and the constitutive equations presented in Tables 2.1 and 2.2, the following conservation of energy equations for both phases were also solved. It is assumed that the particulate phase is homogeneous and the Syamlal et al. (1993) drag model was used as the drag force between phases (Jang and Arastoopour 2014).

# Conservation of Energy

The conservation of energy equation for each phase can be written as

where h is the specific enthalpy, * q* is the heat flux, and

*is the rate of heat transfer between the gas and solid phases. The specific enthalpy (h) and the heat flux (q) in each phase are expressed as*

**Q**_{sg}

where k is the thermal conductivity and C_{p} is the heat capacity

The gas-particle heat transfer coefficient a_{gs} was obtained from the Khotari (1967) expression:

where Nu is the Nusselt number, * d_{p}* is particle diameter, and

*is thermal conductivity of the gas phase.*

**k**_{g}The latent heat due to vaporization of moisture is expressed as (Palancz 1983)

The above equation assumes no effect of the solid moisture on the heat of vaporization.