(592a) Heat Transfer Formulation and Its Validation in Macroscopic Particle Model

Particulate flows in which particle size is comparable to channel dimensions have gained considerable importance with growing interest in biomedical and micro-chemical technologies (Hessel et al., 2005). A usual CFD particle tracking method is not suited to such applications because the particle is usually regarded as a point mass. It is necessary to take into account particle physical volume to model both hydrodynamic and heat transfer which takes into account wall effects in such narrow spaces. Although direct numerical simulation associated with dynamic meshing around a moving particle is expected to be the most accurate method for this purpose, the computing cost is not practical. In our previous study (Agrawal et al., 2009), a novel Macroscopic Particle Model (MPM) proposed by Agrawal et al. (2004) was validated for drag force formulation in terms of a falling velocity of sphere in a quiescent Newtonian liquid in a cylindrical pipe.

This paper is a continuation of our previous work, where Heat transfer from a sphere having a uniform temperature and falling axially in a cylindrical tube filled with an incompressible non-newtonian fluid is numerically investigated using Macroscopic Particle Model. The effects of varying the Reynolds number(Re), Prandtl number (Pr), and the sphere-to-tube diameter ratio (λ) on the mean Nusselt numbers (Nu) have been extensively examined over the wide range of these parameters.

In the MPM approach, particle is treated in a Lagrangian frame of reference. The particle is assumed to span several computational cells. At every time step of the unsteady simulation, a solid body velocity that describes the particle motion as well as particle temperature is fixed for the fluid cells within the particle volume. By fixing the rigid body motion of the particle and the temperature, momentum and energy is effectively added to the fluid as expressed. The integral of the momentum change, linear as well as angular, gives the drag force and torque experienced by each particle. Similarly, integration of heat transfer from fluid to particle is calculated based on local heat transfer coefficient using local temperature and flow conditions. ANSYS FLUENT solver was used in Macroscopic Particle Model for fluid flow and heat transfer calculation for the non-newtonian fluid.