Dynamics and heat transfer of particles in non-uniform and unsteady flows

We study the unified mechanisms of dynamics and heat transfer of particles with different densities, heat capacities, mass inertia and thermal inertia in non-uniform and unsteady flows. Beginning with the dynamical and thermal equations for a point particle in a fluid flow, we derive the nth-order asymptotic solutions of particle temperature, based on the asymptotic solutions of particle velocity. The asymptotic solutions are verified through five illustrative examples with increasing complexity, and the variations of the truncation errors are quantitatively analyzed. The similarities and differences between the particle dynamical and thermal equations are analyzed from both mathematical and physical perspectives. The nth-order asymptotic solutions provide a theoretical basis for selecting an appropriate order to control the error within a required range. Therefore, compared with numerical solutions, asymptotic solutions quantify and control truncation errors, and express the velocity and temperature of particles in analytical form using the velocity and temperature of the flow field, providing convenience for theoretical analysis such as particle clustering, particle dispersion, particle heat transfer. Furthermore, the first two correction terms in the asymptotic solutions for velocity and temperature exhibit a ’duality’: whether a particle’s velocity and temperature exceeds or falls below the local fluid velocity and temperature depends on the particle-to-fluid density and volumetric heat capacity ratio. This ’duality’ provides a convenient approach for analyzing the clustering and thermal conductivity of particles with different densities and volumetric specific heat capacities.