# Study on the unsteady heat transport process of particles in laminar flow

In this dissertation, the unsteady heat transfer from a particle at the low Reynolds and Peclet numbers has been investigated, both analytically and numerically By solving the case of a sphere in an unsteady and non-uniform temperature and velocity flow at very low Reynolds and Peclet numbers, it is discovered that, similar to the momentum transfer, an added mass term and history terms should exist in the total heat transfer rate, and the history term is a Basset-like integral with a kernel of t$\sp{-1/2}$ in the time domain The case of an ellipsoid with small eccentricity is also considered following a so-called 'Domain Perturbation' method. The results show that the Basset-like memory term is only a special case of spherical particle. For a particle with arbitrary shape, the memory term is believed to be much more complicated or at least there will come out some other 'new memory' terms. However, for a slightly deformed sphere, the new memory term is much smaller and decays much faster than the Basset-like memory term A study which allows the internal conduction inside the sphere is also considered. By deriving a reciprocal theorem, we find that one could get the heat transfer rate from the particle by introducing a much simple analogous field, this avoids solving the actual temperature field which probably is much more complicated. The results are given in Laplace domain and some limit cases are discussed A brief introduction of the Symbolic Operator Representing approach is also provided, which can be applied to solve the unsteady diffusion problems By allowing the Peclet numbers to be small but finite, it keeps the convection terms in the governing equations. Several approaches are employed to solve these unsteady convection problems. First a singular perturbation method is used. Following this method, the time and space domain are split into four parts: short time and inner (close to the sphere) region; short time and outer region; long time and inner region; long time and outer region. It applies a different governing equation for each region, together with the appropriate boundary conditions and initial conditions, plus the matching requirements both in the time and space domains. These ideas are further extended to solve a more general problem: the unsteady heat transfer from a particle with arbitrary shape in a unsteady velocity flow A control volume based finite difference method is employed to solve the unsteady heat transfer from a sphere in the arbitrary Reynolds and Peclet numbers, when the sphere experience a step temperature change. The convection terms both in momentum and energy equations are handled by upwind scheme. The comparison is also made between the numerical and analytical results which shows a good agreement