TRANSIENT HEAT-TRANSFER FROM A PARTICLE WITH ARBITRARY SHAPE AND MOTION

A singular perturbation analysis and Green's second theorem are used i n order to obtain a general expression for the heat transfer from a pa rticle at low, Peclet numbers, when advection and conduction are heat transfer modes of comparable magnitude. The particle may have arbitrar y shape, and its motion in the fluid is not constrained to be Stokesia n. In the ensuring analysis the governing equations for the temperatur e fields at short and long times are derived. The expressions are comb ined to yield a general equation for the temperature field and for the total rate of heat transfer The final results for the rate of heat tr ansfer demonstrate the existence of a history integral, whose kernel d ecays faster than the typical history integrals of the purely conducti on regime. As applications of the general results, analytical expressi ons for the Nusselt number are derived in the case of a sphere undergo ing a step temperature change.