The effects of the history term on the energy equation for a spherical particle at Peclet numbers less than one




Dewey, Mey Lin

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This thesis studies the inclusion of the history term (also referred to as the Basset term) on the transient energy equation of a solid sphere moving through a Newtonian fluid. The physical origin of the history term is the diffusion of the transient temperature gradients around the sphere. The history term accounts for the effects of all the previous temperature changes of the sphere to the current temperature changes. The influence of the history term on the unsteady heat transfer process from a solid sphere was analyzed under prescribed/known conditions of particle motion. The calculations were done with three types of unsteady particle motion: (a) a step change in the fluid velocity (b) a constant particle relative velocity with respect to the fluid and (c) a sinusoidal fluid velocity variation. Results from asymptotic analyses were used to calculate the total Nusselt number in both short and long time domains. All calculations and results in this paper are for small but finite Peclet numbers (PeS<1). The results presented the extreme importance on retaining the history term in the unsteady heat transfer equation.



Heat transfer history term, unsteady heat transfer



Mechanical Engineering