Effect of the history term on the transient energy equation for a sphere

This paper addresses the importance of the history term on the transient energy equation of particles. The physical origin of this term is the diffusion of the transient temperature gradients around the sphere. The history term accounts for the effect of all the previous temperature changes of the sphere to the current temperature change. The derivation and analysis of the transient energy equation of rigid particles are presented. In order to solve numerically the transient energy equation, three different fluid temperature fields (step, ramp and sinusoidal) are applied and the temperature of the sphere is computed with and without the history term. The evaluation of the maximum deviation between these two computations allows us to determine for each case the effect of the history term and, especially, when the history term may be neglected. The final results of these computations allow several conclusions and recommendations on the appearance, importance and significance of the history term.