Convective and conductive heat transfer of creeping flow in a multi-particle system

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In this study, a new approach is developed to separately examine conductive and convective heat transfers through an assemblage of solid particles with fluid flowing through it. The inter-particle interactions are taken into account by using the cell model. The energy equations are solved along with the creeping flow field using a finite difference based numerical method for a range of physical and kinematic conditions. One new feature about the developed approach is that it can explicitly separate two mechanisms of conduction and convection by introducing effective convective heat transfer and effective conductive heat transfer coefficients, respectively. Another new aspect is the heat transfer through a multi-particle system when there is an overall temperature gradient in the flow direction. It is demonstrated that convective heat transfer increases linearly with the Peclet number. When the fluid phase is less conductive than the particles, the total effective heat transfer coefficient varies in a small range against the voidage non-monotonically. When the fluid phase is more conductive, although the conductive effect is small, conductive heat transfer increase causes a slight decrease in the fraction of convective heat transfer coefficient from the total heat transfer coefficient. The ratio of fluid and solid particle conductivities has a strong non-linear effect on the heat transfer coefficients. The most significant effect occurs in the range of thermal conductivity ratio of fluid over solid particle between 0.1 and 10. Both the convective and conductive heat transfers are almost linearly proportional to the overall temperature gradient.