Heat transfer to a slowly moving fluid from a dilute fixed bed of heated spheres

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Abstract
Using the method of averaged equations, we examine the difference in temperature between the bulk and fixed heated spherical particles under conditions in which ϕ the volume fraction of the particles and ε the Peclet number of the flow past the particles are both small. If ϕ [Lt ] ε2 the particles are effectively isolated, and so their excess temperature has an O(ε) correction to the pure conduction estimate. On the other hand if ϕ [Gt ] ε2, the bulk heating is of sufficient magnitude to produce a significant temperature gradient throughout the fixed bed. This temperature gradient leads to an O(ϕ½) correction to the pure conduction estimate of the excess temperature of the particles, and the correction depends on the details of the flow even though its magnitude is independent of ε. A study of the leading-order terms when ϕ and ε2 are of the same magnitude finds that the two small effects are not simply additive.

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