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Clausius number, Cl, is a dimensionless group which appears in the analysis of heat conduction in fluid flow. It is expressed as:

where μ is the fluid velocity; ρ, fluid density; λ, fluid thermal conductivity; ΔT, temperature difference; and L is the appropriate linear dimension.

Clausius number represents the ratio of energy transport associated with fluid momentum to energy transfer by thermal conduction, i.e.,

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