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Both numbers have similar definition except that Nusselt numberBiot Number is based on on thermal conductivity of the fluid while Biot Number is based on  the solid body while Nusselt number is based on thermal conductivity of the solid bodythe fluid.

Normally Biot Number indicates whether significant thermal gradient will develop inside a solid body based on the ratio of heat transfer away from the surface of a solid body to heat transfer within the solid body.

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