Newtons Definition of Convection

Consider two solid bodies each with a flat surface, kept at temperatures 7i and Tz. Let the flat surfaces be separated by a distance t. If the space between the flat surfaces were (ideally) fitted with a solid or filled with a stagnant fluid, the heat from one body to the other, as we already learned, would be transferred by conduction (Fig. 1.12), as stated by Eq. (1.44). 

Let the medium between the flat surfaces of two bodies (now a fluid because of practical reasons) flow with a mean velocity V (Fig. 1.13). This flow results from either an imposed pressure drop or an induced buoyancy, respectively called forced and natural convection. Lettheinlettemperatureofthefluidbe72. (Note that the fluid temperature need not be Tz- Selection of Tz for this temperature eliminates temperature gradient near plate 2 and simplifies the following development.) The convection heat transfer from plate 1 is defined as the conduction in the fluid next to plate 1 (in view of the fact 

Here qg denotes the conduction in stagnant fluid, (qKivi the wall value of conduction in moving fluid, and their ratio introduces the definition of the Nusselt number, which is dimensionless. 

Gearly, in each convection problem, the Nusselt number is the wall gradient of the dimensionless fluid temperature, which needs to be analytically or computationally evaluated or to be experimentally determined from 

In reality the variation of the fluid temperature under the influence of motion is confined to a thin thermal boundary layer S. Then, 

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