Combined Free and Forced Convection

plate diagram

Gr and Re versus velocity

fluid temperature (K)

260

length of plate (m)

5

velocity (m/s)

7

plate temperature (K)

430

The Grashof number and the square of the Reynolds number are plotted as functions of the velocity of air as it passes over a flat plate. The plot explores natural or free convection—heat transfer that occurs between a stationary fluid and a solid—versus forced convection—heat transfer between a moving fluid and a solid. The yellow and blue areas of the plot represent regions where the ratio of

2

Re

/Gr<1/5

(free convection dominates) and where

2

Re

/Gr>5

(forced convection dominates), respectively. The dotted red line represents the user-defined velocity, and the computed Nusselt number

Nu

is displayed above the plot for that velocity. The plate diagram is an idealized picture of the system. Changing the temperature of the plate and the air relative to one another helps you understand physically that the Grashof number is proportional to the difference of the two temperatures. This is why raising one of the temperatures can first decrease the free-dominated portion of the graph and then increase the same portion after the other temperature is surpassed.