Suppose a thin vertical flat plate 60-cm-high and 40-cm-wide, is immersed in a fluid flowing parallel to is surface. If the plate is at 40°C and the fluid at 10°C, estimate the Reynolds number at which buoyancy effects are essentially negligible for heat transfer from the plate if the fluid is: (a) mercury, (b) air, and (c) water. Then calculate the corresponding fluid velocity for the three fluids.

Question

GIVEN

? A thin flat plate immersed in a fluid flowing parallel to its surfaces

? Plate height (H) = 60 cm = 0.6 m

? Plate width (w) = 40 cm = 0.4 m

? Plate temperature (Ts) = 40°C

? Fluid temperature (T?) = 10°C

FIND

? The Reynolds number and corresponding fluid velocity (U?) for buoyancy effects to be negligible,

if the fluid is: (a) mercury, (b) air, (c) water

ASSUMPTIONS

? Steady state conditions

SKETCH



PROPERTIES AND CONSTANTS

From Appendix 2, Tables 26, 28 and 13 at the mean temperature of 25°C



The thermal expansion coefficient of mercury can be estimated from

Answer 1

The Grashof number based on height is



For mercury



For this geometry, the ratio that must be satisfied for the natural convection to have an essentially negligible effect is given at the end of Section 8.5 as



For mercury



Applying a similar analysis to the other fluids yields the following results