A 0.1-cm-thick square, flat copper plate, 2.5 m × 2.5 m is to be cooled in a vertical position. The initial temperature of the plate is 90°C with the ambient fluid at 30°C. The fluid medium is either atmospheric air or water.

Question

(a) Calculate the Grashof number

(b) Determine the initial heat transfer coefficient

(c) Calculate the initial rate of heat transfer by convection

(d) Estimate the initial rate of temperature change for the plate

GIVEN

• A vertical flat copper plate in either air or water

• Plate thickness (t) = 0.1 cm = 0.001 m

• Plate dimensions (L × w) = 2.5 m × 2.5 m

• Initial plate temperature (Ts,i) = 90°C

• Ambient fluid temperature (T?) = 30°C

FIND

(a) The Grashof number (Gr)

(b) The rate of heat transfer by convection (qc)

(c) The initial rate of temperature change (dT/dt)t = 0

SKETCH



PROPERTIES AND CONSTANTS

for copper

Density (?c) = 8933 kg/m3

Specific heat (cc) = 383 J/(kg K)

Water at 60°C Air at 60°C

Answer 1

(a) The Grashof number is defined as





(b) The average heat transfer coefficient is



The rate of convective heat transfer is



(c) Since the sheet is very thin and the thermal conductivity of copper is very high, it is safe to assume that the Biot number is less than 0.1 for both cases. The initial rate of temperature change is given by



COMMENTS

The initial cooling rate in water is about 250 times that in air.