A rectangular flat plate is 60 cm long, 12 cm wide and 2 cm thick. The plate has
ID: 1819934 • Letter: A
Question
A rectangular flat plate is 60 cm long, 12 cm wide and 2 cm thick. The plate has an internal electric heater and the plate is lying on a table. The air in the room is at 20 C. It is desired to provide power to the heater so that the temperature of the surface of the plate in contact with the room air is at 120 C. It may be assumed that the side of the plate in contact with the table is perfectly insulated so that no heat flows into the table from the plate. Also, heat transfer from the edges of the plate may be neglected. Finally, it may be assumed that radiation heat transfer is negligible. In short, the only heat transfer from the plate is by natural convection to the air from the plate surface in contact with the room air. What is the required power to the heater to maintain the surface of the plate in contact with the room air at 120 C ?Explanation / Answer
GIVEN DATA: length=60cm=.6meters
width=12cm=.12meters
thickness=2cm=.02meters
ambiemt temperature(t)=20c
room temperature(ts)=120c
film temperature=(20+120)/2=70c
take the properties at 70c
density=1.029kg/m^3
conductivity(k)=.02964w/mc
kinematic viscosity=20.02*10^-6m^2/s
prandtl number(pr)=.694
=1/(273+70)=.002915
grashoff number(GR)=5.28*10^11
modified grasshoff numberGRl)=5.28*10^11*(.12/.6)^3=.4224*10^11
AVERAGE HEAT TRANSFER COEFFICIENT OVER THE SURFAACE OF THE PLATE,h
h=k/l*(.677(pr)^.5*(.952+pr)^(-1/4)*(GRl)^.25)
=.02964/.12*(.677(.694)^.5*(.952+.694)^(-.25)*(.4224*10^11)^.25)
=55.75w/m^2c
HEAT PRODUCED ON THE PLATE
Q=2hA(ts-t)=2*55.75*(.12*.02)(120-20)=26.76w
POWER REQUIRED TO INSULATE
P=(26.76/60)*100=44.6