Estimate the heat loss due to free convection from a 2
feet-wide square plate that is at 130 degrees Fahrenheit to ambient air at 70
degrees Fahrenheit when it is in (a) vertical position and (b) horizontal
position.
Solution:
(See Problem 5.2.1 also). The film temperature is 100
degrees Fahrenheit and the properties of air at this temperature are listed as:
viscosity 0.0491 pound per foot per hour, density 0.071 pounds per cubic foot,
thermal conductivity 0.0156 BTU per hour per foot per degree Fahrenheit, and
specific heat 0.24 BTU per pound per degree Fahrenheit.
Beta, coefficient of thermal expansion, for ideal gases is
given as 1 over T where T is the absolute temperature. It can be found to be equal to 0.00168 per
degree Rankine. Acceleration due to
gravity is 32.174 ft per second squared or 4.17 times 108 foot per
hour squared. Note that the DT is 130
minus 70 equals 60 degrees Fahrenheit.
With these values, Grashof number is calculated to be 7.479
times 108, whereas Prandtl number is 0.755. This gives a value of Raleigh number as
5.649 times 108. Nusselt
number is given as aYb.
(a) For square plate in vertical position, value of
parameter a equals 0.59 and b equals 0.25 (See Perry, Table 10.1). Nusselt number is calculated as 90.96. Nusselt number is h L over k. In this case, L is replaced by d and the
heat transfer coefficient is determined to be 0.709 BTU per hour per foot
squared per degree Fahrenheit.
Heat transfer area is given by L2, where L is the
plate characteristic length. Actual
heat transfer area is twice this area.
Heat transfer is given as h 2A DT or 340.55 BTU per hour.
(b) For square plate in horizontal (FU, hot surface facing
upward), value of parameter a equals 0.14 and b equals 0.333 (See Perry,
Table 10.1). Nusselt number is
calculated as 114.96. Nusselt number is
h L over k. In this case, L is replaced
by d and the heat transfer coefficient is determined to be 0.897 BTU per hour
per foot squared per degree Fahrenheit.
Heat transfer is given as h 2A DT or 430.4
BTU per hour. Note there is another
correlation when hot surface is facing downwards and abbreviated as FD.