Growers use giants fans to prevent grapes from freezing
whenthe effective sky temperature is low. the grape, which may
beviewed as a thin skin of negligible thermal resistance enclosing
avolume of sugar water, is exposed to ambient air and is
irradiatedfrom the sky above and ground below. assume the grape to
be anisothermal sphere of 15-mm diameter, and assume uniform
blackbodyirradiation over its top and bottom hemispheres due to
emissionfrom the sky and the earth, respectively.
a) derive an expression for the rate of change of the
grapetemperature. express your result in terms of a
convectioncoefficient and appropriate temperatures and
radiativequantities.
b)under conditions for which t(sky) = 253k, t(infinite) =273k,
and the fan is off (v = 0), determine whether the grapes
willfreeze. to a good approximation, the skin emissivity is 1 and
thegrape thermophysical properties are those of sugarless
water. however, because of the sugar content, the grape freezes
at-5oc
c)with all conditions remaining the same, except that the
fansare now oerating with v = 1m/s, will the grape freeze?