Growers use giant fans to prevent grapes from freez-ing
Chapter 12, Problem 12.123(choose chapter or problem)
Growers use giant fans to prevent grapes from freez-ing when the effective sky temperature is low. Thegrape, which may be viewed as a thin skin of negligi-ble thermal resistance enclosing a volume of sugarwater, is exposed to ambient air and is irradiatedfrom the sky above and ground below. Assume thegrape to be an isothermal sphere of 15-mm diameter,and assume uniform blackbody irradiation over its top and bottom hemispheres due to emission from thesky and the earth, respectively.(a) Derive an expression for the rate of change of thegrape temperature. Express your result in termsof a convection coefficient and appropriate tem-peratures and radiative quantities.(b) Under conditions for which Tsky?235 K, T??273 K, and the fan is off (V?0), determinewhether the grapes will freeze. To a goodapproximation, the skin emissivity is 1 and thegrape thermophysical properties are those of sug- arless water. However, because of the sugar con-tent, the grape freezes at?5C.(c) With all conditions remaining the same, exceptthat the fans are now operating with V?1 m/s,will the grapes freeze?
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