2. During a cooling process, plate glass is cooled by passing airover its top su

Question

2. During a cooling process, plate glass is cooled by passing airover its top surface such that the
convection heat transfer coefficient is h = 8 W/(m2?K). The bottomsurface of the plate is well
insulated. The temperature gradient at any point in the glass mustnot exceed 12oC/mm to prevent
cracking.
a. At any time, where in the plate has the highest temperaturegradient? Why? Explain
.
b. At any time, where in the plate has the highest temperature?Why? Explain
.
c. What is the maximum heat flux allowed for this coolingprocess?

e. How does the heat flux change with time? Is it increasing ordecreasing? Explain.

Data: The thermal conductivity of the glass is 1.2 W/(m?K) and itssurface emissivity is 0.7.

Explanation / Answer

(a)The highest temperature gradient willbe on the top surface of the glass plate which is exposedto passing air Reason: The passing air takes away the heat of the glass platewhich causes temperature gradient at the top surface as it takestime to trasfer heat from surface below the top surface to topsurface (b) The highest temperature will be at bottom surface ofthe plate which is insulated Reason: As the bottom surface is insulated, there is no heat flowfrom bottom surfacae of the plate to insulation So bottom surfaceof the plate will be at highest temperature (c)maximum heat flux = K*T/x maximum heat flux = 1.2*12/10-3 maximum heat flux =14.4*103 W/m2 (d) Heat flux will be decreasing. Reason: As time increases because of cooling, temperature gradientwill be decreased so heat flux will be decreased

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