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Minchanka [31]
3 years ago
11

A hot brass plate is having its upper surface cooled by impinging jet of air at temperature of 15°c and convection heat transfer

coefficient of 220 w/m2•k. the 10-cm thick brass plate (ρ = 8530 kg/m3, cp = 380 j/kg•k, k = 110 w/m•k, and α = 33.9×10–6 m2/s) has a uniform initial temperature of 700°c, and the bottom surface of the plate is insulated. determine the temperature at the center plane of the brass plate after 3 minutes of cooling. solve this problem using analytical one term approximation method (not the heisler charts).
Physics
1 answer:
Elodia [21]3 years ago
4 0
200 degrees because I need the points
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One end of an insulated metal rod is maintained at 100 ∘C and the other end is maintained at 0.00 ∘C by an ice–water mixture. Th
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k=105.0359\times 10^4\,W.m^{-1}.K^{-1}

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Given:

temperature at the hotter end, T_H=100^{\circ}C

temperature at the cooler end, T_C=0^{\circ}C

length of rod through which the heat travels, dx=0.7\,m

cross-sectional area of rod, A=1.1\times 10^{-4}\,cm^2

mass of ice melted at zero degree Celsius, m=8.7\times 10^{-3}\,kg

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\dot{Q}=k.A.\frac{dT}{dx}......................................(1)

where:

\dot{Q}=rate of heat transfer

dT= temperature difference across the length dx

Now, we need the total heat transfer according to the condition:

we know the latent heat of fusion of ice,  L = 334000\,J.kg^{-1}

Q=m.L

Q=8.7\times 10^{-3}\times 334000

Q=2905.8\,J

Now the heat rate:

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