Question

An aluminum plate with a thickness of L=5 mm is mounted in a horizontal position, and its bottom surface is well insulated. A special, thin coating (with emissivity and solar absorptivity of 0.25) is applied to the top surface. The density ρ and specific heat c of aluminum are known to be 2700 kg/m³ and 900 J/kg · K, respectively. Consider conditions for which the plate is initially at a temperature of ?_?????=25 °C and its top surface is suddenly exposed to ambient air at T_∞ = 20 °C and to solar radiation from large surroundings at temperature ?_???=100 °C. The convection heat transfer coefficient between the surface and the air is h = 20 W/m² · K. Assume uniform temperature for the plate.
(a) Draw the control volume. (2 points)
(b) What is the initial rate of change of the plate temperature? (4 points)
(c) What will be the steady-state temperature of the plate? (4 points)

Answer 1

Tsurr given L= '005m &=&=025 hToo hrad Plany air 2,& control 8=2700 kg/m3 PLATE Volume c=goo J 1kg Insulatim Tplate=25°c = 299k The = 20c ,h=20w/m² (mass m= SAL) Tsur =100% =373K from conservation of energy Principle din-sout Rate of heat storage A&T (517-T") - hA(TPT) = FALC dT -2585:67X100x (3731_2994)–20x125-20) = 2700X1005x900x dt dt dT =50152 x 10 oc/sec at At steady state Qin =yout Axo (Tsu"_Tp,4)=hA (Tpi - Too) • 25x5.67818% (8734 Tp 4) = 20x(Tp1 - 293) 7:0875x16 40/1.9356xldlº-Tp:1) = Tp - 293 306.72 = -7.0915x15 lopp" +Tp" on solving Tpi = 300.9k