Two rectangular plates (0.5 m X 1.0 m) placed parallel to each other, 0.5 m apar

Question

Two rectangular plates (0.5 m X 1.0 m) placed parallel to each other, 0.5 m apart are at temperatures 1273 K and 773 K respectively. They are placed in huge room at 300 K. Emmissivities of the plates are 0.2 and 0.5. See Picture Below

A) If the following circuit is used to model the radiation heat transfer, determine 3 equations and 3 unknowns that can be used to solve for all heat transfer rates. The equations should be in terms of emissivities (), the view factors (F), the areas (A), the Stephan Boltzeman constant, and the radiosities. DO NOT SOLVE EQUATIONS

B) What are the view Factors F(1-2) and F(1-3)?

C)If J1 = 33,470 W/m^2 and J2 = 15,039 W/m^2, what is the heat transfer from surface 1 to surface 2 (Q1-2)?

Explanation / Answer

We know heat transfer for surface 1-surface 2

Q(1-2)=(K*A*(T1-T)/d)...........|;[K=Boltzman const,A=area,T1=1273K,T=373K,d=0.5m]

again heat transfer from surface 2 to surface 1

Q(2-1)=(K*A*(T2-T)/d)..........||;[where T2=773K]

Using view factor(F12),emmisivity(€1),heat transfer from object 1 to objectv2

Q(1-2)=(A*F12*€1*sigma*T1^4)..............|||.[where A=area,F12=view factor]

again heat transfer from object 2 to object 1

Q(2-1)=A*F21*€2*sigma*T2^4......|V..[where F21=view factor,emissivity of surface 2=€2]

Now comparing equn | & equn ||

K*A*(T1-T)/d=A*F12*€1*sigma*T1^4

F12=(K*A*(T1-T))/(A*€1*d*sigma*T1^4)....V

Again from equn |||& |V

F21=(K*A*(T2-T))/(A*€2*d*sigma*T2^4)......V|

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