problem4-72 - PROBLEM 4.72 KNOWN: Thin metallic foil of...

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PROBLEM 4.72 KNOWN : Thin metallic foil of thickness, t, whose edges are thermally coupled to a sink at temperature T sink is exposed on the top surface to an ion beam heat flux, ¢¢ q s , and experiences radiation exchange with he vacuum enclosure walls at T t sur . F IND : Temperature distribution across the foil. SCHEMATIC : ASSUMPTIONS : (1) One-dimensional, steady-state conduction in the foil, (2) Constant properties, (3) Upper and lower surfaces of foil experience radiation exchange, (4) Foil is of unit length normal to the age. p ANALYSIS : The 10-node network representing the foil is shown below. From an energy balance on node n, in out EE 0 = ±± , for a unit depth, abcde qqqqq ′′′′′ ++++= 0 () ( ) ( ) ( ) ( )( ) s r,n sur n n 1 n sur n n qxh xT T k tT T xh xT T x0 +− ′′ Δ+ Δ + Δ + Δ= (1) where the linearized radiation coefficient for node n is ( ) 22 sur n sur n hT T T εσ =+ + T (2) Solving Eq. (1) for T n find, ( ) ( ) ( ) 2 nn 1 n 1 r , n s u r s r , n TTT 2 h x k t T x k t q h x k t 2 + Δ + Δ Δ + ⎡⎤ ⎢⎥ ⎣⎦
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problem4-72 - PROBLEM 4.72 KNOWN: Thin metallic foil of...

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