Midterml 1. Determine the equilibrium temperature distribution fo a one- dimensional Ford with constant thermal properties with the following sources and boundary Conditions. arzt & ( x ,t ) XE ( 01 2 ) () Q = 0 01 . 7 = 0, U ( L ) = T ii ) Q = 0 , 20 107 =0, 0(4 ) = T (ii) 8 = 1 , V ( . ) = T1, U(4 ) = 72 ( v ) 2 = 0, U ( . ) = T ) ; ( L ) + 0 ( 4 ) =0 2. Consider: 20 = k- JXL - Au XE () 2 ) U(olt ) = 0 , 0(4it ) =0, U(X 10) = $ (x).Assuming A LO discuss : i) The possible equilibrium temperature iii ) Find the temperature distribution Ulx,t ) distributions. iv ) plot the solution ii ) Solve the problem and analyze the temperature fu laye times ( t -0. ) 4. Solve and compare with pact i ). at = k ju J X 2 in (OIL ) 3 Consider the problem U ( o , t ) = 0 = UCL it ) OCX2 5 U ( x 10 ) = f ( x ) = . 2 x 2 ) 3 SLXLY 20 ( 0, t ) = 02 0 O ox ( 5 it ) x 25 2 X U ( x 1 0 ) = - 4 Sin 31 x i ) Solve the problem ii ) Plot the solution fu L= 5. and " ) Find the total energy in the nod . K = 1. Discuss your results. Discuss your result from the playsical point of view . 5. Consider Juz + Q ( x ) . Rlt ) in ( o , L ) ii) Find the equilibrium temperature. to 70 (olt ) =0 = 20 ( 2 , t ) U ( x 10 ) = f(x ).Assuming that SQ(x,dx to find a possible periodic source function RH) ii) + x - B Such that the thermal energy in the ban equals a given level to at a prescribed 20 (o, t ) = 0 , 20 (L ,t ) =o time T. (i. . . , Find periodic R such that U ( x 1 0) = f ( * ) ECT. ) = E. fu given To and desired energy level E. , where ELt ) is the thermal energy in the nod as a function of time ). 6 . Determine an equilibrium temperature distribution (if one exists ) . In what values of B one there Solutions ? Explain physically in ( o, L ) DX Cost ) = 1 , 3 x ( L it ) = B U ( x 10 ) = f (x )