Introduction to Mathematical PhysicHomework 2 , Due 18 January 2019 at 17:50 am at MANDE – B 210Boundary ConditionsDetermine solutions of the steady – state heat eheat equation with no sources ina bar of length II subject to the following boundary conditions andthermal conductivity Ko . Give a physicalhisical interpretation of each boundarycondition . If a steady- state solution does not exist , give a physical reasonwhy( 2 ) KO = 3 , de = 0 ( 20 = 0 ) , 21 = 4 ( 2 = D )( b ) R( 20 – I )( C ) R( 2 – 210 ) ( 2 = 0 ) , u = 0 ( 2 = [ ) , where Hand uo are constants .
How isLow is your solution affected as A( d ) Ko = ( 20 + 2 ) – 1 2 = 0 ( 20 = 0 )1 ( 20 = I )( e ) I1 dro0 ) . die( 2 = I ) What additional informa -tion do you need to specify the steady state temperature ?2 . Effect of a sourceConsider the equilibrium temperature distribution u ( x ) inside a uniformone- dimensional rod ( with cross -sectional area A length I – 1 , and theand thermal conductivity K1 ) with a source of thermal energy ? ( 20 )To sin ( Tac )( a ) Write down the ODE satisfied by u ( 20 )( b ) Solve the ODE subject to the boundary conditions w ( 0 )and4 ( 1 ) = 0( . ) Find the thermal energy generated by the solthe source per unit time insidethe rod . The specific heateat is cand the density p , both constants( 1 ) Find the thermal energy flux leaving the rod at a = 0 and a( e ) What is the relatiolationship between your answers to parts ( c ) and ( d ) ?Explain this relationship in physical terms3 . Newton’s law of cooling
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