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74891865 heat and mass transfer notes

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B BALAMUGUNDAN SENIOR LECTURER PANIMALAR ENGG COLLEGE CHENNAI UNIT I CONDUCTION HEAT TRANSFER 1. Deri ve gener al heat con duct ion equ atio n in Carte ian coordinate! Consider a small rectanglar element o! sides d"# d$ and d% as s&o'n in !igre( T&e energ$ )alance o! t&is rectanglar element is o)tained !rom !irst la' o! t&ermod$namics Net heat conducted into ele"ent #ro" all the coordinate direction $ Heat generated %ithin the ele"ent & Heat tored in the ele"ent '''''1 Net heat conducted into ele"ent #ro" all the coordinate direction( As *er t&e +orier la' o! &eat condction t&e rate o! &eat !lo' into t&e element in ,# -# . directions t&rog& !ace ABCD# ABE+# ADHE are ) *  & '+ d, d- d x  x T ∂ ∂   ) ,  & '+ d* d- d y  y T ∂ ∂   '''''''''''''' ''''/ ) -  & '+ d, d* d z  z T ∂ ∂   T&e rate o! &eat !lo' ot o! t&e element in , direction t&rog& t&e !ace E+GH is ) * $ d*  & ) *  $ ( )d x Q x  x ∂ ∂  ''''''0 S) E/ 0 in E/ 1 ) *   ) *$ d*  & )* 2) *  $ ( )d x Q x  x ∂ ∂ ) *   ) *$ d* & 2 3  x T kdydzdx  x  ∂ ∂ ∂ ∂ ) *   ) *$ d* & 0 0  x T kdxdydx ∂ ∂ ) *   ) *$ d* & 0 0  x T kdxdydx ∂ ∂  ''''''3 Si"ilarl, ) ,   ) ,$ d, & 0 0  y T kdxdydx ∂ ∂  ''''''4

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