The Model Describing the Temperature in a Rod Where the Temperature

The model describing the temperature in a rod where the temperature at the left end is zero and where there is heat transfer from the right boundary into the external medium is

A) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( 0 , t ) = 0 , \frac { \partial u } { \partial x } = ( L , t ) = - h u ( L , t ) , h > 0 , u ( x , 0 ) = f ( x )$
B) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( 0 , t ) = 0 , \frac { \partial u } { \partial x } = ( L , t ) = h u ( L , t ) , h > 0 , u ( x , 0 ) = f ( x )$
C) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial u } { \partial t } , u ( 0 , t ) = 0 , \frac { \partial u } { \partial x } = ( L , t ) = - h u ( L , t ) , h > 0 , u ( x , 0 ) = f ( x )$
D) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial u } { \partial t } , u ( 0 , t ) = 0 , \frac { \partial u } { \partial x } = ( L , t ) = h u ( L , t ) , h > 0 , u ( x , 0 ) = f ( x )$
E) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } = 0 , u ( 0 , t ) = 0 , \frac { \partial u } { \partial x } = ( L , t ) = - h u ( L , t ) , h > 0 , u ( x , 0 ) = f ( x )$

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