Consider the Steady-State Temperature Distribution in a Circular Cylinder of Radius

question 33

Multiple Choice

Consider the steady-state temperature distribution in a circular cylinder of radius 2 and height 3, with zero temperature at $r = 2$ and at $z = 3$ and a temperature of 10 at $z = 0$ . The mathematical model for this problem is

• A) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 1 } { r } \frac { \partial u } { \partial r } - \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } = 0 , u ( 2 , z ) = 0 , u ( r , 3 ) = 0 , u ( r , 0 ) = 10\)
• B) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } - \frac { 1 } { r } \frac { \partial u } { \partial r } - \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } = 0 , u ( 2 , z ) = 0 , u ( r , 3 ) = 0 , u ( r , 0 ) = 10\)
• C) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } - \frac { 1 } { r ^ { 2 } } \frac { \partial u } { \partial r } + \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } = 0 , u ( 2 , z ) = 0 , u ( r , 3 ) = 0 , u ( r , 0 ) = 10\)
• D) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 1 } { r } \frac { \partial u } { \partial r } + \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } = 0 , u ( 2 , z ) = 0 , u ( r , 3 ) = 0 , u ( r , 0 ) = 10\)
• E) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 1 } { r ^ { 2 } } \frac { \partial u } { \partial r } + \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } = 0 , u ( 2 , z ) = 0 , u ( r , 3 ) = 0 , u ( r , 0 ) = 10\)

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