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

question 27

Multiple Choice

Consider the steady-state temperature distribution in a circular disc of radius $C$ centere at the origin, with temperature given as a function, $f ( \theta )$ on the boundary. The mathematical model of this situation is

• A) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } - \frac { 1 } { r } \frac { \partial u } { \partial r } + \frac { 1 } { r ^ { 2 } } \frac { \partial ^ { 2 } u } { \partial \theta ^ { 2 } } = 0 , u ( c , \theta ) = f ( \theta )\)
• B) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 1 } { r } \frac { \partial u } { \partial r } - \frac { 1 } { r ^ { 2 } } \frac { \partial ^ { 2 } u } { \partial \theta ^ { 2 } } = 0 , u ( c , \theta ) = f ( \theta )\)
• C) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } - \frac { 1 } { r } \frac { \partial u } { \partial r } - \frac { 1 } { r ^ { 2 } } \frac { \partial ^ { 2 } u } { \partial \theta ^ { 2 } } = 0 , u ( c , \theta ) = f ( \theta )\)
• D) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 1 } { r ^ { 2 } } \frac { \partial u } { \partial r } + \frac { 1 } { r } \frac { \partial ^ { 2 } u } { \partial \theta ^ { 2 } } = 0 , u ( c , \theta ) = f ( \theta )\)
• E) \(\frac { \partial ^ { 2 } u } { \partial r ^ { 2 } } + \frac { 1 } { r } \frac { \partial u } { \partial r } + \frac { 1 } { r ^ { 2 } } \frac { \partial ^ { 2 } u } { \partial \theta ^ { 2 } } = 0 , u ( c , \theta ) = f ( \theta )\)

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Definitions:

Production Possibility Curve

A graphical representation showing the maximum combination of goods and services that can be produced with a given set of resources and technology.

Comparative Advantage

The aptitude of any individual, corporation, or country for producing a good or offering a service at an opportunity cost that is reduced in comparison to that of the competition.

Specialization

The process of focusing resources on the activities that lead to the greatest efficiency and output in production or services.

Nations

Significant populations sharing a common ancestry, historical background, cultural practices, or language, living together in a specific nation or region.