University Physics with Modern Physics with Mastering Physics (11th Edition)

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17.121: For a spherical or cylindrical surface, the area (17.21) Eq. in A is not constant, and the material must be considered to consist of shells with thickness dr and a temperature difference between the inside and outside of the shell . dT The heat current will be a constant, and must be found by integrating a differential equation. a)Equation (17.21) becomes . 4 or ) 4 ( 2 2 dT k πr dr H dr dT πr k H = = Integrating both sides between the appropriate limits, ). ( 1 1 4 1 2 T T k b a π H - = - In this case the “appropriate limits” have been chosen so that if the inner temperature 2 T is at the higher temperature 1 T , the heat flows outward; that is, . 0 < dr dT Solving for the heat current, . ) ( 4 1 2 a b T T πab k H - - = b) Of the many ways to find the temperature, the one presented here avoids some intermediate calculations and avoids (or rather sidesteps) the sign ambiguity mentioned above. From the model of heat conduction used, the rate of changed of temperature with
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problem17_p121 - 17.121 For a spherical or cylindrical...

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