Thermodynamics HW Solutions 129

Thermodynamics HW Solutions 129 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-89 Heat is generated uniformly in a spherical radioactive material with specified surface temperature. The mathematical formulation, the variation of temperature in the sphere, and the center temperature are to be determined for steady one-dimensional heat transfer. Assumptions 1 Heat transfer is steady since there is no indication of any changes with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the mid point. 3 Thermal conductivity is constant. 4 Heat generation is uniform. Properties The thermal conductivity is given to be k = 15 W/m °C. Analysis ( a ) Noting that heat transfer is steady and one-dimensional in the radial r direction, the mathematical formulation of this problem can be expressed as r o 0 T s =80°C k g r constant with 0 1 2 2 = = + g k g dr dT r dr d r & & and 80 ° C (specified surface temperature) Tr T s () 0 == dT dr 0 0 = (thermal symmetry about the mid point) ( b ) Multiplying both sides of the differential equation by r 2 and rearranging gives 2 2 r k g dr dT r dr d & = Integrating with respect to r gives r dT
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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