Thermodynamics HW Solutions 147

Thermodynamics HW Solutions 147 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-126 A spherical liquid nitrogen container is subjected to specified temperature on the inner surface and convection on the outer surface. The mathematical formulation, the variation of temperature, and the rate of evaporation of nitrogen are to be determined for steady one-dimensional heat transfer. Assumptions 1 Heat conduction is steady and one-dimensional since there is no change with time and there is thermal symmetry about the midpoint. 2 Thermal conductivity is constant. 3 There is no heat generation. Properties The thermal conductivity of the tank is given to be k = 18 W/m °C. Also, h fg = 198 kJ/kg for nitrogen. Analysis ( a ) Noting that heat transfer is one-dimensional in the radial r direction, the mathematical formulation of this problem can be expressed as 0 2 = dr dT r dr d and Tr T () 11 196 == − ° C −= k dT r dr hTr T [( ) ] 2 2 ( b ) Integrating the differential equation once with respect to r gives r dT dr C 2 1 = r 1 r 2 h T r -196°C N
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