Thermodynamics HW Solutions 114

Thermodynamics HW Solutions 114 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation Assumptions 1 Heat conduction is steady and one-dimensional since there is no change with time and there is thermal symmetry about the mid point. 2 Thermal conductivity is constant. 3 There is no heat generation in the container. Properties The thermal conductivity is given to be k = 1.5 W/m °C. The specific heat of water at the average temperature of (100+20)/2 = 60 ° C is 4.185 kJ/kg ⋅° C (Table A-9). Analysis ( a ) Noting that the 90% of the 500 W generated by the strip heater is transferred to the container, the heat flux through the outer surface is determined to be 2 2 2 2 2 W/m 0 . 213 m) (0.41 4 W 500 90 . 0 4 = × = = = ππ r Q A Q q s s s & & & Noting that heat transfer is one-dimensional in the radial r direction and heat flux is in the negative r direction, the mathematical formulation of this problem can be expressed as 0 2 = dr dT r dr d and Tr T () 11 100 == ° C k dT r dr q s & 2 = ( b ) Integrating the differential equation once with respect to r gives r dT dr C 2 1 = r 1 r 2 T 1 k
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