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class 8

# class 8 - Transient Conduction Spatial Effects and the Role...

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Transient Conduction: Spatial Effects and the Role of Analytical Solutions Chapter 5 Sections 5.4 to 5.5

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The Biot Number and Validity of The Lumped Capacitance Method c hL Bi k convection or radiation coefficient h Physical Interpretation : / / 1/ c s cond solid s conv solid fluid L kA R T Bi hA R T = : : 1 Bi << Ts1 Bi<<1 Ts2 Bi=1 Ts2 Bi >>1 Ts2 ( 29 ( 29 Bi k hL R R hA kA L T T T T T T hA T T L kA conc cond s s s s s s = = = - - - = - / 1 / 2 , 2 , 1 , 2 , 2 , 1 , R T q =

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Consider a packed bed of solid aluminum spheres (75 mm diameter, ρ = 2700 kg/m 3 , c = 950 J/kg-K, k = 240 W/m-K) that is charged (hot gas at T gi = 300 o C flows through the system). If the initial temperature of the spheres is T i = 25 o C and the convection coefficient h = 75 W/m 2 -K, how long does it take a sphere near the inlet of the system to accumulate 90 % of the maximum possible thermal energy ?
ASSUMPTIONS: (1) Constant properties, (2) Negligible coating thermal capacitance, (3) Negligible radiation.

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class 8 - Transient Conduction Spatial Effects and the Role...

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