Chemical Engineering Hand Written_Notes_Part_8

Chemical Engineering Hand Written_Notes_Part_8 - 18 1...

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18 1. MATHEMATICAL MODELING AND SIMULATION Figure 10. Double Pipe Heat Exchanger equations for this case can be stated as ρ t C pt A t ∂T t ( z,t ) ∂t = ρ t C pt V t A t ∂T t ( z,t ) ∂z + πDQ ( z,t ) (2.65) ρ s C pt A s ∂T s ( z,t ) ∂t = ρ s C ps V s A s ∂T s ( z,t ) ∂z πDQ ( z,t ) (2.66) Q ( z,t )= U [ T s ( z,t ) T t ( z,t )] (2.67) where subscript t denotestubesideandsubscript s denotes shell side. The initial and boundary conditions become T t ( t, 0) = T t 0 at z =0 and t º 0: Boundary condition (2.68) T (0 ,z )= T t 0 ( z ): Initial temperature pro f le (2.69) T s ( t, 1) = T s 1 at z =1 and t º 0: Boundary condition (2.70) T (0 ,z )= T s 0 ( z ): Initial temperature pro f le (2.71) Thesearecoup ledPDEsandhavetobeso lvedsimu ltaneous lytounderstandthe transient behavior. The steady state problem can be stated as ρ t C pt V t A t dT t ( z,t ) dz = πDU [ T s ( z ) T t ( z )] (2.72) ρ s C ps V s A s dT s ( z,t
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Chemical Engineering Hand Written_Notes_Part_8 - 18 1...

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