present initialin out flow in flow out r h r amount

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Unformatted text preview: + Δr − r ȹ Ⱥ t ȹ 2 ȹ 2 2 ȹ = φhC j π ȹ r + 2rΔr + Δr − r ȹ Ⱥ t ȹ ( ( ) ( ) ) () ( ≅ 2πrΔr φhC j )t Microscopic Balances... present-initial=in- out Flow in Flow out r h Δr Amount of j into CV during Δt In ( ( ) ) () = 2π r + Δr hN j Δt = 2πh rN j Δt r + Δr r + Δr Amount of j from CV during Δt From () = 2πh rN j Δt r Microscopic Balances... Flow in Flow out r h Δr present-initial=in- out ( ) t+ Δt −2πrΔr (φhCj ) t = 2πh ( rN j ) Δt −2π ( rN j ) Δt r + Δr r 2πrΔr φhC j Microscopic Balances... present-initial=in- out Flow in Flow out r h Δr ( ) t+ Δt − 2πrΔr (φhCj ) t = 2πh ( rN j ) Δt − 2πh ( rN j ) Δt r + Δr r (φCj ) t+ Δt − (φCj ) t = (rN j ) r+ Δr − (rN j ) r 2πrΔr φhC j Δt Δr Microscopic Balances... Flow in Flow out r h Δr In the limit of Δr, Δt approaching 0 ȹ ∂ φC ȹ ȹ ∂ rN ȹ j j ȹ ȹ = 1 ȹ ȹ r ȹ ∂r ȹ ȹ ∂t ȹ ȹ Ⱥ r ȹ Ⱥ t () () Microscopic Balances... Constant thickness () () ȹ ∂ φC...
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