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MATEMATIKA TEKNIK KIMIA

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Kerjakan Soal no 1.5, 1.7, dan 1.8 Dari buku : Applied Mathematics and Modelling for Chemical Engineers Tulisan : Richard G.Rice dan Duong D. Do

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Soal 1.5 Distributed Thermal Model for Thermocouple We wish to estimate the dynamics of a cold thermocouple probe suddenly placed in a hot flowing fluid stream for the purpose of temperature measurement. The probe consists of two dissimilar metal wires joined by soldering at the tip, and the wires are then encased in a metal sheath and the tip is finally coated with a bead of plastic to protect it from corrosion. If the plastic of the plastic bead covering the tip of the thermocouple described before is quite large, and since plastic usually sustains a very low value of thermal conductivity, then the simple lumped model solution becomes quite inaccurate. To improve the model, we need to account for thermal conductivity in the (assumed) spherical shape of the plastic bead. (a) Assuming the bead is a perfect sphere, contacted everywhere by external fluid of temperature Tf, perform a shell balance on an element of volume 4πr 2 ∆r and show that (b) Perform an elemental heat balance at the surface of the sphere and deduce

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qrqr r qrqr r + ∆r Thermocouple model (a) Heat balance 0 0 Input – output + generasi – konsumsi = akumulasi = qrqr qrqr r + ∆r r –

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Soal 1.7

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Akumulasi = input – output + generasi Input = output = 0

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Uo L.A.C z=x + ((1-ε).-De.A. (dc/dx z=x )+Kc.a. V. (c*-c) = Uo L.A.C z=x+∆x + ((1-ε).-De.A. (dc/dx z=x+∆x ) Akumulasi = input – output + generasi Input = output = 0 Dan lain-lain

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Input, O 2(g) z + Δ z Berdasarkan Hukum kekekalan massa Akumulasi = input – output + generasi Pada proses ini aliran steady state, sehingga akumulasi =0 Persamaan neraca massa menjadi Input – output + generasi = 0 Sodium sulfate (aq) z ΔzΔz Neraca Massa Oksigen dalam system Input – output + generasi = 0

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