Soal Matematika Tekkim Ilustrasi 58ma

MATEMATIKA TEKNIK KIMIA

Kerjakan Soal no 1.5, 1.7, dan 1.8

Dari buku Tulisan

: Applied Mathematics and Modelling for Chemical Engineers : Richard G.Rice dan Duong D. Do

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 ed 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 for thermal conductivity in the (assumed) spherical shape of the plastic bead. (a) Assuming the bead is a perfect sphere, ed everywhere by external fluid of temperature Tf, perform a shell balance on an element of volume 4πr2∆r and show that

(b) Perform an elemental heat balance at the surface of the sphere and deduce

Thermocouple model

qr r q r r + ∆r

(a) Heat balance 0 0 Input – output + generasi – konsumsi = akumulasi qr

r –

qr r + ∆r

=

Soal 1.7

=0

=0

Akumulasi = input – output + generasi

Input = output

=0

=0

Akumulasi = input – output + generasi Input = output UoL .A.Cz=x + ((1-ε).-De.A. (dc/dxz=x)+Kc.a. V. (c*-c) = UoL .A.Cz=x+∆x + ((1-ε).-De.A. (dc/dxz=x+∆x )

Dan lain-lain...........

Input, O2(g)

Sodium sulfate (aq)

z Δz z + Δz

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

Neraca Massa Oksigen dalam system Input – output + generasi = 0