2 KerjakanSoal no 1.5, 1.7, dan 1.8Dari buku : Applied Mathematics and Modelling forChemical EngineersTulisan : Richard G.Rice dan Duong D. Do
3 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 4πr2∆r and show that(b) Perform an elemental heat balance at the surface of the sphere and deduce
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