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Q: In a biomedical supplies manufacturing process, a requirement exists for a large platen that is to be maintained at 45 ± 0.25°C. The proposed design features the attachment of heating tubes to the platen at a relative spacing S. The thick-walled, copper tubes have an inner diameter of D; = 8 mm and are attached to the platen with a high thermal conductivity solder, which provides a contact width of 2D j. The heating fluid (ethylene glycol) flows through each tube at a fixed rate of In = 0.06 kg/s. The platen has a thickness of w = 25 mm and is fabricated from a stainless steel with a thermal conductivity of]5 W/m · K.
Considering the two-dimensional cross section of the platen shown in the inset, perform an analysis to determine the heating fluid temperature Tm and the tube spacing S required to maintain the surface temperature of the platen, T(x, w), at 45 ± 0.25 D C, when the ambient temperature is 25°C and the convection coefficient is 100 W/m2 · K.
