Chapter 8, Problem 8.76P

In a biomedical supplies manufacturing process, a requirement exists for a large platen that is to be maintained at $45\pm 0.25°C$ . The proposed design features the attachment of heating tubes to the platen at a relative spacing $\pounds$ The thick-walled, copper tubes have an inner diameter of $D_i=8mm$ and are attached to the platen with a high thermal conductivity solder, which provides a contact width of $2D_i$ . The heating fluid (ethylene glycol) flows through each tube at a fixed rate of $\stackrel{\dot{}}{m}=0.06\text{kg/s}$ . The platen has a thickness of $w=25\text{mm}$ and is fabricated from a stainless steel with a thermal conductivity of $15\text{W/m}\cdot \text{K}$ .

Considering the two-dimensional cross section of the platen shown in the inset, perform an analysis to determine the heating fluid temperature $T_m$ and the tube spacing S required to maintain the surface temperature of the platen, $T\left(x,w\right),\text{ at }45\pm 0.25°C$ , when the ambient temperature is 25°C and the convection coefficient is $100{\text{W/m}}^2\cdot \text{K}$ .