A platen of thermal conductivity k = 15 W/m ∙ K is heated by flow of a hot fluid through channels of width L = 20mm, with T_∞,i = 200°C and hi = 500W/m² ∙ K. The upper surface of the platen is used to heat a process fluid at T_∞.o = 25°C with a convection coefficient of h n = 250 W/m² ∙ K. The lower surface of the platen is insulated. To heat the process fluid uniformly, the temperature of the platen's upper surface must be uniform to within 5°C. Use a finite-difference method, such as that of IHT, or the finite-element method of FEHT to obtain the following results.

(a) Determine the maximum allowable spacing, W, between the channel centerlines that will satisfy the specified temperature uniformity requirement.

(b) What is the corresponding heat rate per unit length from a flow channel?

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To.0 = 25°C h, = 250 W/m²-K Fluid O'00 Temperature uniformity of 5°C required Platen, k = 15 W/m•K Heating channel Toi = 200°C h; = 500 W/m2.K %3D L/2 Insulation W.