Rectangular flow channels are formed by milling long rectangular slots into flat metal plates, and brazing the plates together as shown below. Either large channels (Configuration A) or twice as many small channels (Configuration B) can be formed by shifting the plates relative to one another prior to brazing. Consider isothermal plates at \(T_{s}=67^{\circ} \mathrm{C}\) with ethylene glycol at \(T_{m}=27^{\circ} \mathrm{C}\) flowing at a rate of \(0.1 \mathrm{~kg} / \mathrm{s}\) in each of the large channels. The flow rate in each small channel is \(0.05 \mathrm{~kg} / \mathrm{s}\). For dimensions \(a=10 \mathrm{~mm}\) and \(b=30 \mathrm{~mm}\), determine the heat transfer rate per unit channel length for one large channel and for a pair of small channels. Also determine the pressure gradient in the fluid associated with Configurations A and B.

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a 2a Interface b b Configuration A Aligned slots Configuration B Non-aligned slots