Plug flow with forced-convection heat transfer. Very thick slurries and pastes sometimes move in channels almost as a solid plug. Thus, one can approximate the velocity by a constant value v₀ over the conduit cross section. 

(a) Rework the problem of S10^o8 for plug flow in a circular tube of radius R. Show that the temperature distribution analogous to Eq. 10.8-31 Θ (ζ, ζ) = 2ζ + ½ζ² – 1/4 is in which ζ = kz/pC_pv₀ R², and Θ and ζ are defined as in S10.8. 

(b) Show that for plug flow in a plane slit of width 2B the temperature distribution analogous to Eq. 10B.7-4 is Θ(ζ, ζ) = ζ + ½ σ² – 1/6 in which ζ = kz/pC_pv₀B², and Θ and σ are defined as in Problem 1013.7.

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Power supply Ti Ambient air tempe rature Ta Pipe wall