Forced-convection heat transfer in flow between parallel plates (Fig. 10B.7), a viscous fluid with temperature-independent physical properties is in fully developed laminar flow between two flat surfaces placed a distance 2B apart. For z < 0 the fluid temperature is uniform at T = T₁. For z > 0 heat is added at a constant, uniform flux q₀ at both walls. Find the temperature distribution T(x, z) for large z. 

(a) Make a shell energy balance to obtain the differential equation for T(x, z). Then discard the viscous dissipation term and the axial heat conduction term.

(b) Recast the problem in terms of the dimensionless quantities

(c) Obtain the asymptotic solution for large z:

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90 90 Z4 - z = 0 D, (x) Direction of flow Fully developed slit flow at z = 0; inlet temperature is T X = +B Part (a) x =-B т-т, kz - = } pĈ,V=ma„B? B 9oB/k 2,max Part (b) O(7, 5) = } + o? – io . 39 280 |Heating element Heating element