A viscous fluid with temperature-independent physical properties is in fully developed laminar flow between two flat surfaces placed a distance of 2B apart. For z < 0 the fluid temperature is uniform at T = T,. For z > 0 heat is added at a constant, uniform flux qo 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:

  

Fig. 10B.7. Laminar, incompressible flow between parallel plates, both of which are being heated by a uniform wall heat flux q, starting at z = 0. 40 Fully developed slit flow at z = 0; inlet temperature is T1 v, (x) Direction of flow X=-B X = +B Heating element Heating element