Solve the following:
Q: A hot fluid passes through circular channels of a cast iron platen (A) of thickness LA = 30 mm which is in poor contact with the cover plates (B) of thickness L B = 7.5 mm. The channels are of diameter D = 15 mm with a centerline spacing of La = 60 mm. The thermal conductivities of the materials are k A = 20 W/m · K and k B = 75 W/m · K, while the contact resistance between the two materials is Rt,c = 2.0 X 10-4 m2 · K/W. The hot fluid is at Ti = 150°C and the convection coefficient is 1000 W/m2 · K. The cover plate is exposed to ambient air at T8 = 25°C with a convection coefficient of 200 W/m2 · K. The shape factor between one channel and the platen top and bottom surfaces is 4.25.
(a) Determine the heat rate from a single channel per unit length of the platen normal to the page, q;.
(b) Determine the outer surface temperature of the cover plate, Ts.
(c) Comment on the effects that changing the centerline spacing will have on q; and Ts. How would insulating the lower surface affect qi and Ts?
