ON LIMITING NUSSELT NUMBERS FROM MEMBRANE ANALOGY FOR COMBINED FREE AND FORCED CONVECTION THROUGH VERTICAL DUCTS

Solutions of membrane vibration problems have been utilized for study of fully developed combined free and forced laminar convection through straight vertical triangular ducts of shapes (i) equilateral, (ii) 30°-60°-90° and (iii) right-angled isosceles. Steady state conditions are assumed. All fluid properties are considered constant, except for variation of density in the buoyancy terms. Wall temperature is assumed varying linearly in the flow direction, while it is considered uniform in the transverse direction. Presence of uniform volume heat source has been considered. Exact analytical expressions in the form of infinite series have been presented for velocity, temperature and Nusselt numbers for the three triangular tubes considered. The difference between the Nusselt number for the three triangles becomes relatively small as the value of the Rayleigh number increases. Small values of heat source parameter decreases the Nusselt number. © 1969.