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Combined free and forced convection through vertical non-circular ducts with and without peripheral wall conduction Khatry, Abdul Kader

Abstract

Analysis of combined free and forced convection through vertical non-circular ducts has been carried out using variational technique. Fully developed flow with uniform axial heat input is assumed. All fluid properties are considered invariant with temperature except the variation of density in the buoyancy term of the equation of motion. A general study of the problem has been made in three stages: (i) Forced convection without circumferential wall conduction. For this case, a known velocity expression is used and a particularly simple variational expression has been presented. Nusselt numbers are calculated for rectangular, rhombic, isosceles triangular, and right-angled triangular ducts. Results compared with the available solutions have shown excellent agreement. (ii) Combined free and forced convection without circumferential wall conduction. Nusselt numbers have been computed for rectangular and rhombic ducts. A finite-difference procedure has also been carried out and the results are presented for rhombic duct only. In both of the above cases (i) and (ii), the condition of uniform peripheral heat flux has been directly utilized in deriving the variational expression, thus releasing the thermal boundary condition from satisfying exactly the condition at the wall. The condition of uniform circumferential heat flux results in lower values of Nusselt numbers as compared to that of uniform circumferential wall temperature. This difference in Nusselt number values decreases with the increase in Rayleigh number. At higher values of Rayleigh number, both the conditions tend to produce about the same results. (iii) Conjugate problem of combined free and forced convection when peripheral wall conduction is included. The equations coupling heat conduction in the walls with the convection inside the fluid are solved to establish the influence of peripheral wall conduction. The problem has been solved in a generalized way and the results have been presented for rectangular ducts. It is found that large values of the free convection effects and/or of the conduction parameter tend to minimize the asymmetries in circumferential wall temperature.