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Combined free and forced convection through vertical noncircular ducts and passages Ansari, Saghir A.

Abstract

The problem of laminar combined free and forced convection through vertical noncircular ducts and passages in the fully developed region has been treated. The fluid properties are considered to be constant, except the variation of the density in the buoyancy term of the momentum equation. Pressure work and viscous dissipation terms of the energy equation have been neglected. Heat flux has been considered to be constant in the flow direction. A general solution to the problem has been obtained in "the form of infinite series containing modified Bessel functions. Two possible thermal boundary conditions on the circumference of the heated wall have been analyzed, Case 1 - uniform circumferential wall temperature, and Case 2 - uniform circumferential wall heat flux. Information of engineering interest like Nusselt number, heat flux, ratio, shear stress ratio, temperature distribution on the' wall, velocity and temperature distributions in the flow field have been obtained for two sets of geometries, namely, (i) flow through regular polygonal ducts, and (ii) flow between cylinders arranged in regular arrays. For flow through regular polygonal ducts, the case of uniform circumferential wall temperature results in higher values of Nusselt numbers as compared to the case of uniform circumferential wall heat flux. This difference in Nusselt number values decreases as the number of sides of the regular polygon is increased, until for a circle it completely disappears. For both the cases, at higher values of Rayleigh number, the Nusselt number is less sensitive to the number of sides of the polygon. Also, at higher values of Rayleigh number, both the cases tend to produce the same results. For low sided polygons, an increase in Rayleigh number tends to shift the maximum value of shear stress from the centre of the duct wall towards the apex of the duct. For flow between cylinders arranged in regular arrays, Case 1 results in higher values of Nusselt number compared to Case 2, for low spacing ratios. However, as the spacing ratio is increased, the two cases tend to produce the same results. Cylinders arranged in equilateral triangular arrays produce higher values of Nusselt number compared to those in square arrays. This difference in Nusselt number values decreases when the spacing ratio is high. For higher values of Rayleigh number, however, the results are less sensitive to the type of arrays. Also, at higher values of Rayleigh number, both the cases tend to produce the same results.

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