NATURAL-CONVECTIVE FLOW THROUGH A VERTICAL DUCT WITH A RESTRICTED ENTRY

This paper describes a study of laminar convective heat transfer to a fluid induced to flow by buoyancy forces through a heated vertical duct with a flow restriction at its lower end. The duct has a circular cross-section and the heating provides a uniform surface temperature. The entry restriction is formed by an unheated downward extension of the duct. The equations that govern the laminar natural-convective flow through the duct were solved by a step-by-step numerical technique. The relationship between the overall Nusselt number and the Rayleigh number is presented graphically in terms of the dimensionless flow rate and also in terms of the ratio of the unheated length of the duct to the heated length. This length ratio provides a measure of the severity of the entry restriction. An important finding of the study was that if the entry restriction exceeds a certain size, laminar upward flow throughout the whole of the heated part of the duct is not physically possible. This occurs if the ratio of the unheated length to the heated exceeds 18 for values of Rayleigh number up to 20 and exceeds only 2 for Rayleigh numbers in excess of 103. Some experimental work was undertaken to corroborate the theoretical relationship and also to examine the nature of the flow in ducts for which the value of the unheated to heated length ratio for laminar flow throughout is exceeded. © 1978.