Fluid flow and heat transfer in variable cross section annular passages

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Subrata Sengupta, Committee Chair


A mathematical model has been developed to solve for laminar flow and heat transfer in annular passages with axially varying flow cross-section. Axisymmetric coordinate system with an algebraic transformation in the radial direction has been used. Fully elliptic vorticity-stream function and energy equations in the transformed coordinates are solved using an iterative ADI scheme. The model has been applied to study the thermal-hydraulics of annuli with single blockage/cavity, periodic wavy surfaces/circular fins on the inner tube.In an annulus with a smooth blockage, main features of the flow are established at a Reynolds number of 1000. At Reynolds numbers greater than 100, the flow separates immediately downstream of the blockage. The pressure drop is drastic near the maximum constriction. The heat flux is high in the constricted zones and at a location where the fluid re-attaches itself to the wall. Increase in the total pressure drop is about a magnitude greater than that in the average Nusselt number. In an axisymmetric annular cavity, a recirculating zone occupies the entire cavity at high Reynolds numbers and low cavity aspect ratios. In general the heat transfer decreases within the cavity. However, a strong recirculating eddy in the cavity enhances heat transfer in the cavity and downstream of it. Increases in the total pressure drop and the average Nusselt number are of the same order of magnitude.With a wavy tube, the pressure drop is influenced significantly by the wave (promoter) height and the annular gap. For heat transfer, promoter height is the only significant parameter. Effects of promoter length and spacing are small. At a Reynolds number of 1000 and a Prandtl number of 5, heat transfer from the wavy tube annulus is 8 times that from the circular tube annulus while the pressure drop is only twice. With circular fins the major contribution to heat transfer is from the fin side at the downstream end. At Prandtl numbers less than 2, use of the fins may not be justified since increase in the pressure drop is more pronounced than in the heat transfer.


Engineering, Mechanical

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