Abstract
The paper investigates the heat transfer characteristics of a channel system consisting of mean axial flow and oscillatory cross flow components. A numerical model has been developed to solve the governing equations associated with the flow. The paper identifies advection, diffusion, and oscillation time scales and intensity of squeezing in the channel as critical parameters controlling system behavior. The total Reynolds number parameter is considered in the paper to understand the combined effect of axial and transverse Reynolds numbers on the Nusselt number. Flow visualization techniques are employed to understand the boundary layer changes that occur over an oscillation cycle. Nusselt number is found to increase with a reduction in advection and oscillation time scales. A linear relationship is observed between the Nusselt number and total Reynolds number when the axial and transverse Reynolds numbers are comparable. Non-dimensional pressure drop is primarily defined by only two parameters: axial Reynolds number and squeezing fraction. The flow visualization results indicate significant heat transfer enhancement in a small fraction of the oscillation cycle characterized by flow conditions similar to Couette flow.
During each active oscillation cycle, the vesicle shape undergoes a symmetry-breaking transformation from an up-down symmetric to an up-down asymmetric dumbbell followed by the reverse symmetry-restoring transformation.
In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.
A combined oscillation cycle involving self-excited thermo-acoustic and hydrodynamic instability mechanisms
