Abstract
This study demonstrates a global, nonparametric, noniterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of nonautonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.
Highlights
Considering that a partial differential equation system with holonomic constraints is discretized to be an ordinary differential equation system (ODEs), it is meaningful for us to begin with the following system with forcing dx dt v(x) +
Let us confirm that the main objective of this study is to present such a general framework of non-parametric, non-iterative optimization on ODEs (1)
This study presents a non-parametric, non-iterative optimization of time-mean value of an inner-product-type index on any non-autonomous ODEs when a base field without forcing is stable steady state and the amplitude a of vibrational forcing is sufficiently small
Summary
Numerous studies have been carried out in many fields on maxima or minima of time-averaged quantities [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] They include the optimization of temperatures [1,2,3], heating rate [4], beam to wave power transfer efficiency [5], current density [6], reaction rate [7], flow vorticity [8] and velocity [9,10], drag reductions [11,12], heat transfer rates [13,14,15,16,17], shear stresses [18,19,20] and so on. Iterative algorithms were utilized to maximize time-averaged system energy efficiency [25], and to maximize time-averaged transmission rate [28], and so on
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
