A theoretical study of rayleigh benard convection problem with realistic and artificial boundary conditions

Abstract

In this thesis we present linear and weakly non-linear study of Rayleigh Bénard newlineconvection subject to general boundary condition, which includes both physically newlinerealistic and artifcial boundaries. A horizontal confguration is adopted, wherein newlinethe horizontal surfaces are attached to porous blocks, which allows for the inclusion newlineof rough boundaries modelled by the Robin boundary condition on velocity. The Robin boundary condition is utilised to model boundary condition on temperature as well. Adding nanoparticles to a base and#64258;uid results in an increased thermal conductivity of the base and#64258;uid. The objective of this research is to present a conducive understanding of the eand#64256;ect of nanoparticles and its enhanced thermophysical properties eand#64256;ects on the onset of convection. Eand#64256;ects of Rough Boundaries on Rayleigh-Bénard Convection in Nanoand#64258;uids A linear and weakly non-linear stability analysis of Rayleigh-Bénard convection in a Newtonian nanoand#64258;uid between two rough boundaries is carried out. A newlinesingle-phase description of nanoand#64258;uids is adopted in the study. Water-alumina and newlinewater-copper are nanoand#64258;uids in consideration for the study. The values of thermophysical quantities of nanoand#64258;uids are obtained using either the mixture theory or phenomenological laws. The boundary eigenvalue problem arising in the study is solved using the Maclaurin series. Also, a single-term Galerkin technique is adopted to obtain the guess value of the Rayleigh number and the wave number. Further, improved values of the Rayleigh number and the wave number are obtained using the Newton-Raphson method. The minimal Fourier series representation is used to arrive at the generalised Lorenz model. A detailed discussion is made on the eand#64256;ect newlineof rough boundaries on the onset of convection in nanoand#64258;uids. The study aims to newlinepresent a theoretical comparison between the results of the two nanoand#64258;uids considered and the destabilizing eand#64256;ect showcased by each of the nanoparticles on the onset of convection.