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dc.contributor.authorFilentinus, Otulo Onyango
dc.date.accessioned2023-08-10T12:21:17Z
dc.date.available2023-08-10T12:21:17Z
dc.date.issued2023
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/26753
dc.descriptionA Research Project Submitted in Partial Fulfillment of the Requirement for the Award of Degree of Master of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University. May 2023en_US
dc.description.abstractTurbulent natural convection in an enclosure plays a big part in heat transmission and the building environment. Sophisticated buildings around the world are outfitted with costly heaters and coolers to maintain comfortable temperatures for human existence, manufacturing, and sophisticated farming methods, a scenario that many people cannot afford. Over a time researchers have consistently developed a number of numerical study models to simulate the natural turbulent flow in these rectangular enclosures to solve complex problems associated with turbulent flows. In spite of several experimental studies and model simulations on the structure of natural turbulence convection, the fundamental mechanism in turbulent phenomena is still incomplete. Significant variations in experimental data and model simulation data in previous studies have been noted. This is because the unknown turbulent correlation coefficients resulting from the nonlinear terms of the turbulent flow control equations make it difficult to accurately determine fluid flow variables such as mean velocity distribution, temperature distribution and kinetic energy in a model simulation. Thus an accurate numerical prediction of natural turbulence convection is crucial to solving the nonlinear equations for subsequent practical applications. The performance of a numerical turbulence model k-ε in estimating the amount of heat transfer that occurs as a result of the naturally occurring turbulent convection that takes place within an air-filled rectangular enclosure is investigated in this work using vorticity vector formulation. The workflow of simulating the heat transfer which results from the action of natural convection within an enclosed rectangular cavity takes into account the effect of turbulence for the Rayleigh numbers Ra = 1.552×1010, Ra = 9.934×1011, Ra = 1.552×1013 and Ra = 2.425×1014. The Low-Reynolds-number turbulence k-ε model was employed in this numerical study to model the non linear relations ∇· ρu′ iu′ j and ∂CpT′u′ i ∂ xi in the averaged Navier Stokes equation and energy equation respectively to complete the governing equations. Apart from the hot and cold walls, which are maintained at 308K and 288K, respectively, all of the walls of the enclosure are adiabatic. The vorticity vector formulation allowed the pressure term to be removed from the momentum equation. Finite difference approximations were used in the FLUENT program to solve the vorticity, energy, vector potential, and two resultant equations for each model together with their boundary conditions. The outcomes of the study for the distribution of the velocity and temperature components are presented, demonstrating that the number of contours and vortices increases proportionally with the Rayleigh Number. In addition, a higher Rayleigh number indicates more turbulence, which in turn implies a higher absolute value of the velocity hence increased Kinetic energy.en_US
dc.description.sponsorshipKenyatta Universityen_US
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectNumericalen_US
dc.subjectSimulationen_US
dc.subjectNaturalen_US
dc.subjectTurbulenten_US
dc.subjectConvectionen_US
dc.subjectVorticityen_US
dc.subjectVectoren_US
dc.subjectFormulationen_US
dc.titleNumerical Simulation of Natural Turbulent Convection with Vorticity Vector Formulationen_US
dc.typeThesisen_US


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