Date of Defense
7-4-2025 10:00 AM
Location
F3-238
Document Type
Dissertation Defense
Degree Name
Doctor of Philosophy in Mathematics
College
COS
Department
Mathematical Sciences
First Advisor
Prof. Qasem M. Al-Mdallal
Keywords
High Order Compact Scheme, Reynolds Number, Prandtl Number, Nanoparticles, Circular Cylinder, Elliptical Cylinder, Aspect Ratio, Concentration Factor.
Abstract
This thesis presents a numerical study of flow induced by an infinitely long heated circular or elliptical cylinder in a uniform stream π0 of a viscous, incompressible nanofluid. The study is based on solving the full conservation equations of mass, momentum, and heat. The methodology includes the mathematical formulation of the problem, which suits the initial development of the flow and the large time numerical simulations. For the numerical technique, high-order compact (HOC) scheme is developed for circular and elliptical geometries. The numerical scheme is verified by applying it to the cases of uniform flow past a stationary elliptical cylinder; the validation includes grid independence studies and comparisons with existing numerical results.
For circular cylinder, the effects of different nanoparticles namely π΄πβπβ, πππβ, πππ πππβ, at various concentrations, with a fixed Reynolds number of π
π = 200, showed that π΄πβπβ nanoparticles are the most efficient for improving heat transfer, while πππβ and πππβ provide more moderate improvements, with πππβ being less effective due to its higher viscosity and reduced flow disturbances. The time evolution of Nusselt number and temperature variations with πππβ nanoparticles leading to more noticeable thermal oscillations comparative to π΄πβπβ and πππβ, showing more stable heat transfer characteristics. For a circular cylinder, nanoparticle concentration altered the flow structure but had minimal effect on vortex shedding frequency, while impacting flow stability and turbulence.
For an elliptical cylinder, higher nanoparticle concentrations improve convective heat transfer and the Nusselt number, with increased fluctuations indicating enhanced efficiency. π΄πβπβ nanoparticles are the most effective, while πππβ offers moderate improvement, and πππβ provides the weakest enhancement due to its higher density and reduced flow disturbances. The analysis of both 00 and 900 orientations show that 900 cylinder orientation enhances turbulence, causing greater Nusselt number fluctuations and dynamic heat transfer, while the 00 orientation leads to more stable flow and uniform heat transfer. Lower aspect ratios increase turbulence and Nusselt number fluctuations, while higher aspect ratios promote stable heat transfer. Optimizing aspect ratio and nanoparticle concentration is key to maximizing heat transfer efficiency in nanofluid systems.
AN ACCURATE NUMERICAL METHOD FOR IMPULSIVELY STARTED FLOW PAST AN ELLIPTICAL CYLINDER IN NANOFLUIDIC MEDIUM
F3-238
This thesis presents a numerical study of flow induced by an infinitely long heated circular or elliptical cylinder in a uniform stream π0 of a viscous, incompressible nanofluid. The study is based on solving the full conservation equations of mass, momentum, and heat. The methodology includes the mathematical formulation of the problem, which suits the initial development of the flow and the large time numerical simulations. For the numerical technique, high-order compact (HOC) scheme is developed for circular and elliptical geometries. The numerical scheme is verified by applying it to the cases of uniform flow past a stationary elliptical cylinder; the validation includes grid independence studies and comparisons with existing numerical results.
For circular cylinder, the effects of different nanoparticles namely π΄πβπβ, πππβ, πππ πππβ, at various concentrations, with a fixed Reynolds number of π
π = 200, showed that π΄πβπβ nanoparticles are the most efficient for improving heat transfer, while πππβ and πππβ provide more moderate improvements, with πππβ being less effective due to its higher viscosity and reduced flow disturbances. The time evolution of Nusselt number and temperature variations with πππβ nanoparticles leading to more noticeable thermal oscillations comparative to π΄πβπβ and πππβ, showing more stable heat transfer characteristics. For a circular cylinder, nanoparticle concentration altered the flow structure but had minimal effect on vortex shedding frequency, while impacting flow stability and turbulence.
For an elliptical cylinder, higher nanoparticle concentrations improve convective heat transfer and the Nusselt number, with increased fluctuations indicating enhanced efficiency. π΄πβπβ nanoparticles are the most effective, while πππβ offers moderate improvement, and πππβ provides the weakest enhancement due to its higher density and reduced flow disturbances. The analysis of both 00 and 900 orientations show that 900 cylinder orientation enhances turbulence, causing greater Nusselt number fluctuations and dynamic heat transfer, while the 00 orientation leads to more stable flow and uniform heat transfer. Lower aspect ratios increase turbulence and Nusselt number fluctuations, while higher aspect ratios promote stable heat transfer. Optimizing aspect ratio and nanoparticle concentration is key to maximizing heat transfer efficiency in nanofluid systems.
