A STUDY ON NATURAL CONVECTION FLOW IN CYLINDRICAL GEOMETRIES WITH TIME-PERIODIC HEAT INPUT
A STUDY ON NATURAL CONVECTION FLOW IN CYLINDRICAL GEOMETRIES WITH TIME-PERIODIC HEAT INPUT
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Date
2016-09
Authors
ONI, Michael Oluwakayode
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Abstract
This dissertation investigatesthe effect of steady-periodic heating at the surfaces of the cylinders on natural convection flow in a tube and an annulus.Two problemsare considered in this work. In both problems, the fluid was assumed to be fully developed and the mathematical equations governing the flow were derived. The first problem presents the impact of time-periodic heating at the surface of a tube on fluid velocity, temperature, rate of heat transfer and skin friction.While the second problem examines the effect of periodic heating at the surfaces ofthe cylinders on natural convection flow in an annulus.Using suitable transformation, the partial differential governing equations were transformed to their corresponding ODE, representing the steady and periodic regimes.Closed-form expressions for velocity, temperature, skin-friction, mass flow rate and rate of heat transfer which was expressed as Nusselt number were obtained in terms of modified Besselβs function of first and second kinds for both cases.The solutions obtained were graphically represented and the effects of periodic heating (Strouhal number ππ‘), Prandtl number ππ and aspect ratio π on fluid velocity, temperature, rate of heat transfer and skin-friction were investigated. Result indicates that the role of Strouhal number, Prandtl number and aspect ratio is to decrease fluid velocity, temperature, and skin-friction at the surfaces of the cylinders.Also, the rate of heat transfer between the surfaces of the cylinders and the fluid increases with increase in Strouhal number ππ‘ , Prandtl number ππ and aspect ratio π .Furthermore, for small Strouhal number ππ‘ ,velocity, temperature, rate of heat transfer, mass flow rate and skin-friction of the time-periodic regime (periodic part) reduces to steady regime. At this point, the steady and periodic regimes make equal contributions on overall velocity. In addition, for large Strouhal number ππ‘ , the periodic regime contributes an adverse effect on the overall fluid temperature and velocity.
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A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES AHMADU BELLO UNIVERSITY, ZARIA, IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE DEGREE IN MATHEMATICS DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA
Keywords
STUDY,, NATURAL CONVECTION,, CYLINDRICAL GEOMETRIES,, TIME-PERIODIC HEAT INPUT