Date of Award

2021

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)

Administrative Home Department

Department of Mechanical Engineering-Engineering Mechanics

Advisor 1

Hassan Masoud

Committee Member 1

Fernando Ponta

Committee Member 2

Kazuya Tajiri

Committee Member 3

Cecile Piret

Abstract

In the area of heat transfer, like other fields of science and engineering, full- and semi-analytical solutions of elementary problems are regarded as invaluable resources that can be used to identify relevant dimensionless parameters, to obtain basic insights into the phenomena under consideration, to quickly quantify the effects of key factors, and, ultimately, to pave the way for understanding more complex problems arising in practice. These solutions can also serve as excellent benchmarks for calibrating experimental setups and validating numerical techniques. In this dissertation, we theoretically study three classical heat transfer problems, with the ultimate goal of deriving analytical or approximate expressions for the Nusselt number (denoted by Nu), which is a key dimensionless parameter that quantifies the transfer of heat to and from a surface. First, we consider heat transfer by conduction from oblate spheroidal and bispherical surfaces into a stationary, infinite medium. The surfaces are presumed to maintain a constant heat ux. Assuming steady-state condition and uniform thermal conductivity, we analytically solve the Laplace equation for the temperature distribution and discuss the challenge of dealing with the Neumann (uniform flux) versus more convenient Dirichlet (isothermal) boundary condition. The solutions are obtained in boundary-fitting coordinate systems using the method of separation of variables and eigenfunction expansion. And, exact expressions for the average Nusselt number are presented along with their approximations. Next, we examine forced convection heat transfer from a single particle in uniform laminar flows. Asymptotic limits of small and large Peclet numbers (denoted by Pe) are considered. For Pe <> 1 and small or moderate Reynolds numbers. Specific results are given for the heat transfer from spheroidal particles in Stokes ow. Finally, we revisit the problem of steady-state heat transfer from a single particle in a uniform laminar ow with the assumption that the thermal conductivity of the fluid changes linearly with the temperature. We use a combination of asymptotic and scaling analyses to derive approximate expressions for the Nusselt number of arbitrarily shaped particles. The results cover the entire range of the Peclet number. We find that, for a constant temperature boundary condition and fixed geometry, the Nusselt number is essentially equal to the product of two terms, one of which is only a function of Pe while the other one is nearly independent of Pe and mainly depends on the proportionality constant of the conductivity-temperature relation. We also show that, in contrast, when a uniform heat flux is imposed on the surface of the particle, the Nusselt number can be estimated as a summation of a Pe-dependent piece and one that solely varies with the proportionality constant.

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