Table Of ContentPHYSICS RESEARCH AND TECHNOLOGY
U H
NDERSTANDING EAT
CONDUCTION
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HYSICS ESEARCH AND ECHNOLOGY
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PHYSICS RESEARCH AND TECHNOLOGY
U H
NDERSTANDING EAT
CONDUCTION
WILLIAM KELLEY
EDITOR
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CONTENTS
Preface vii
Chapter 1 Cooling Kinetics in Stone Fruits 1
Francisco Javier Cuesta and
María Dolores Alvarez
Chapter 2 Sensitivity of Numerical Modeling Technique for
Conjugate Heat Transfer Involving High Speed
Compressible Flow over a Cylinder 73
Laurie A. Florio
Chapter 3 Advances in Heat Conduction Analysis
with Fundamental Solution Based Finite
Element Methods 123
Qing-Hua Qin
Index 165
PREFACE
The first chapter of this book proposes an analytical Fourier series
solution to the equation for heat transfer by conduction in a spherical shell
with an internal stone consisting of insulating material as a model for the
kinetic of temperature in stone fruits both as a general solution and a mass
average value. The chapter also considers an internal heat source linearly
reliant on temperature. The second chapter focuses on the sensitivity of the
numerical modeling technique for conjugate heat transfer involving high
speed compressible flow over a cylinder. The last chapter presents an
overview of the fundamental solution (FS) based finite element method
(FEM) and its application in heat conduction problems. First, basic
formulations of FS-FEM are presented, such as the nonconforming intra-
element field, auxiliary conforming frame field, modified variational
principle, and stiffness equation. Then, the FS-FE formulation for heat
conduction problems in cellular solids with circular holes, functionally
graded materials, and natural-hemp-fiber-filled cement composites are
described.
Chapter 1 - Stone fruits, like plums, cherries, olives and so forth, have
approximately spherical or ellipsoid geometries, but inside they contain a
ligneous core -the seed- whose physical and thermo-physical parameters
are radically different from those of the edible part, the pulp. Moreover, the
contact surface between this seed and the pulp is in practice the deepest
viii William Kelley
point that can be reached in the fruit and it performs the role of a "thermal
centre" which in homogeneous solid objects is performed by the geometric
centre. There are a number of important issues that need to be known in
food chilling, for example the time required to reach a given temperature at
the thermal centre of the product, or how much heat has to be extracted to
reach that temperature, or what is the average temperature of the product
once it has reached a given temperature at its thermal centre or on the
surface, etc. This chapter proposes an analytical Fourier series solution to
the equation for heat transfer by conduction in a spherical shell with an
internal stone consisting of insulating material as a model for the kinetic of
temperature in stone fruits both a general solution and a mass average
value. The chapter also considers an internal heat source linearly reliant on
temperature. The first approximations to the general equations are used to
derive the model equations for calculation of the above mentioned issues
and also for indirect calculations of Biot number, or the thermal diffusivity
when the Biot number is given.
Chapter 2 - The surface heating due to conjugate heat transfer is often
the main source of conduction heat transfer through solid materials moving
through or impinged upon by high speed compressible flows. High
temperature gradients and large heat fluxes at the fluid-solid interfaces
develop under such conditions. Since high temperatures and high
temperature gradients affect the solid material properties and thus material
strength, an understanding of these conjugate heat transfer phenomena is
important. The compressible flow around a fixed cylinder or due to a
moving cylinder is a well-established baseline for comparison. Numerical
models can be used to investigate and predict the resulting thermal
conditions for such flow and heat conduction effects, but the numerical
modeling methods must be attuned to properly capture the conditions
unique to this type of flow. Among the factors influencing the numerical
results are the mesh size, the time step and time discretization, various
discretization methods including gradient calculations and gradient limiters
as well as the turbulence model and associated parameters and options.
When a moving object requiring some mesh motion is added to the
simulation, additional options become available. A sliding type of mesh
