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CHME 333 Workbook
Chapter 2 – Introduction to Conduction
•
Objectives
o
Develop a better understanding of Fourier’s Law
Origins
Different geometries
Definition of thermal conductivity
Calculation of heat fluxes
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Develop Heat Equation and apply common Boundary Conditions
How temperature depends on position and time, e.g.
T(x,y,z,t) or T(r,
θ
,z,t)
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Introduction
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In Chapter 1 you were introduced to the concept of heat transfer by conduction.
You were given the equation for Fourier’s Law and you learned how to apply it to
very simple cases.
In Chapter 2, we will take a more detailed look at Fourier’s
Law, and combined with a thermal energy balance, derive what is called the Heat
Diffusion Equation.
This Heat Diffusion Equation will enable you to calculate the
temperature distribution in an object – T = T(x, y, z, t).
In some cases, you will
want to calculate the temperature as a function of position and time.
In other cases,
you will be asked to calculate heat transfer rates.
You will do this by simply
plugging in the temperature distribution equation (T = T(x, y, z, t)) into Fourier’s
Law.
We will do this for rectangular, cylindrical, and spherical geometries.

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Fourier’s Law – look at it more in depth
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A phenomenological rate equation that allows determination of the conduction heat
flux from knowledge of the temperature distribution in a medium
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General form
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Implications
Heat transfer is in the direction of _________________________ (reason for
minus sign).
Fourier’s Law serves to define the thermal conductivity of the medium
Thermal diffusivity
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α
= ____________
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What are the units of
α?
Direction of heat transfer is ___________
to lines of
__________________________________
.
Heat flux is a vector quantity (direction and
magnitude) and may be resolved into orthogonal
components.
Fourier’s Law in coordinate systems