Fourier Series
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Transcript of Fourier Series
What is Heat Transfer?
Fourier SeriesConsider a set of eigenfunctions n that are orthogonal, where orthogonality is defined as
for m nAn arbitrary function f(x) can be expanded as series of these orthogonal eigenfunctions
or
Due to orthogonality, we thus know
all other nAmm integrate to zero because m nThus, the constants in the Fourier series are
AME 60634 Int. Heat Trans.D. B. Go # Cartesian Sturm-LiouvilleCharacteristic Value Problemp(x) = 1; q(x) = 0; w(x) = 1
homogeneous B.C.
After Applying Final B.C.Typical B.C.
DirichletNeumannRobinAME 60634 Int. Heat Trans.D. B. Go # Cartesian Sturm-Liouville
Kakac & YennerHeat Conduction, 3rd Ed.AME 60634 Int. Heat Trans.D. B. Go # Cylindrical Sturm-LiouvilleCharacteristic Value Problemp(r) =r; q(r) = 2/r; w(r) = r
homogeneous B.C.
After Applying Final B.C.Typical B.C.
DirichletNeumannRobin
AME 60634 Int. Heat Trans.D. B. Go # Cylindrical Sturm-Liouville
homogeneous B.C.
Typical B.C.
DirichletNeumannRobinSpecial B.C. case: a = 0, b = r0After Applying Final B.C.
AME 60634 Int. Heat Trans.D. B. Go # Cylindrical Sturm-LiouvilleKakac & YennerHeat Conduction, 3rd Ed.
AME 60634 Int. Heat Trans.D. B. Go # Inhomogeneous BC to Homogeneous BC
+=
+AME 60634 Int. Heat Trans.D. B. Go #