An Accurate and Efficient Evaluation of Planar Multilayered Green's Functions Using Modified Fast Hankel Transform Method

2011 ◽  
Vol 59 (11) ◽  
pp. 2798-2807 ◽  
Author(s):  
Joshua Le-Wei Li ◽  
Ping-Ping Ding ◽  
Said Zouhdi ◽  
Swee-Ping Yeo
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Hankel Transform ◽  
Transform Method

Transient Temperature Fields in Crossflow Heat Exchangers With Finite Wall Capacitance

1988 ◽  
Vol 110 (1) ◽  
pp. 49-53 ◽  
Author(s):  
M. Spiga ◽  
G. Spiga
Keyword(s):  
Heat Capacity ◽  
Heat Exchangers ◽  
Green's Functions ◽  
Green’S Functions ◽  
Temperature Fields ◽  
Transient Temperature ◽  
Inlet Temperature ◽  
Transform Method ◽  
Transfer Resistance ◽  
Primary Fluid

Solutions are provided in nondimensional form for the transient analysis of direct-transfer crossflow heat exchangers, with both fluids unmixed and finite wall heat capacity. The two-dimensional transient temperature distributions of core wall and both fluids are determined by analytical methods for any externally applied variation of the primary fluid inlet temperature. The general solutions are derived by the local energy balance equations, and are presented as simple integrals of the Green’s functions, which represent the pulse response following a deltalike perturbation in the inlet temperature of the primary fluid, and are deduced using the Laplace transform method. The Green’s functions are expressed as integrals of modified Bessel functions, in terms of the heat capacity ratios, number of transfer units, heat transfer resistance and flow capacitance ratios.

scholarly journals Electromagnetic modeling of three‐dimensional bodies in layered earths using integral equations

Geophysics ◽  
1984 ◽  
Vol 49 (1) ◽  
pp. 60-74 ◽  
Author(s):  
Philip E. Wannamaker ◽  
Gerald W. Hohmann ◽  
William A. SanFilipo
Keyword(s):  
Integral Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Computation Time ◽  
Vector Current ◽  
Hankel Transform ◽  
Transverse Magnetic ◽  
Electromagnetic Modeling ◽  
Method Of Integral Equations

We have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three‐dimensional bodies in layered earths. The inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions. A matrix equation is constructed using the electric tensor Green’s function appropriate to a layered earth, and it is solved for the vector current in each cell. Subsequently, scattered fields are found by integrating electric and magnetic tensor Green’s functions over the scattering currents. Efficient evaluation of the tensor Green’s functions is a major consideration in reducing computation time. We find that tabulation and interpolation of the six electric and five magnetic Hankel transforms defining the secondary Green’s functions is preferable to any direct Hankel transform calculation using linear filters. A comparison of responses over elongate three‐dimensional (3-D) bodies with responses over two‐dimensional (2-D) bodies of identical cross‐section using plane wave incident fields is the only check available on our solution. Agreement is excellent; however, the length that a 3-D body must have before departures between 2-D transverse electric and corresponding 3-D signatures are insignificant depends strongly on the layering. The 2-D transverse magnetic and corresponding 3-D calculations agree closely regardless of the layered host.

The Full-Space Elastodynamic Green’s Functions for Time-Harmonic Radial and Axial Ring Sources in a Homogeneous Isotropic Medium

1999 ◽  
Vol 66 (3) ◽  
pp. 639-645
Author(s):  
Y. Lu
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Hankel Transform ◽  
Legendre Functions ◽  
Linear Elastic ◽  
Time Harmonic ◽  
Stress Components ◽  
Axial Ring ◽  
Logarithmic Singularities ◽  
Half Degree

The elastodynamic Green’s functions for time-harmonic radial and axial ring sources in a homogeneous, isotropic, linear elastic full-space medium are derived using the Fourier-Hankel transform. The Green’s functions are found to have the same logarithmic singularities as the Legendre functions of positive and negative half-degree of the second kind. As the frequency approaches zero, the Green’s functions approach the corresponding elastostatic Green’s functions. The far-field displacement and stress components are also derived.

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