Fast transient thermal analysis of Fourier and non-Fourier heat conduction

Loh, J. S.; Azid, Ishak Abdul; Seetharamu, K.N.; Quadir, G.A.

doi:10.1016/j.ijheatmasstransfer.2007.03.021

Cited by 28 publications

(14 citation statements)

References 16 publications

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“…. , N ), it is convenient to express solution (19) in terms of the polar coordinates (r k , k ). This can be done with the aid of the following addition theorem for the solutions of the modified Helmholtz equation (10) [31]:…”

Section: Superposition Solutionmentioning

confidence: 99%

“…Substituting expressions (20) (for l = k) and (23) (for l = k) into Equation (19),T (x, s) is expressed in coordinates (r k , k ) as follows:…”

Section: Superposition Solutionmentioning

confidence: 99%

“…. , M. The transformed temperatureT (x, s) is obtained from Equations (19), (21) and (35), and the transformed temperatureT in k (x, s) is obtained from Equation (34). The transformed boundary fluxesĤ k (x, s) andĤ in k (x, s) are then obtained from Equation (15) by computing the involved derivatives.…”

Section: Computation Of the Transformed Temperature And Fluxmentioning

confidence: 99%

“…Solution (19) for problem (ii) satisfies Equations (10) and (12) due to the linearity of the problem. The unknown coefficients X l n (s) in series (20) should be chosen such that the boundary conditions (13) and (14) are satisfied.…”

Section: Superposition Solutionmentioning

confidence: 99%

“…General-purpose numerical methods such as finite element and boundary element methods can be used, combined with either time-stepping (e.g. [16][17][18][19]) or Laplace transform (e.g. [20-22]) to treat the time dependency.…”

mentioning

confidence: 99%

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Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

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SUMMARYA two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two-and threedimensional problems demonstrates the effect of the dimensionality.

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Section: Superposition Solutionmentioning

confidence: 99%

“…Substituting expressions (20) (for l = k) and (23) (for l = k) into Equation (19),T (x, s) is expressed in coordinates (r k , k ) as follows:…”

Section: Superposition Solutionmentioning

confidence: 99%