Two dimensional heat conduction in graded materials using conformal mapping.

*(English)*Zbl 1016.65070Summary: Heat conduction through non-homogeneous materials has numerous applications, since many of the man-made materials that are used in various disciplines such as aerospace, construction, electronics, etc., are composites with carefully manufactured properties that yield desirable thermal characteristics. To that end, fundamental solutions for the heterogeneous heat conduction problem in two dimensions are derived in this work by employing a conformal mapping technique. These functions, besides being useful in their own right, can also be used within the context of integral equation formulations for the solution of boundary-value problems. Finally, numerical examples for a material described by a family of radially symmetric conductivity are given as an illustration of the proposed method.

##### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

35K05 | Heat equation |

30C30 | Schwarz-Christoffel-type mappings |

##### Keywords:

conformal mapping; Green’s function; heat conduction; inhomogeneous media; variable conductivity; integral equation method; numerical examples
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\textit{R. P. Shaw} and \textit{G. D. Manolis}, Commun. Numer. Methods Eng. 19, No. 3, 215--221 (2003; Zbl 1016.65070)

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