{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T20:24:15Z","timestamp":1760646255236,"version":"3.41.2"},"reference-count":24,"publisher":"Emerald","issue":"7","license":[{"start":{"date-parts":[[2014,8,26]],"date-time":"2014-08-26T00:00:00Z","timestamp":1409011200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,8,26]]},"abstract":"<jats:sec>\n               <jats:title content-type=\"abstract-heading\">Purpose<\/jats:title>\n               <jats:p> \u2013 A number of works have been published in the scientific literature proposing the solution of heat diffusion problems by first transforming the relevant partial differential equation to the frequency domain. The purpose of this paper is to present a mesh-free strategy to assess transient heat propagation in the frequency domain, also allowing incorporating initial non-zero conditions. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title>\n               <jats:p> \u2013 The strategy followed here is based in Kansa's method, using the MQ RBF as a basis function. The resulting method is truly mesh-free, and does not require any domain or boundary integrals to be evaluated. The definition of good values for the free parameter of the MQ RBF is also addressed. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Findings<\/jats:title>\n               <jats:p> \u2013 The strategy was found to be accurate in the calculation of both frequency and time-domain responses. The time evolution of the temperature considering an initial non-uniform distribution of temperatures compared well with a standard time-marching algorithm, based on an implicit Crank-Nicholson implementation. It was possible to calculate frequency-dependent values for the free parameter of the radial basis function. <\/jats:p>\n            <\/jats:sec>\n            <jats:sec>\n               <jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title>\n               <jats:p> \u2013 As far as the authors are aware, previous implementations of the frequency domain heat transfer approach required domain integrals to be evaluated in order to implement non-zero initial conditions. This is totally avoided with the present formulation. Additionally, the method is truly mesh-free, accurate and does not require any element or background mesh to be defined.<\/jats:p>\n            <\/jats:sec>","DOI":"10.1108\/hff-11-2012-0258","type":"journal-article","created":{"date-parts":[[2014,11,10]],"date-time":"2014-11-10T07:47:32Z","timestamp":1415605652000},"page":"1437-1453","source":"Crossref","is-referenced-by-count":2,"title":["Formulation of Kansa's method in the frequency domain for the analysis of transient heat conduction"],"prefix":"10.1108","volume":"24","author":[{"given":"Luis","family":"Godinho","sequence":"first","affiliation":[]},{"given":"Fernando","family":"Branco","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2020122922360359900_b8","unstructured":"Ant\u00f3nio, J.\n               , \n                  Tadeu, A.\n               , \n                  Godinho, L.\n                and \n                  Sim\u00f5es, N.\n                (2005), \u201cBenchmark solutions for three-dimensional transient heat transfer in two-dimensional environments via the time Fourier transform\u201d, Computers, Materials, Continua, Vol. 2 No. 1, pp. 1-12."},{"key":"key2020122922360359900_b14","unstructured":"Atluri, S.N.\n                (2004), The Meshless Method (MLPG) for Domain & BIE Discretizations, Tech Science Press, Encino, CA."},{"key":"key2020122922360359900_b1","doi-asserted-by":"crossref","unstructured":"Chang, Y.P.\n               , \n                  Kang, C.S.\n                and \n                  Chen, D.J.\n                (1973), \u201cThe use of fundamental green functions for solution of problems of heat conduction in anisotropic media\u201d, Int. 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