Integral transform solution to the endometrial ablation problem

Abstract

Integral Transform Solution to the Endometrial Ablation Problem

Analysis of the influence of pellet-to-cladding gap on the transient heat transfer in nuclear fuel rods via the integral transform technique

“…The integral transform technique [11][12][13][14][15][16][17][18][19] is a wellknown methodology disseminated in the literature that analytically transforms the governing partial differential equation and its initial and boundary conditions into a set of ordinary differential equations suitable to being solved by a numerical method.…”

Solution of hyperbolic bioheat transfer problems by numerical green's functions: the ExGA-linear θ method

“…Among these, the Pennes' bioheat equation is frequently adopted in applications such as cancer hyperthermia therapies, cryosurgery, laser surgery, thermal diagnostics, skin burns and thermal comfort analysis. The literature reports a great deal of works on the numerical modelling of the parabolic Pennes equation considering different numerical techniques (Chan, 1992;Torvi and Dale, 1994;Liu and Xu, 2000;Dai, Yu and Nassar, 2004;Rubinsky, 2006;Presgrave, Guedes and Scofano Neto, 2009), e.g., finite difference, finite element and boundary element methods, each of them with its own advantages and disadvantages depending on the problem under consideration. However, there are some applications of extremely short time duration or at very low temperature (e.g., cryogenic surgery, laserinduced thermal damage, etc.)…”

Hybrid integral transforms analysis of the bioheat equation with variable properties

“…Nevertheless, the solution of the corresponding auxiliary eigenvalue problem [14] demands the use of computational methodologies, such as the Generalized Integral Transform Technique (GITT) [16e20]. In the present work we also make use of the GITT, which has already been successfully applied to the solution of bioheat problems with constant coefficients under Pennes' model [21]. However, a hybrid numericaleanalytical solution variant is here exploited so as to automatically handle any general functional form of the space variable coefficients, besides the possible nonlinear variation of the blood perfusion rates with temperature, especially during hyperthermia treatments.…”