Improved lumped-differential formulations in hyperbolic heat conduction

Approximate analytical methodology for calculating friction factors in flow through polygonal cross section ducts

“…Since its development, the CIEA has been applied to many problems. Among these studies, deserve mention the ones involving phase change [3], heat transfer in fins [4], heat exchangers [5,6], linear heat conduction [7], hyperbolic heat conduction [8], radiative cooling [9], ablation [10], drying [11], heat diffusion with temperaturedependent conductivity [12], and combined convectiveradiative cooling [13,14]. A very similar approach was also used in the work of Keshavarz and Taheri [15].…”

Integral transform solution for hyperbolic heat conduction in a finite slab

“…One may observe in Table 1 the excellent agreement between the results of the present GITT approach with the exact solution for Q(τ) = 0 and τ r = 0 for both Biot numbers considered, Bi = 0.1 and 1.0, as well as with the results from a Laplace transform method with numerical inversion (LTM) and the method of lines variant employing finite volumes for the spatial discretization and Gear's method for the time integration (FVGM). However, when Biot number is increased, the lumped-differential formulation H 1,1 / H 1,1 given by Reis et al [17] looses adherence with respect to the other fully local formulations of the hyperbolic heat conduction problem.…”

“…The numerical code was also validated with comparisons against the exact integral transform solution for the classical heat conduction problem (τ r = 0) and with the approximate formulation obtained with the coupled integral equations approach (CIEA) [32], employing the improved lumped-differential formulation represented by the formulae H 1,1 /H 1,1 [17]. Thus, the present results for the average temperature were compared with those from reference [17], for the situation Q(τ) = 0 and τ r = 10 − 5 .…”

“…The numerical code was also validated with comparisons against the exact integral transform solution for the classical heat conduction problem (τ r = 0) and with the approximate formulation obtained with the coupled integral equations approach (CIEA) [32], employing the improved lumped-differential formulation represented by the formulae H 1,1 /H 1,1 [17]. Thus, the present results for the average temperature were compared with those from reference [17], for the situation Q(τ) = 0 and τ r = 10 − 5 . One may observe in Table 1 the excellent agreement between the results of the present GITT approach with the exact solution for Q(τ) = 0 and τ r = 0 for both Biot numbers considered, Bi = 0.1 and 1.0, as well as with the results from a Laplace transform method with numerical inversion (LTM) and the method of lines variant employing finite volumes for the spatial discretization and Gear's method for the time integration (FVGM).…”

“…To overcome this limitation, Vernotte [1] and Cattaneo [2], based on the concept of heat transmission by waves, independently introduced an improvement of Fourier's law to describe problems involving high rates of temperature change, heat flow in an extremely short period of time or very low temperatures near absolute zero. Afterwards, a number of research contributions have been dedicated to the study of problems involving hyperbolic heat conduction [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”