Error Analysis and Improved Formulations for Extended Surfaces

Improved lumped-differential formulations and hybrid solution methods for drying in porous media

“…Different levels of approximation in such mixed lumped-differential formulations can be used, starting from the plain and classical lumped system analysis, towards improved formulations, obtained through Hermite-type approximations for integrals [1,2]. Such approach has been already exploited in different heat and fluid flow problems [3][4][5][6][7][8][9][10], including phase change problems, extended surfaces (fins), anisotropic heat conduction, heat exchangers analysis, Navier-Stokes equations and drying problems themselves, and shall be reviewed within this section.…”

“…First, a problem reformulation strategy is reviewed, based on Hermite integration schemes [1,2] and known as the coupled integral equations approach (CIEA) [3][4][5][6][7][8][9][10], which offers improved lumped-differential formulations in different classes of problems, in comparison with classical lumping schemes, allowing for a reduction on the number of independent variables to be considered in specific formulations, thus reducing simulation costs.…”

Hybrid methods: the generalizaed integral transform technique

“…The potential of the integral transform approach in dealing with different classes of nonlinear problems in heat transfer is now briefly illustrated. The examples selected include diffusion in irregular geometries [12][13][14][15][16][17][18], here related to fin calculations, diffusion with coupled equations [19][20][21][22][23][24], as formulated by the Luikov equations of drying, convection-diffusion in the boundary layer formulation [25][26][27][28][29], demonstrated with a mixed convection example, and convection-diffusion in the full Navier-Stokes formulation [30][31][32][33][34][35][36][37][38][39][40], represented by natural convection in enclosures. Additional details on the application of the method can be readily obtained from the original papers that correspond to these topics, and/or from the compilations in [2,10], where several other topics not presented here are also discussed.…”

“…The temperature at the fin base is assumed uniform and heat losses through the fin tip are disregarded. In dimensionless form, the problem formulation is given as [12]: where the various dimensionless groups are defined by…”