Integral transform solutions of diffusion problems with nonlinear equation coefficients

Serfaty, Ricardo; Cotta, Renato M.

doi:10.1016/0735-1933(90)90030-n

Cited by 43 publications

(16 citation statements)

References 6 publications

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“…The GITT has been successfully applied to various classes of nonlinear convection-diffusion problems and is fully documented in different sources (Cotta, 1990;Serfaty and Cotta, 1990;Cotta, 1993;Cotta, 1994;Cotta and Mikhailov, 2006;Ribeiro et al, 2002;Knupp et al, 2012;Knupp et al, 2014).…”

Section: Solution Methodologymentioning

confidence: 99%

“…Therefore, it is necessary to use numerical or numerical-analytical methods to solve the related partial differential systems. In this work, the Generalized Integral Transform Technique (GITT) (Cotta, 1990;Serfaty and Cotta, 1990;Cotta, 1993;Cotta, 1994;Cotta and Mikhailov, 2006) is used to solve the nonlinear mathematical model for mass transfer in biodiesel synthesis occurring in microreactors, offering a robust error controlled solution within a low computational cost. This approach combines analytical eigenfunction expansions with the numerical solution of the ordinary differential equations for the integral transformed potentials.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mass transfer simulation of biodiesel synthesis in microreactors

Pontes

Chen

Naveira-Cotta

et al. 2016

Computers & Chemical Engineering

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Section: Solution Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mass transfer simulation of biodiesel synthesis in microreactors

Pontes

Chen

Naveira-Cotta

et al. 2016

Computers & Chemical Engineering

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“…iro et al, 2009;Cotta and Mikhailov, 1993;Cotta, 1994;Serfaty and Cotta, 1990;Naveira et al, 2007) and with the aid of Eqs. (5.10) and (5.11), Eq.…”

Section: Problem Solutionmentioning

confidence: 99%

“…The advantage of using the integral transform techniques is that it provides a systematic and straight-forward approach to the solution of a certain class of heat equations (Monteiro et al, 2009;Cotta and Mikhailov, 1993;Cotta, 1994;Serfaty and Cotta, 1990;Naveira et al, 2007). The method is particularly suitable for the solution of both homogeneous and nonhomogeneous boundary value problems of heat conduction.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

Helal

2012

Journal of King Saud University - Science

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A method of solving heat conduction problems in multilayered spherical media is presented; it is based on producing an alternative formulation in which the inner layer of the composite sphere is lumped and the transient temperature distribution in the outer layer is obtained, in this, the nonlinear boundary conditions are treated as a source. The temperature distribution of the alternative formulation is then solved analytically. Different parametric studies are worked out and plotted to compare the two formulations for different values of Biot number and different thermal characteristic ratio with those obtained from a numerical solution developed using an explicit finite difference method, and to find the limiting criterion where breakdown of the approximation occurs.

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“…Other investigators (Hays and Curd, 1968;Mastanaiah and Muthunayagam, 1975;Mehta, 1977;Serfaty and Cotta, 1990) developed conduction models with variable k (linear dependence on temperature) for various systems but they did not validate their models with experimental data. To account for temperaturedependent physical properties of material, Olsson (1970) and Aziz and Benzies (1976) suggested the use of a perturbation method for linearization of the nonlinear heat transfer equation.…”

Section: Introductionmentioning

confidence: 99%

An experimental and theoretical study of the nonlinear heat conduction in dry porous media

Pourhashemi

Hao

Chawla

1999

Int. J. Energy Res.

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Heat transfer in porous media is important in various engineering fields, including contaminated soil incineration. Most heat transfer models are theoretical in nature. Consequently, this study was undertaken to perform both theoretical and experimental studies of heat transfer in two different sand matrices. A mathematical model based on Fourier's law of heat conduction for a one‐dimensional system with the variable thermal conductivity was developed. The experimental part included heating sand samples placed in a small reactor within an infrared furnace. The transient temperature profiles of the sand layers were monitored by thermocouples. The bulk thermal conductivity was estimated to be linearly proportional to the temperature. The temperature profiles predicted by the model of heat conduction with a variable bulk thermal conductivity was compared by the observed temperatures in Quartz and Sea sands matrices up to 1300 K. Copyright © 1999 John Wiley & Sons, Ltd.

show abstract

Integral transform solutions of diffusion problems with nonlinear equation coefficients

Cited by 43 publications

References 6 publications

Mass transfer simulation of biodiesel synthesis in microreactors

Mass transfer simulation of biodiesel synthesis in microreactors

Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

An experimental and theoretical study of the nonlinear heat conduction in dry porous media

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