The variational method for the solution of the combined heat and mass transfer problems

Glazunov, Yu.T.

doi:10.1016/s0017-9310(83)80152-5

Cited by 12 publications

(3 citation statements)

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“…Scientists Dimova et al (2006) and Glazunov (1983) used a variational method for solving the differential diffusion equation and developed the following solution by the Equation 11 taking into account the natural salinity of fish:…”

Section: Solution Of the Differential Diffusion Equationmentioning

confidence: 99%

Mathematical model and dependence of fish salting process duration to a given salt concentration

Khomiakova

2023

Braz. J. Food Technol.

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The purpose of this scientific work is to build a diffusion model based on Fick's second law. The model is designed to determine the salting process duration and salt concentration in the fish muscle tissue (Atlantic herring). The method of photon correlation spectroscopy (PCS) by a certified Photocor FC correlator device was used. The device operating principle is based on Rayleigh radiation scattering, which allows us to directly determine the effective diffusion coefficients, taking into account all factors, without singling out a specific one. This research presents the spatiotemporal distributions of effective diffusion coefficients in a herring sample during brine salting. Formulas for calculating the salting duration and the average salt concentration in the thickness of fish muscle tissue are presented, and the time of reaching the sample center by salt and the average salt concentration in it were estimated. These parameters could be widely used for the finished product quality and the technical and economic indicators of production improvement. The average effective diffusion coefficient De through the sample thickness was used for calculation. The salting duration for a 30 mm thick herring sample with a saturated salt solution was 8.74 hours until the average salinity of the sample was 4.7%.

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Section: Solution Of the Differential Diffusion Equationmentioning

confidence: 99%

Mathematical model and dependence of fish salting process duration to a given salt concentration

Khomiakova

2023

Braz. J. Food Technol.

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“…The variational principles for the flow of a viscous fluid (with different limitations of applicability) are proposed in [105][106][107][108][109][110], including for turbulent flows [111][112][113][114]. Some variants of the variational principles for diffusion and heat conduction are given in [115][116][117][118]. The variational estimates for the limit intensity of turbulent transport are obtained in [119,120].…”

Section: Extremal Principles For Dissipative Systems Not Directly Rel...mentioning

confidence: 99%

On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review

Donskoy

2022

Energies

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A brief review of the development of ideas on extremal principles in the theory of heat and mass transfer processes (including those in reacting media) is given. The extremal principles of non-equilibrium thermodynamics are critically examined. Examples are shown in which the mechanical use of entropy production-based principles turns out to be inefficient and even contradictory. The main problem of extremal principles in the theory of irreversible processes is the impossibility of their generalization, often even within the framework of a class of problems. Alternative extremal formulations are considered: variational principles for heat and mass transfer equations and other dissipative systems. Several extremal principles are singled out, which make it possible to simplify the numerical solution of the initial equations. Criteria are proposed that allow one to classify extremal principles according to their areas of applicability. Possible directions for further research in the search for extremal principles in the theory of irreversible processes are given.

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“…Many approximate as well as numerical solutions have been proposed to solve the nonlinear Luikov system including variations of classical methods such as the Finite Element method and the Finite Differences method. Some of them are listed here, including a particular two dimensional problem: Comini and Lewis (1976), Thomas et al (1980), Glazunov (1983), Lobo (1988), Ferguson and Lewis (1991), and Rai and Pandey (1976). Lobo (1988) and Ribeiro (1995) also studied the case of radiation heat exchange at the porous medium boundary surface.…”

Section: Introductionmentioning

confidence: 99%

On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

Lobo

2002

Computational Mechanics

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A three-time-level scheme is employed to obtain numerical solutions of heat and mass transfer potentials for the nonlinear Luikov system. Relative errors are examined when the numerical solutions are compared to the analytical solutions for a single layer linear problem using different finite difference techniques. As a final example, comparisons also are made when the numerical schemes are used to solve a two-layer multi-region nonlinear approach, considering that the thermal conductivity and mass conductivity of the material are dependent on temperature and moisture transfer potential respectively. List of symbolsBi m Biot number for mass transfer, a m L=k m Bi q Biot number for heat transfer, a q L=k q Fo Fourier number, a q s=L 2 Ki m dimensionless mass flux, Lw m =k m / / Ki q dimensionless heat flux, Lw q =k q t t Ko Kossovitch number, qc m /=c q t Lu Luikov number, a m =a q Pn Posnov number, d t t=c m / / r r dimensionless coordinate, r=L e phase change criterion, where, for the boundary conditions of the second kind t t ¼ t 0 ; / / ¼ / 0 and for the boundary conditions of the third kind t t ¼ t s À t 0 ;/ / ¼ / 0 À / Ã a m diffusion coefficient of moisture, m 2 /s a q thermal diffusivity coefficient, m 2 /s c m specific isothermal mass capacity, 1/ M c q specific heat capacity, kJ/Kg C L half thickness of the layer, m q specific heat of evaporation, kJ/kg t temperature, C r coordinate perpendicular to the surface, m a m mass transfer coefficient, kg/m 2 s M a q heat transfer coefficient, kJ/m 2 s C d thermal gradient coefficient, 1/ C k m moisture conductivity, kg/m s M k q thermal conductivity, kJ/m s C s time, s / moisture transfer potential, M w m mass flux, kg/m 2 s w q heat flux, kg/m 2 s Subscripts 0 initial s surrounds or surface Ã in equilibrium with surroundings j region i space node Superscript n geometry h time level IntroductionThere is a continuously increasing activity in the field of heat and mass transfer in capillary porous media due to its wide research as well industrial applications. Besides its applications as ground water pollution, heat transfer in the ground, drying processes, and multiphase flow under nonisothermal conditions, it is also been used in space research, especially in devices for liquid and energy transfer (heat pipes, heat exchangers, insulation of highly conducting wire nets, etc.) due to the fact that the performance of capillary porous materials does not depend on a gravitational field (Pandey et al., 1999). Because of the complexities of the mechanism involved, it is very difficult to model the process. The phenomena appropriate for moisture, pressure and enthalpy distributions are coupled. The transport of associated matter of all phases and the transfer of enthalpy must be considered simultaneously. Luikov (1965Luikov ( , 1966Luikov ( , 1975) developed a uniquely model for a simultaneous heat and moisture transfer in capillary porous materials, which is based on non-equilibrium thermodynamics of irreversible transfer processes. This model is applicable for both ...

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The variational method for the solution of the combined heat and mass transfer problems

Cited by 12 publications

References 2 publications

Mathematical model and dependence of fish salting process duration to a given salt concentration

Mathematical model and dependence of fish salting process duration to a given salt concentration

On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review

On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

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