Formation and dispersion of an electrolyte film on an ice electrode melting as a result of Joule heat evolution

Григорьев, А. И.; Морозов, В. В.; Shiryaeva, S. O.

doi:10.1134/1.1514801

Cited by 3 publications

(5 citation statements)

References 7 publications

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“…We can define the same transformations (10), (11) and (14) as were done for the previous problem, and we obtain (15)- (19) and…”

Section: Solution Of the Free Boundary Problem With A Heat Flux Condimentioning

confidence: 98%

“…(23) has a unique solution λ > 0. We invert relations (14), (10) and (11) in order to obtain an explicit solution of problem (1)-(5), (7)-(9) with the source terms g j defined by (3). 2 Remark 1.…”

Section: Theorem 1 Equationmentioning

confidence: 99%

“…Bhattacharya et al [3], Carslaw, Jaeger [6], Feng [9], Grigor'ev et al [11], Mercado et al [15], Ratanadecho et al [17], Ward [23]. In Scott [20] there is a mathematical model for sublimation-dehydration with volumetric heating of a particular exponential type from which analytical solutions for dimensionless temperature, vapor concentration, and pressure were obtained for two different temperature boundary conditions.…”

Section: Introductionmentioning

confidence: 98%

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Explicit solutions for a two-phase unidimensional Lamé–Clapeyron–Stefan problem with source terms in both phases

Briozzo

Natale

Tarzia

2007

Journal of Mathematical Analysis and Applications

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A two-phase Stefan problem with heat source terms of a general similarity type in both liquid and solid phases for a semi-infinite phase-change material is studied. We assume the initial temperature is a negative constant and we consider two different boundary conditions at the fixed face x = 0, a constant temperature or a heat flux of the form −q 0 / √ t (q 0 > 0). The internal heat source functions are given byare functions with appropriate regularity properties, ρ is the mass density, l is the fusion latent heat by unit of mass, a 2 j is the diffusion coefficient, x is the spatial variable and t is the temporal variable. We obtain for both problems explicit solutions with a restriction for data only for the second boundary conditions on x = 0. Moreover, the equivalence of the two free boundary problems is also proved. We generalize the solution obtained in [J.L. Menaldi, D.A. Tarzia, Generalized Lamé-Clapeyron solution for a one-phase source Stefan problem, Comput. Appl. Math. 12 (2) (1993) 123-142] for the one-phase Stefan problem. Finally, a particular case where β j (j = 1, 2) are of exponential type given by β j (x) = exp(−(x + d j ) 2 ) with x and d j ∈ R is also studied in details for both boundary temperature conditions at x = 0. This type of heat source terms is important through the use of microwave energy following [E.P. Scott, An analytical solution and sensitivity study of sublimation-dehydration within a porous medium with volumetric heating, J. Heat Transfer 116 (1994) 686-693]. We obtain a unique solution of the similarity type for any data when a temperature boundary condition at the fixed face x = 0 is considered; a similar result is obtained for a heat flux condition imposed on x = 0 if an inequality for parameter q 0 is satisfied.

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“…We can define the same transformations (10), (11) and (14) as were done for the previous problem, and we obtain (15)- (19) and…”

Section: Solution Of the Free Boundary Problem With A Heat Flux Condimentioning

confidence: 98%

Section: Theorem 1 Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Explicit solutions for a two-phase unidimensional Lamé–Clapeyron–Stefan problem with source terms in both phases

Briozzo

Natale

Tarzia

2007

Journal of Mathematical Analysis and Applications

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“…Substituting expansions (7) and (8) into the set of boundary and initial conditions (2)-(6) with regard to (9) and (10) and collecting terms of the same orders of smallness in ε, we come to a set of linear boundary value problems in functions ξ (m) (ϑ, t), ψ (m) (r, t), and Φ (m) (r, t). These equations are rather easy to solve, although the solution is fairly cumbersome.…”

Section: Electrical Field Pressurementioning

confidence: 99%

“…Analysis of the linear and nonlinear oscillations of the charged surface of an incompressible conducting liquid layer covering a solid core was repeatedly con ducted under various complicated physical conditions as applied to the problems of thunderstorm electricity [1][2][3][4][5][6] and analytical instrument making [7,8]. In some of previous investigations, the possibility of inter nal nonlinear resonance energy exchange between the oscillation modes was noted (see, for example, [6]).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

2012

Self Cite

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Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscilla tions and behind energy transfer between the modes both in degenerate and in secondary combination reso nances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.

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A numerical and experimental investigation of the modelling of microwave melting of frozen packed beds using a rectangular wave guide

Ratanadecho

Aoki

Akahori

2001

International Communications in Heat and Mass Transfer

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Formation and dispersion of an electrolyte film on an ice electrode melting as a result of Joule heat evolution

Cited by 3 publications

References 7 publications

Explicit solutions for a two-phase unidimensional Lamé–Clapeyron–Stefan problem with source terms in both phases

Explicit solutions for a two-phase unidimensional Lamé–Clapeyron–Stefan problem with source terms in both phases

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

A numerical and experimental investigation of the modelling of microwave melting of frozen packed beds using a rectangular wave guide

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