Exact solutions of nonlinear heat- and mass-transfer equations
The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions of one-, two-, and three-dimensional heat equations are obtained. Anisotropic media with a nonlinear heat source of general form are consider...
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| Published in: | Theoretical foundations of chemical engineering Vol. 34; no. 5; pp. 403 - 415 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Springer Nature B.V
2000
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| Abstract | The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions of one-, two-, and three-dimensional heat equations are obtained. Anisotropic media with a nonlinear heat source of general form are considered for the case in which the main thermal diffusivities show a power or an exponential dependence on the spatial coordinates. Equations with a logarithmic heat source are analyzed in detail. The results obtained are applied to the problem of thermal explosion in an anisotropic medium. |
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| AbstractList | The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions of one-, two-, and three-dimensional heat equations are obtained. Anisotropic media with a nonlinear heat source of general form are considered for the case in which the main thermal diffusivities show a power or an exponential dependence on the spatial coordinates. Equations with a logarithmic heat source are analyzed in detail. The results obtained are applied to the problem of thermal explosion in an anisotropic medium. |
| Author | Zhurov, A. I. Polyanin, A. D. Vyaz’min, A. V. |
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| CitedBy_id | crossref_primary_10_1016_j_na_2010_03_007 crossref_primary_10_1016_S0017_9310_02_00027_3 crossref_primary_10_1155_2018_7179160 crossref_primary_10_1016_j_camwa_2014_10_015 crossref_primary_10_1134_S0040579513020061 crossref_primary_10_1002_ppap_201000021 crossref_primary_10_1016_j_apm_2012_09_012 crossref_primary_10_1142_S0129183118500547 crossref_primary_10_1007_s00009_016_0827_0 crossref_primary_10_1007_s00707_017_1829_0 crossref_primary_10_1007_s00033_015_0549_3 crossref_primary_10_3390_axioms12040323 crossref_primary_10_1016_j_ijsolstr_2018_12_030 crossref_primary_10_1016_j_imu_2023_101279 crossref_primary_10_1016_j_heliyon_2022_e12774 |
| Cites_doi | 10.1115/1.3408821 |
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| Copyright | MAIK Nauka/Interperiodica 2000. |
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| References | D.A. Frank-Kamenetskii (BF02827383_CR14) 1987 L.G. Loitsyanskii (BF02827383_CR19) 1959 V.A. Galaktionov (BF02827383_CR26) 1989; 29 H.S. Carslaw (BF02827383_CR1) 1959 (BF02827383_CR25) 1994 L. Robillard (BF02827383_CR21) 1971; 38 V.A. Galaktionov (BF02827383_CR29) 1995; 31 R.C. Reid (BF02827383_CR10) 1977 H. Schlichting (BF02827383_CR20) 1968 Ya.B. Zel’dovich (BF02827383_CR4) 1980 G.I. Barenblatt (BF02827383_CR16) 1978 S. Bretsznajder (BF02827383_CR8) 1962 BF02827383_CR31 Yu.P. Gupalo (BF02827383_CR5) 1985 L.V. Ovsyanikov (BF02827383_CR18) 1978 (BF02827383_CR13) 1963 A.D. Polyanin (BF02827383_CR28) 1998 R. Clift (BF02827383_CR7) 1978 T.K. Sherwood (BF02827383_CR11) 1975 L.I. Sedov (BF02827383_CR17) 1972 V.A. Dorodnitsyn (BF02827383_CR23) 1982; 22 A.I. Vol’pert (BF02827383_CR32) 1975 V.F. Zaitsev (BF02827383_CR24) 1996 S.S. Kutateladze (BF02827383_CR2) 1979 V.V. Dil’man (BF02827383_CR9) 1988 A.M. Kutepov (BF02827383_CR12) 1996 V.G. Levich (BF02827383_CR6) 1959 R. Kersner (BF02827383_CR30) 1978; 32 A.A. Samarskii (BF02827383_CR22) 1963; 3 (BF02827383_CR27) 1980 A.V. Lykov (BF02827383_CR3) 1967 A.A. Samarskii (BF02827383_CR15) 1987 |
| References_xml | – volume: 38 start-page: 550 issue: 2 year: 1971 ident: BF02827383_CR21 publication-title: J. Appl. Mech. doi: 10.1115/1.3408821 contributor: fullname: L. Robillard – volume-title: Metody model’nykh uravnenii i analogii (Model Equation and Analog Methods) year: 1988 ident: BF02827383_CR9 contributor: fullname: V.V. Dil’man – volume-title: Gruppovoi analiz differentsial’nykh uravnenii (Group Analysis of Differential Equations) year: 1978 ident: BF02827383_CR18 contributor: fullname: L.V. Ovsyanikov – volume-title: Spravochnik po differentsial’nym uravneniyam s chastnymi proizvodnymi (tochnye resheniya) (Handbook of Partial Differential Equations: Exact Solutions) year: 1996 ident: BF02827383_CR24 contributor: fullname: V.F. Zaitsev – volume: 31 start-page: 253 issue: 2 year: 1995 ident: BF02827383_CR29 publication-title: Differentsial’nye Uravneniya contributor: fullname: V.A. Galaktionov – volume-title: Teoriya teploprovodnosti (Heat Conduction Theory) year: 1967 ident: BF02827383_CR3 contributor: fullname: A.V. Lykov – volume-title: Bubbles, Drops and Particles year: 1978 ident: BF02827383_CR7 contributor: fullname: R. Clift – volume-title: Boundary-Layer Theory year: 1968 ident: BF02827383_CR20 contributor: fullname: H. Schlichting – volume-title: Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii (Quasilinear Parabolic Equations: Problems with Sharpening) year: 1987 ident: BF02827383_CR15 contributor: fullname: A.A. Samarskii – volume-title: Podobie, avtomodel’nost’, promezhutochnaya asimptotika (Similarity, Self-similarity, and Intermediate Asymptotics) year: 1978 ident: BF02827383_CR16 contributor: fullname: G.I. Barenblatt – volume-title: CRC Handbook of Lie Group to Differential Equations year: 1994 ident: BF02827383_CR25 – volume-title: Conduction of Heat in Solids year: 1959 ident: BF02827383_CR1 contributor: fullname: H.S. Carslaw – volume-title: Osnovy teorii teploperedachi (Fundamentals of the Heat-Transfer Theory) year: 1979 ident: BF02827383_CR2 contributor: fullname: S.S. Kutateladze – volume-title: Diffuziya i teploperedacha v khimicheskoi kinetike (Diffusion and Heat Transfer in Chemical Kinetics) year: 1987 ident: BF02827383_CR14 contributor: fullname: D.A. Frank-Kamenetskii – volume: 3 start-page: 702 issue: 4 year: 1963 ident: BF02827383_CR22 publication-title: Zh. Vychisl. Mat. Mat. Fiz. contributor: fullname: A.A. Samarskii – volume-title: Metody podobiya i razmernosti v mekhanike (Similarity and Dimensionality Methods in Mechanics) year: 1972 ident: BF02827383_CR17 contributor: fullname: L.I. Sedov – volume: 32 start-page: 301 issue: 3/4 year: 1978 ident: BF02827383_CR30 publication-title: Acta Math. Acad. Sci. Hung. contributor: fullname: R. Kersner – volume-title: Analiz v klassakh razryvnykh funktsii i uravneniya matematicheskoi fiziki (Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics) year: 1975 ident: BF02827383_CR32 contributor: fullname: A.I. Vol’pert – volume-title: Matematicheskaya teoriya goreniya i vzryva (Mathematical Theory of Combustion and Explosion) year: 1980 ident: BF02827383_CR4 contributor: fullname: Ya.B. Zel’dovich – volume-title: The Properties of Gases and Liquids year: 1977 ident: BF02827383_CR10 contributor: fullname: R.C. Reid – volume-title: Wlasności gazów i cieczy year: 1962 ident: BF02827383_CR8 contributor: fullname: S. Bretsznajder – volume-title: Khimicheskaya gidrodinamika (Chemical Fluid Dynamics) year: 1996 ident: BF02827383_CR12 contributor: fullname: A.M. Kutepov – volume: 29 start-page: 497 issue: 4 year: 1989 ident: BF02827383_CR26 publication-title: Zh. Vychisl. Mat. Mat. Fiz. contributor: fullname: V.A. Galaktionov – volume-title: Fiziko-khimicheskaya gidrodinamika (Physicochemical Fluid Dynamics) year: 1959 ident: BF02827383_CR6 contributor: fullname: V.G. Levich – volume-title: Solitons year: 1980 ident: BF02827383_CR27 – volume-title: Laminarnyi pogranichnyi sloi (Laminar Boundary Layer) year: 1959 ident: BF02827383_CR19 contributor: fullname: L.G. Loitsyanskii – ident: BF02827383_CR31 – volume-title: Spravochnik po tochnym resheniyam uravnenii teploi massoperenosa (Handbook of Exact Solutions to Heat- and Mass-Transfer Equations) year: 1998 ident: BF02827383_CR28 contributor: fullname: A.D. Polyanin – volume-title: Massoteploobmen reagiruyushchikh chastits s potokom (Mass and Heat Transfer between Reactive Particles and Flow) year: 1985 ident: BF02827383_CR5 contributor: fullname: Yu.P. Gupalo – volume-title: Mass Transfer year: 1975 ident: BF02827383_CR11 contributor: fullname: T.K. Sherwood – volume: 22 start-page: 1393 issue: 6 year: 1982 ident: BF02827383_CR23 publication-title: Zh. Vychisl. Mat. Mat. Fiz. contributor: fullname: V.A. Dorodnitsyn – volume-title: Chemical Engineer’s Handbook year: 1963 ident: BF02827383_CR13 |
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| SubjectTerms | Anisotropic media Anisotropy Exact solutions Mass transfer Mathematical analysis Thermodynamics |
| Title | Exact solutions of nonlinear heat- and mass-transfer equations |
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