Self-similar analysis of the time-dependent compressible and incompressible boundary layers including heat conduction

Barna, Imre Ferenc; Hriczó, Krisztián; Bognár, Gabriella; Mátyás, László

doi:10.1007/s10973-022-11574-3

Cited by 5 publications

(2 citation statements)

References 41 publications

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“…(1). Therefore this Ansatz is original among others and can help to find physically relevant disperse solutions to other physical systems like the Bénard convection problem [19] or a heated boundary layer flow [20].…”

Section: Cartesian Casementioning

confidence: 98%

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Barna,

Mátyás

2023

Preprint

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In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

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Section: Cartesian Casementioning

confidence: 98%

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Barna,

Mátyás

2023

Preprint

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“…where f (η) is the shape function with the reduced variable η, the two self-similar exponents α and β are responsible for the decay and spreading of the solutions if both have non-negative values. In the last decades we generalized this kind of Ansatz to multiple spatial dimension and applied it to the Rayleigh-Bénard convection problems [35,36] or to the heated boundary layer equations [37].…”

Section: Self-similar Analysismentioning

confidence: 99%

Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations

Barna

Mátyás

2022

Mathematics

Self Cite

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We study the diffusion equation with an appropriate change of variables. This equation is, in general, a partial differential equation (PDE). With the self-similar and related Ansatz, we transform the PDE of diffusion to an ordinary differential equation. The solutions of the PDE belong to a family of functions which are presented for the case of infinite horizon. In the presentation, we accentuate the physically reasonable solutions. We also study time-dependent diffusion phenomena, where the spreading may vary in time. To describe the process, we consider time-dependent diffusion coefficients. The obtained analytic solutions all can be expressed with Kummer’s functions.

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The impact of the heat source/sink on triple component magneto-convection in superposed porous and fluid system

Manjunatha,

Yellamma,

Sumithra

et al. 2023

Mod. Phys. Lett. B

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Effective thermal management is necessary for electronic devices to prevent overheating and guarantee optimal performance. The development of cutting-edge cooling methods may be aided by research into Triple Component Magneto-Convection (TCMC) in a superposed porous and fluid system with heat source/sink effects. It is feasible to improve the thermal management of electronic parts and systems by managing convective heat transfer via the optimization of heat source/sink spot and design. An investigation into the issue of TCMC in a horizontally infinite composite layer is presented in this work. The investigation takes into account of a consistent heat source or sinks in both layers as well as a uniform vertical magnetic field. The upper enclosure of the fluid layer is either free and adiabatic or isothermal, while the bottom enclosure of the porous layer is rigid and adiabatic. By employing normal mode analysis, the resulting system of ordinary differential equations is solved in closed form to obtain the eigenvalue, specifically the thermal Marangoni number (tMn). The investigation focuses on two different combinations of thermal boundaries: (i) adiabatic–adiabatic and (ii) adiabatic–isothermal. During the inquiry, the influence of major elements on TCMC in connection to the depth ratio is fully investigated. This work aims at understanding the stability of the superposed porous-fluid system using adiabatic and isothermal boundaries in the presence of a heat source or sink.

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Self-similar analysis of the time-dependent compressible and incompressible boundary layers including heat conduction

Cited by 5 publications

References 41 publications

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations

The impact of the heat source/sink on triple component magneto-convection in superposed porous and fluid system

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