Analytical Solutions of Temperature Distribution in a Rectangular Parallelepiped

Kumar, Dinesh; Ayant, Frédéric; Cesarano, Clemente

doi:10.3390/axioms11090488

Axioms

2022

DOI: 10.3390/axioms11090488

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Analytical Solutions of Temperature Distribution in a Rectangular Parallelepiped

Dinesh Kumar¹,

Frédéric Ayant²,

Clemente Cesarano

Abstract: In the present article, we give analytical solutions for temperature distribution in a rectangular parallelepiped with the help of a multivariable I-function. The results established in this paper are of a general character from which several known and new results can be deduced. We also give the special and particular cases of our main findings.

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2024

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Cited by 2 publications

References 6 publications

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Analytical results for a linear hardening elasto-plastic spring investigated via a hemivariational formulation

Placidi,

Misra,

Kandalaft

et al. 2024

Constructive Mathematical Analysis

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We investigate the linear hardening phenomena with a method that is not standard in the literature, i.e. with a hemivariational method. As a result, we do not introduce any flow rules, and the number of assumptions is reduced to the generalized variational principle with proper definition of a new set of kinematic descriptors and, as a function of them, with a new definition of the energy functional. The variational framework guarantees the rationality of the deduction. Analytical derivation of the force displacement hysteretic loop is also derived and, finally, the dissipation energy is furnished with respect to both the final value of the dissipation energy potential or by the corresponding area of the hysteretic loop.

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Analytical results for a linear hardening elasto-plastic spring investigated via a hemivariational formulation

Placidi,

Misra,

Kandalaft

et al. 2024

Constructive Mathematical Analysis

View full text Add to dashboard Cite

show abstract

Development of Methods and Computational Algorithms Parallelepiped in the Presence of Temperature and Heat Exchange

Rysgul,

Azat,

Rakhatay

et al. 2023

International Journal of Mechanics

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The article describes computational algorithms for estimating the law of distribution of body temperature in the form of a rectangular parallelepiped. The case is studied when a conditioned temperature is maintained on one of the boundaries of a rectangular parallelepiped, and heat exchange with the environment occurs on the opposite side. In addition, there are cases when other faces of the parallelepiped are thermally insulated or are under the influence of the environment. A polynomial is chosen as the approximating function. In accordance with the proposed layout, a function is formed that considers temperature, heat exchange with the environment, and insulation of the faces of a rectangular parallelepiped. The temperatures at the nodal points are determined by minimizing the function. Further, the temperature distribution law is determined according to the proposed approximating polynomial. The estimation of temperature distribution law is calculated for different amounts of partitioning into elements of a rectangular parallelepiped.

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Analytical Solutions of Temperature Distribution in a Rectangular Parallelepiped

Cited by 2 publications

References 6 publications

Analytical results for a linear hardening elasto-plastic spring investigated via a hemivariational formulation

Analytical results for a linear hardening elasto-plastic spring investigated via a hemivariational formulation

Development of Methods and Computational Algorithms Parallelepiped in the Presence of Temperature and Heat Exchange

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