Analytical solutions for heat conduction problems with three kinds of periodic boundary conditions and their applications

Xu, Xin; Li, Gaosheng; Zhao, Yuqin; Liu, Tiejun

doi:10.1016/j.amc.2022.127735

Cited by 4 publications

(3 citation statements)

References 28 publications

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“…Recently, researchers have conducted analytical and numerical investigations on the phenomenon of unsteady flow. Analytical solutions to heat conduction issues with three different forms of periodic boundary conditions were discovered by Xu et al (2023), along with applications of these solutions. In their study conducted in 2023, Yahaya et al (2023) identified the presence of dual solutions throughout the computational process, instigating an investigation into the stability of the solution.…”

Section: Introductionmentioning

confidence: 99%

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

2024

JQMA

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The evaluation of high thermal efficiency has garnered considerable interest in the context of the unique properties demonstrated by hybrid nanofluids. Therefore, the present study investigates the impact of heat radiation on the unsteady rear stagnation point magnetohydrodynamic (MHD) flow of hybrid nanofluids. The utilisation of similarity transformations allows for the conversion of differential equations with several variables into a specific class of ordinary differential equations. The mathematical model is solved with the bvp4c function. The findings suggest that the unsteady rear stagnation MHD flow in hybrid nanofluid exhibits enhanced heat transfer properties compared to both nanofluid types. The augmentation of nanoparticle concentration and the influence of suction are discovered to have a positive effect on the skin friction coefficient. As the thermal radiation parameter is elevated, a concomitant reduction in the rate of heat transmission is observed. Furthermore, the findings illustrate the presence of two distinct solutions within a particular range.

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Section: Introductionmentioning

confidence: 99%

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

2024

JQMA

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“…Fang and Jing [3] discovered the exact solutions in the unsteady rear stagnation point flow. The analytical and numerical study of the heat transfer and boundary layer flow in the unsteady flow of nanofluid may be obtained in Saidin et al, [4], Fathinia and Hussein [5], Yahaya et al, [6], and Xu et al, [7].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Unsteady Flow and Heat Transfer of Rear Stagnation Point in Hybrid Nanofluids with Thermal Radiation and Magnetic Impact

Nurul Amira Zainal,

Iskandar Waini,

Najiyah Safwa Khashi’ie

et al. 2024

ARFMTS

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In this study, the stability analysis is conducted in order to observe the reliability of the generated solutions. The influence of several parameters is taken into consideration including magnetic parameter, radiation parameter, and heat transfer. The well-known heat transfer fluid that is Al2O3-Cu/H2O hybrid nanofluid past a rear stagnation point is implied. The similarity equations are achieved after implying suitable similarity transformation which then needed to be solved numerically using bcp4c, embedded in MATLAB software. Dual solutions are observed along the investigation within specified values of involved parameters. It is important to note that verification results show excellent concordance with pre-existing reports.

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“…During the initial stages of research on frozen soil mechanics, scholars conducted unconfined compression strength tests and creep tests to examine the mechanical properties of frozen soils (Andersland and Akili 1967;Takegawa et al 1979;Vyalov et al 1979;Tsytovich et al 1981;Finborud and Berggren 1981). Subsequently, various researchers employed conventional triaxial test systems to investigate the effect of different factors such as temperature (Zhang et al 2017;Ma et al 2023b), water content (Sun et al 2022;Li et al 2023), strain rate (Xie et al 2016;Ma et al 2019;Ma et al 2023a), and stress path (Shen et al 2021;Xu et al 2022Xu et al , 2023 on the mechanical properties of frozen soil, yielding fruitful outcomes. However, the test systems solely permit the application of axial and radial principal stresses, primarily reflecting the mechanical characteristics of frozen soils under axisymmetric stress states, while neglecting the influence of intermediate principal stresses (Kong et al 2021;Zhao et al 2022).…”

Section: Introductionmentioning

confidence: 99%

Mechanical Properties and Constitutive Model of Artificially Frozen Sandy Soils Under Different Intermediate Principal Stresses

Huang,

Ma,

Cai

et al. 2023

Preprint

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Triaxial compression tests were conducted on frozen sandy soils under a constant minimum principal stress (σ3 = 1.6 MPa) and various intermediate principal stresses (σ2 = 1.6, 3.4, 5.2, 7.0, 8.8, 9.8 MPa). The purpose of the research was to investigate the influence of intermediate principal stress (σ2) on the characteristic stress levels and the deformation characteristics. The test results obtained demonstrated that the crack damage stress and failure stress initially increase and then decrease with an increase in the σ2. However, the crack initiation stress exhibits an initial increase up to a specific value, after which it stabilizes. The difference in deformation between the σ2 and σ3 directions increased with increasing σ2. From the perspective of crack propagation, the influence mechanism of σ2 on the strength is discussed. The deformation difference was revealed using the stress superposition principle and Poisson’s effect. Finally, the constitutive model based on the Weibull distribution and Drucker-Prager strength criterion can accurately represent the stress-strain relationships of frozen sandy soils under various σ2 conditions.

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Analytical solutions for heat conduction problems with three kinds of periodic boundary conditions and their applications

Cited by 4 publications

References 28 publications

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

Thermal Radiation Effect on Unsteady MHD Rear Stagnation Point in Al2O3-Cu/H2O Hybrid Nanofluids

Stability Analysis of Unsteady Flow and Heat Transfer of Rear Stagnation Point in Hybrid Nanofluids with Thermal Radiation and Magnetic Impact

Mechanical Properties and Constitutive Model of Artificially Frozen Sandy Soils Under Different Intermediate Principal Stresses

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