Variable transform-based semi-analytical methods for solving convective straight fins problem with temperature-dependent thermal conductivity

Adewumi, A. O.; Akindeinde, Saheed Ojo; Lebelo, Ramoshweu Solomon

doi:10.1016/j.sciaf.2022.e01122

Cited by 2 publications

(4 citation statements)

References 20 publications

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“…Specifically, the PINN equation is designed to approximate the solution Θ ∶ [0, 𝜏] × Γ → ℜ of a nonlinear evolution equation in a domain Γ ∈ [0, 1] is represented by Equation (21). The time coordinates are spanned over 𝜏, the differential operator N[Θ] which is nonlinear in nature dynamically affects Θ, capturing the dynamics of the system as it evolves within the bounded domain Γ ⊂ ℜ 𝑐 .…”

Section: Physics Informed Neural Networkmentioning

confidence: 99%

“…The variable thermal conductivity attributes of the straight fin were deliberated by Adewumi et al. [21] by utilizing a semi‐analytical approach. The improvement of heat transport rate with the radiative longitudinal extended surface was discussed by Din et al.…”

Section: Introductionmentioning

confidence: 99%

“…Using metal foam and fins in a concentric tube heat exchanger system during the melting process was examined by Moghaddam et al [20]. The variable thermal conductivity attributes of the straight fin were deliberated by Adewumi et al [21] by utilizing a semi-analytical approach. The improvement of heat transport rate with the radiative longitudinal extended surface was discussed by Din et al [22].…”

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confidence: 99%

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A physics‐informed machine learning prediction for thermal analysis in a convective‐radiative concave fin with periodic boundary conditions

Kumar,

Srilatha,

Karthik

et al. 2024

Z Angew Math Mech

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The present research is focused on the inspection of unsteady heat dissipation through a radiative‐convective concave profiled fin along with the periodic boundary conditions. Additionally, the long‐short‐term memory machine learning (LSTM‐ML) approach is used in this study to examine the periodic fluctuation in the temperature of the fin. The current research is devoted to solving the highly non‐linear equation using a physics‐informed neural network (PINN) approach. Using the proper dimensionless terms, the associated fin problem is transformed into a non‐dimensional system, and the resulting partial differential equation (PDE) is then numerically solved using the finite difference method (FDM). Using the data‐driven LSTM‐ML technique, the time‐dependent periodic heat transmission in the concave fin is also examined. The impact of various factors on the temperature profile of the concave extended surface is explained, and the results are visually displayed. The temperature distribution in the concave fin diminishes as the convection‐conduction parameter and radiation‐conduction parameter rise. As the amplitude and thermal conductivity parameters improve, so does the temperature of the concave fin. Furthermore, it is demonstrated that although LSTM‐ML and PINN closely matched the FDM findings during the training domain, only PINN with designed characteristics has the potential to predict accurately beyond the trained region by capturing the physics of the problem.

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Section: Physics Informed Neural Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A physics‐informed machine learning prediction for thermal analysis in a convective‐radiative concave fin with periodic boundary conditions

Kumar,

Srilatha,

Karthik

et al. 2024

Z Angew Math Mech

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“…This novel transformation was improved with perturbation as well as decomposition techniques and used to solve significant problems by many investigators. In recent years, many analytical and numerical techniques were proposed to solve the nonlinear fin problems [22][23][24][25][26][27] but only a few research works are found on the application of Sumudu transform method (STM) for tackling the fin problems. Patel and Meher [28] executed the Adomian Decomposition Sumudu Transform Method (ADSTM) to resolve the heat transfer equation of a fin by considering the generation of internal heat.…”

Section: Introductionmentioning

confidence: 99%

Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

et al. 2023

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Temperature distribution, and efficiency of a rectangular profiled longitudinal fin are examined in this investigation with the impact of the magnetic field. By exploiting appropriate non‐dimensional terms, the heat transfer equation incorporating temperature‐dependent thermal conductivity, heat transfer coefficient, and Maxwell expression for the effect of the magnetic field yield a dimensionless nonlinear ordinary differential equation (ODE) with corresponding boundary conditions (BCs). Sumudu transform method with Pade approximant (STM‐PA) has been employed to obtain an analytical solution for the temperature profile of a longitudinal rectangular fin subjected to a uniform magnetic field under multi‐boiling heat transfer. The STM‐PA results are compared to the Runge‐Kutta Fehlberg's fourth‐fifth (RKF‐45) order technique for computational verification and are observed to be in good accordance. The behavior of dimensionless temperature profile has been explicated graphically for diverse values of non‐dimensional parameters such as thermal conductivity parameter, Hartmann number, and thermogeometric parameter. The results of this study show that as the thermal conductivity parameter enriches, the temperature profile of the longitudinal fin improves, whereas it declines for the Hartmann number and thermogeometric parameter. Under multi‐boiling heat transference, fin efficiency varies significantly depending on the impact of pertinent variables.

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Variable transform-based semi-analytical methods for solving convective straight fins problem with temperature-dependent thermal conductivity

Cited by 2 publications

References 20 publications

A physics‐informed machine learning prediction for thermal analysis in a convective‐radiative concave fin with periodic boundary conditions

A physics‐informed machine learning prediction for thermal analysis in a convective‐radiative concave fin with periodic boundary conditions

Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

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