Dynamics through three-inlets of t-shaped ducts: Significance of inlet velocity on transient air and water experiencing cold fronts subject to turbulence

Wang, Fuzhang; Animasaun, I.L.; Al-Mdallal, Qasem M.; Saranya, S.; Muhammad, Taseer

doi:10.1016/j.icheatmasstransfer.2023.107034

Cited by 19 publications

(3 citation statements)

References 28 publications

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“…Remark 4: The continuous scheme (10) which has a coefficients in matrix form in ( 10) and ( 11) must be a continuous function, differentiable, and the limit must exist.…”

Section: Formulation Of Implicit Six-point Block Scheme (Isbs)mentioning

confidence: 99%

“…Partial Differential Equations (PDEs) are a useful tool for the mathematical expression of many natural phenomena and are useful in the solution of physical and other issues requiring functions of several variables. The transmission of heat/sound, fluid movement, turbulent flow, heat transfer analysis, elasticity, electrostatics, and electrodynamics are a few examples of these issues; see Ahsan et al [ 1 ], Wang and Guo [ 2 ], Arif et al [ 3 , 4 ], Adoghe et al [ 5 ], Nawaz et al [ 6 ], Animasaun et al [ 7 ], Devnath et al [ 8 ], Ahsan et al [ 9 ], Wang et al [ 10 ], Rufai et al [ 11 ], Nawaz and Arif [ 12 ], Ramakrishna et al [ 13 ], El Misilmani et al [ 14 ]). According to Quarteroni and Valli [ 15 ], numerical approximation techniques for partial differential equations (PDEs) constitute a cornerstone in diverse scientific and engineering disciplines.…”

Section: Background Informationmentioning

confidence: 99%

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Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Olaoluwa Omole,

Olusheye Adeyefa,

Iyabo Apanpa

et al. 2024

PLoS ONE

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In the era of computational advancements, harnessing computer algorithms for approximating solutions to differential equations has become indispensable for its unparalleled productivity. The numerical approximation of partial differential equation (PDE) models holds crucial significance in modelling physical systems, driving the necessity for robust methodologies. In this article, we introduce the Implicit Six-Point Block Scheme (ISBS), employing a collocation approach for second-order numerical approximations of ordinary differential equations (ODEs) derived from one or two-dimensional physical systems. The methodology involves transforming the governing PDEs into a fully-fledged system of algebraic ordinary differential equations by employing ISBS to replace spatial derivatives while utilizing a central difference scheme for temporal or y-derivatives. In this report, the convergence properties of ISBS, aligning with the principles of multi-step methods, are rigorously analyzed. The numerical results obtained through ISBS demonstrate excellent agreement with theoretical solutions. Additionally, we compute absolute errors across various problem instances, showcasing the robustness and efficacy of ISBS in practical applications. Furthermore, we present a comprehensive comparative analysis with existing methodologies from recent literature, highlighting the superior performance of ISBS. Our findings are substantiated through illustrative tables and figures, underscoring the transformative potential of ISBS in advancing the numerical approximation of two-dimensional PDEs in physical systems.

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“…Remark 4: The continuous scheme (10) which has a coefficients in matrix form in ( 10) and ( 11) must be a continuous function, differentiable, and the limit must exist.…”

Section: Formulation Of Implicit Six-point Block Scheme (Isbs)mentioning

confidence: 99%

Section: Background Informationmentioning

confidence: 99%

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Olaoluwa Omole,

Olusheye Adeyefa,

Iyabo Apanpa

et al. 2024

PLoS ONE

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“…Shih et al [11] depicted and explained the results obtained from the living tissues models with employing sinusoidal heat flux on skin surface. Fluid flow with thermal shock involves the sudden exposure of a fluid system to extreme temperature variations, inducing rapid thermal expansions or contractions are investigated by Fuzhang et al [12]. For the estimation of the localized and concentrated heat transfer in the spherical system regarding time dependent and analytical analysis of bioheat equation was presented and discussed by Gutierrez [13] that required for the ablation of the cancerous cells.…”

Section: Introductionmentioning

confidence: 99%

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

Riaz,

Rehman,

Martinovic

et al. 2024

PLoS ONE

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The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier’s law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter’s influence, such as α, β, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings.

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Application of machine learning to model the pressure poisson equation for fluid flow on generic geometries

Sousa,

Afonso,

Veiga Rodrigues

2024

Neural Comput & Applic

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This study addresses the importance of enhancing traditional fluid-flow solvers by introducing a Machine Learning procedure to model pressure fields computed by standard fluid-flow solvers. The conventional approach involves enforcing pressure–velocity coupling through a Poisson equation, combining the Navier–Stokes and continuity equations. The solution to this Poisson equation constitutes a substantial percentage of the overall computational cost in fluid flow simulations, therefore improving its efficiency can yield significant gains in computational speed. The study aims to create a versatile method applicable to any geometry, ultimately providing a more efficient alternative to the conventional pressure solver. Machine Learning models were trained with flow fields generated by a Computational Fluid Dynamics solver applied to the confined flow over multiple geometries, namely wall-bounded cylinders with circular, rectangular, triangular, and plate cross-sections. To achieve applicability to any geometry, a method was developed to estimate pressure fields in fixed-shape blocks sampled from the flow domain and subsequently assemble them to reconstruct the entire physical domain. The model relies on multilayer perceptron neural networks combined with Principal Component Analysis transformations. The developed Machine Learning models achieved acceptable accuracy with errors of around 3%. Furthermore, the model demonstrated enhanced computational efficiency, outperforming the classical PISO algorithm by up to 30 times.

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Dynamics through three-inlets of t-shaped ducts: Significance of inlet velocity on transient air and water experiencing cold fronts subject to turbulence

Cited by 19 publications

References 28 publications

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

Application of machine learning to model the pressure poisson equation for fluid flow on generic geometries

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