Thermoelectric Fluid Heat Transfer and Fluid Circulation Using a Fractional Approach Using Local Kernel

Riley Gilbert^*
*Correspondence: Riley Gilbert, Department of Mechanics, Chulalongkorn University, Pathumwan, Thailand, Email:

Keywords

Anti-magnetization • Integral transforms • Temperature prediction

Introduction

A state of matter that yields to shearing or sideways forces is called a fluid. Fluids include both gases and liquids. The physics of fluids that remain stationary is fluid statics. A substance or object's density is its mass per unit volume, while its pressure is its force per unit perpendicular area. The sum of the liquid's depth, density and acceleration due to gravity is the pressure caused by the weight of the liquid. At least since Archimedes investigation of fluid statics and buoyancy in ancient Greece, when he published his famous law, now known as the Archimedes principle, in his work on floating bodies generally regarded as the first major fluid mechanics work—the field of fluid mechanics has been studied. Leonardo da Vinci's observations and experiments, Evangelista Torricelli's invention of the barometer, Isaac Newton's investigation of viscosity, Blaise Pascal's research on hydrostatics and the formulation of Pascal's law and Daniel Bernoulli's introduction of mathematical fluid dynamics in Hydrodynamica (1739) all contributed to the rapid development of fluid mechanics.

Numerous mathematicians (Jean le Rond d Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace and Siméon Denis Poisson) conducted additional research on in viscid flow and numerous engineers (Jean Léonard Marie Poiseuille and Gotthilf Hagen) investigated viscous flow. In the Navier– Stokes equations, Claude-Louis Navier and George Gabriel Stokes provided additional mathematical justification and scientists like Osborne Reynolds, Andrey Kolmogorov and Geoffrey Ingram Taylor advanced our understanding of fluid viscosity and turbulence by studying boundary layers (Ludwig Prandtl, Theodore von Kármán).

Description

Due to increasing power density, it is a well-established fact that thermal analysis of various materials has emerged as the primary focus of numerous thermal industries and technologies. The interaction of thermal, optical and electronic sensation is crucial to the performance of various power devices in numerous industries. Due to its significant applications in numerous fields, including sensors of thermal energy, superconductors, aerospace and the space industries, among others, thermoelectric devices are required by a number of thermal industries and technologies for the attainment of electrical and thermal stability. Numerous scientists, mathematicians and researchers have investigated the stability of thermoelectric analysis because of its significant applications. Potential uses for thermoelectric devices and an analysis of the devices stability. Thermoelectric uses in electronic cooling coolers. Their examination gave a computational method to the limit of the cooling junction temperature coefficient execution and warm obstruction of an intensity sink [1].

Thermoelectric cooler's performance for packages with more power and precise temperature junction and cooling power solutions were discovered. Generalized thermoelectric properties with magnetic effects based on Laplace transform in a Casson fluid with a porous medium and exact solutions for thermal analysis. a thermoelectric module system and presented the results of an experiment. Thermoelectric properties can be studied in depth and continuously; we refer to for more information. Fractional order derivatives are the foundation of the majority of thermal studies differential models; this is because of the dynamical significance it plays in a variety of applications, including engineering, biological and physical applications, computational fluid dynamics, viscoelastic problems and more. Non-singularity and non-locality in a kernel of fractional operators are the fractional operators most interesting properties that are the focus of the research [2].

Due to its heredity property, the precise analysis of several thermoelectric problems has become a focal point for numerous researchers, mathematicians and scientists. From Riemann-Liouville to Caputo, Caputo to the modification of Riemann-Liouville, Caputo to Caputo-Fabrizio, Caputo-Fabrizio to the modified Caputo-Fabrizio, an extended form of Caputo with a kernel modification and Caputo-Fabrizio to the Atangana-Baleanu fractional operators, the fractional operators have been followed. Abel first used the Riemann-Liouville fractional operator to solve Tautochrone problems. However, due to its objectionable initial and boundary conditions, the Riemann-Liouville fractional operator did not perform well in research. The derivative of the constant was the primary flaw of Riemann-Liouville. The Riemann-Liouville fractional operator then overcame Caputo's fractional derivative. Numerous researchers have proposed the Caputo fractional derivative as suitable. In the meantime, this operator's primary flaw is the singular kernel, which is unable to collect the domain's memory impacts. Based on the claim of the non-singular exponential kernel, the Caputo-Fabrizio fractional operator was introduced in this continuity. Using a Fourier spectral algorithm, Owolabi and Gomez-Aguilar simulated the classical system of differential equations into fractional differential equations. On the fractional Korteweg-de Vries, Korteweg-de Vries-Burgers equations, Khader and Saad used a precise numerical procedure that combined the spectral Chebyshev collocation method and a finite difference method. Their research was centered on convergence analysis and the properties of thirdtype Chebyshev polynomials [3].

Numerous scientists have utilized the study of various fractional operators in various scientific fields; for example, electricity fluids and nanofluids, chemistry, biology and a few recent attempts in various fields. The authors primary objective is to present the prediction for thermoelectric fluid's maximum and optimal heat transfer efficiency using the differential operator's nonclassical approach, drawing inspiration from the aforementioned studies that focused on various aspects of research. Through temperature distribution and velocity field analysis, a fractionalized mathematical model is also developed to examine the efficiency and characteristics of thermoelectric fluid. For the purpose of finding analytical solutions through a dynamic investigation of the temperature distribution and velocity field, integral transforms and Cardano's method are used. On the basis of anti-magnetization magnetization, which describes the behavior of sine and cosine sinusoidal waves, the dynamic investigation of thermoelectric fluid temperature distribution and velocity field is explored. According to the rheological parameters, a temperature gradient in the heat flow occurs when the thermoelectric effect is increased by a smaller temperature difference [4,5].

Conclusion

This study demonstrated that magnetization, a promising method for transferring heat continuously and uninterruptedly, can efficiently convert thermoelectric energy. For the purpose of thermal analysis of fluid flow, a mathematical model based on the thermoelectric effect is developed that employs a local kernel approach to capture the rheological behavior. The most significant findings can be summed up as follows: A temperature gradient in the heat flow results from increasing the thermoelectric effect three times. This is because the efficiency of the thermoelectric conversion improves with time.

By increasing the velocity field's effects, the mosaic magnetic-domain structure and the effects of the magnetic field can be achieved. At three distinct Prandtl values, the temperature and velocity fields are coupled, revealing a higher heat transfer of thermoelectric fluid at lower Prandtl numbers. The elements of the fragmentary administrator of Caputo-Fabrizio on the speed field show asymptotic remarkable rot. According to the comparison, the fractional approach of Caputo-Fabrizio's velocity and temperature distribution is more stable and accurate than that of other solutions.

Acknowledgement

None.

Conflict of Interest

None.

References

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