Vertical Single-Well Pulse Testing of a Three-Layer Stratified Reservoir

A two-dimensional advection-diffusion model accompanied with a parabolic velocity profile of Poiseuille flow is considered for the chemical species transport in a tube with a constant wall concentration. The Reynolds decomposition technique is applied to reduce it to an equivalent one-dimensional model for advective-dispersive transport in a tube through which the effective advection coefficient, the dispersion coefficient, and the effective Sherwood number are developed for the problem under study. The derived and the classical Taylor models are also compared in order to find the difference between the two arrangements. The reduced-order model for the transport equation shows that the effective advection coefficient increases, whereas the dispersion coefficient in the tube decreases as compared to the classical Taylor equation. The effective Sherwood number for the steady state form of the developed model is found to be only a function of the Peclet number, which varies in the range of 3.215 Sh 4. These results find application in design of experiments and improve our understanding of mass transfer in microfluidic devices.

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“…Lee et al [28] proposed the range of 4 at D 5. To obtain desired results, the values of n ¼ 10 4 and at D ¼ 4 are used throughout this study.…”

Section: Solution Of the Governing Equationmentioning

confidence: 99%

“…It is required to optimize the parameters α and n for improving the accuracy. Lee et al proposed the range of 4 ≤ αt D ≤ 5. To obtain desired results, the values of n = 10 4 and αt D = 4 are used throughout this study.…”

Section: Theoretical Modellingmentioning

confidence: 99%

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

Dejam

Chen

2017

Can J Chem Eng

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“…Moreover, from Lee et al, 42 the values of

a_{p} τ

lies between 4 and 5. So, Equation (28) converges more quickly due to the noninclusion of oscillating sine and cosine functions where the optimal value is:

a_{p} τ = 4.7 \Rightarrow a_{p} = \frac{4.7}{τ} .

…”

Section: Present Solution: Integral Transform Methodsmentioning

confidence: 82%

Transient analysis of functionally graded material fin under the effect of Lorentz force using the integral transform method for improved electronic packaging

2020

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In the present work, transient analysis of longitudinal fin of functionally graded material under the influence of Lorentz force is considered. The governing equations of the linear, quadratic, and exponential functions are solved via Bessel, Legendre, and modified Bessel functions, respectively. The study investigates the effects of Lorentz force on the performance of the fin. The study shows that the transient response of the fin is lower in the linear law function compared with the exponential law function. The power law function shows significant energy‐saving capability than the linear class functionally graded material heatsink. Moreover, the thermal characteristic of the fin improves with an increase in the convective, radiative, magnetic field parameter, and nonhomogeneous index. The temperature prediction of the present study using the integral transform method is verified with the fourth‐order Runge‐Kutta method with an excellent agreement established.

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“…Lee et al [50] suggested values of a p τ ranging between 4 and 5. Equations (41)- (43) and (45) converge more quickly because it does not contain oscillating cosine and sine functions.…”

Section: Case 1 Linear Variation Of Thermal Conductivity With the Fimentioning

confidence: 99%

Nonlinear Transient Thermal Modeling and Analysis of a Convective-Radiative Fin with Functionally Graded Material in a Magnetic Environment

Sobamowo

Oguntala

Yinusa

2019

Modelling and Simulation in Engineering

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Nonlinear transient thermal analysis of a convective-radiative fin with functionally graded materials (FGMs) under the influence of magnetic field is presented in this study. The developed nonlinear thermal models of linear, quadratic, and exponential variation of thermal conductivity are solved approximately and analytically using the differential transformation method (DTM). In order to verify the accuracies of the nonlinear solutions, exact analytical solutions are also developed with the aids of Bessel, Legendre, and modified Bessel functions. Good agreements are established between the exact and the approximate analytical solutions. In the parametric studies, effects of heat enhancement capacity of fin with functionally graded material as compared to fin with homogeneous material are investigated. Also, influence of the Lorentz force and radiative heat transfer on the thermal performance of the fin are analyzed. From the results, it is shown that increase in radiative and magnetic field parameters as well as the in-homogeneity index improve the thermal performance of the fin. Also, the transient responses reveal that the FGM fin with quadratic-law and exponential-law function shows the slowest and fasted thermal responses, respectively. This study will provide a very good platform for the design and optimization of an improved heat transfer enhancement in thermal systems, where the surrounding fluid is influenced by a magnetic field.

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Vertical Single-Well Pulse Testing of a Three-Layer Stratified Reservoir

Cited by 31 publications

References 16 publications

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

Transient analysis of functionally graded material fin under the effect of Lorentz force using the integral transform method for improved electronic packaging

Nonlinear Transient Thermal Modeling and Analysis of a Convective-Radiative Fin with Functionally Graded Material in a Magnetic Environment

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