Journal of Engineering Mathematics最新文献_第2页

Asymptotic solution of electromagnetic heating of skin tissue with lateral heat conduction 横向热传导皮肤组织电磁加热的渐近解法

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-08-08 DOI: 10.1007/s10665-024-10390-y

Ulises Jaime-Yepez, Hongyun Wang, Shannon E. Foley, Hong Zhou

{"title":"Asymptotic solution of electromagnetic heating of skin tissue with lateral heat conduction","authors":"Ulises Jaime-Yepez, Hongyun Wang, Shannon E. Foley, Hong Zhou","doi":"10.1007/s10665-024-10390-y","DOIUrl":"https://doi.org/10.1007/s10665-024-10390-y","url":null,"abstract":"We study the temperature evolution in the three-dimensional skin tissue exposed to an electromagnetic beam of millimeter wavelength. The skin absorption coefficient of the beam frequency determines how deep the electromagnetic energy penetrates into the skin tissue, which gives a sub-millimeter penetration depth for a 94 GHz wave. In contrast, in the lateral directions perpendicular to the depth, the beam size is usually much larger than the penetration depth. Based on this separation of length scales, we establish an asymptotic formulation in which each term has separable dependences on the depth coordinate and on the lateral coordinates. We solve it analytically to obtain a two-term asymptotic solution of the temperature distribution in the three-dimensional skin tissue. This closed-form analytical solution provides a practical and accurate way of predicting the temperature. When the beam size is moderately larger than the penetration depth (a ratio of 20), the effect of lateral heat conduction is well captured in the asymptotic solution with maximum error less than 0.0017 in the normalized temperature of magnitude well above 1.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On modeling tear breakup dynamics with a nematic lipid layer 利用向列脂质层建立泪液破裂动力学模型

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-07-29 DOI: 10.1007/s10665-024-10385-9

M. J. Taranchuk, R. J. Braun

{"title":"On modeling tear breakup dynamics with a nematic lipid layer","authors":"M. J. Taranchuk, R. J. Braun","doi":"10.1007/s10665-024-10385-9","DOIUrl":"https://doi.org/10.1007/s10665-024-10385-9","url":null,"abstract":"One of the main roles of the lipid layer (LL) of the tear film (TF) is to help prevent evaporation of the aqueous layer (AL). The LL thickness, composition, and structure all contribute to its barrier function. It is believed that the lipid layer is primarily nonpolar with a layer of polar lipids at the LL/AL interface. There is evidence that the nonpolar region of the LL may have liquid crystalline characteristics. We investigate the structure and function of the LL via a model of the tear film with two layers, using extensional flow of a nematic liquid crystal for the LL and shear-dominated flow of a Newtonian AL. Evaporation is taken into account and is affected by the LL thickness, internal arrangement of its rod-like molecules, and external conditions. We conduct a detailed parameter study with a focus on the evaporative resistance parameter, the Marangoni number, and primary liquid crystal parameters including the Leslie viscosities and director angle. This new model responds similarly to previous Newtonian models in some respects; however, incorporating internal structure via the orientation of the liquid crystal molecules affects both evaporation and flow. As a result, we see new effects on TF dynamics and breakup.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lubrication flow in grinding 磨削过程中的润滑流

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-07-25 DOI: 10.1007/s10665-024-10383-x

Zak Crowson, John Billingham, Paul Houston

引用次数: 0

Liquid drop shapes on hexagonal substrates: corner dewetting in the context of vapor–liquid–solid growth of nanowires 六角形基底上的液滴形状：纳米线气-液-固生长过程中的角脱胶现象

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-07-25 DOI: 10.1007/s10665-024-10382-y

Brian J. Spencer

{"title":"Liquid drop shapes on hexagonal substrates: corner dewetting in the context of vapor–liquid–solid growth of nanowires","authors":"Brian J. Spencer","doi":"10.1007/s10665-024-10382-y","DOIUrl":"https://doi.org/10.1007/s10665-024-10382-y","url":null,"abstract":"We consider the equilibrium shape of a liquid drop on a hexagonal substrate as motivated by vapor–liquid growth of nanowires. We numerically determine the energy-minimizing liquid drop shape on a hexagonal base using the software Surface Evolver in conjunction with an efficient regridding algorithm and convergence monitoring. The drop shape depends on two nondimensional parameters, the drop volume, and the equilibrium contact angle. We show that sufficiently large drops are well approximated away from the base by a spherical cap drop with geometric parameters determined by the area of the hexagonal base. Notably, however, the drop/base contact region does not extend to the corners of the hexagonal base, even in the limit of large volume V. In particular, there is a self-similar structure to the dry corner region with a length scale proportional to (V^{-3/2}). Since steady-state growth of faceted hexagonal nanowires by vapor–liquid–solid growth requires the liquid drop to be commensurate with the underlying wire cross-section, our findings mean that steady-state growth of hexagonal wires is not strictly compatible with an equilibrium liquid drop acting as a catalyst.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Magnetohydrodynamic instability of fluid flow in a bidisperse porous medium 双分散多孔介质中流体流动的磁流体力学不稳定性

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-07-17 DOI: 10.1007/s10665-024-10369-9

Shahizlan Shakir Hajool, Akil J. Harfash

{"title":"Magnetohydrodynamic instability of fluid flow in a bidisperse porous medium","authors":"Shahizlan Shakir Hajool, Akil J. Harfash","doi":"10.1007/s10665-024-10369-9","DOIUrl":"https://doi.org/10.1007/s10665-024-10369-9","url":null,"abstract":"The investigation focuses on the hydrodynamic instability of a fully developed pressure-driven flow within a bidisperse porous medium containing an electrically conducting fluid. The study explores this phenomenon using the Darcy theory for micropores and the Brinkman theory for macropores. The system involves an incompressible fluid under isothermal conditions confined in an infinite channel with a constant pressure gradient along its length. The fluid moves in a laminar fashion along the pressure gradient, resulting in a time-independent parabolic velocity profile. Two Chebyshev collocation techniques are employed to address the eigenvalue system, producing numerical results for evaluating instability. Our findings indicate that enhancing the values of the Hartmann numbers, permeability ratio, porous parameter, and interaction parameter contributes to an enhanced stability of the system. The spectral behavior of eigenvalues in the Orr-Sommerfeld problem for Poiseuille flow demonstrates noteworthy sensitivity, influenced by various factors, including the mathematical characteristics of the problem and the specific numerical techniques employed for approximation.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the thermal flow through a porous annular region 关于通过多孔环形区域的热流

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-07-04 DOI: 10.1007/s10665-024-10379-7

Eduard Marušić-Paloka, Igor Pažanin

引用次数: 0

Comparison of conical hybrid journal bearing performances for varying speeds 不同转速下锥形混合轴颈轴承性能的比较

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-06-27 DOI: 10.1007/s10665-024-10368-w

Prashant Govindrao Khakse, Vikas M. Phalle

引用次数: 0

Mathematical modeling of breakthrough curves in dynamic column adsorption: analytical solutions and validation 动态柱吸附突破曲线的数学建模：分析解决方案与验证

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-06-27 DOI: 10.1007/s10665-024-10375-x

Jimena B. Dima, Mariano A. Ferrari, Noemi Zaritzky

{"title":"Mathematical modeling of breakthrough curves in dynamic column adsorption: analytical solutions and validation","authors":"Jimena B. Dima, Mariano A. Ferrari, Noemi Zaritzky","doi":"10.1007/s10665-024-10375-x","DOIUrl":"https://doi.org/10.1007/s10665-024-10375-x","url":null,"abstract":"Water pollution is a critical global problem. The fixed- bed continuous adsorption column provides the most practical application in the industry for wastewater treatment. The mass transfer process in the column can be described using a mass balance differential equation, and a sorbate–adsorbent interaction rate equation. The objective of this work was to describe the mass transfer in an adsorption column, analyzing the differential equations of the process and their analytical solutions. A general rate equation with four parameters was proposed, adding a zero-order parameter. The general model was solved using Laplace Transform method. The model proposed was applied to describe the adsorption of hexavalent chromium on chitosan biopolymer. The theoretical solution found was satisfactory to estimate the experimental breakthrough curves, and the estimated parameters allowed to predict other curves with different operational conditions. The zero-order parameter added relates to the baseline height of the breakthrough curve. The general model proposed generalizes already known plug flow models based on a single rate equation. The present model uses the information obtained from the column and from the equilibrium batch isotherm, which constitutes a useful tool for describing the dynamic adsorption process and to make decisions on column design.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Unsteady suspended sediment distribution in an ice-covered channel through fractional advection–diffusion equation 通过分数平流-扩散方程计算冰封河道中的非稳定悬浮泥沙分布

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-06-27 DOI: 10.1007/s10665-024-10380-0

Sweta Narayan Sahu, Sumit Sen, Sourav Hossain, Koeli Ghoshal

{"title":"Unsteady suspended sediment distribution in an ice-covered channel through fractional advection–diffusion equation","authors":"Sweta Narayan Sahu, Sumit Sen, Sourav Hossain, Koeli Ghoshal","doi":"10.1007/s10665-024-10380-0","DOIUrl":"https://doi.org/10.1007/s10665-024-10380-0","url":null,"abstract":"Despite several applications of the fractional advection–diffusion equation (fADE) in studying sediment transport in an open channel flow, its application is limited to apprehending the non-local movement of sediment particles in an ice-covered channel with a steady, uniform flow field. An unsteady fADE is considered where the space term is non-local with a non-integer order and the mathematical model with Caputo fractional derivative is able to estimate the variation of sediment concentration along a vertical as well as with time in the ice-covered channel. An eddy viscosity expression is used, which includes the variation in roughness between the channel bed and ice cover surface. The Chebyshev collocation method and the Euler backward method are used to solve the fADE with the initial and boundary conditions and the convergence of the methods is established. The temporal variation of concentration shows that for a zero initial condition, the concentration profile first increases and then becomes stable after a certain time; for a non-zero initial concentration, the profile decreases with an increase in time and eventually a steady state is achieved. The effect of the order of the fractional derivative on the vertical variation of concentration at different times for zero and non-zero initial concentrations is studied and it is found that the order of the fractional derivative has a greater impact at smaller times. The impact of several parameters on concentration profiles is studied at different times and the validation of the model is done by comparing it with experimental studies under restricted conditions.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Perspective on the description of viscoelastic flows via continuum elastic dumbbell models 通过连续弹性哑铃模型描述粘弹性流动的视角

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2024-06-25 DOI: 10.1007/s10665-024-10374-y

Evgeniy Boyko, Howard A. Stone

{"title":"Perspective on the description of viscoelastic flows via continuum elastic dumbbell models","authors":"Evgeniy Boyko, Howard A. Stone","doi":"10.1007/s10665-024-10374-y","DOIUrl":"https://doi.org/10.1007/s10665-024-10374-y","url":null,"abstract":"Non-Newtonian fluid mechanics and computational rheology widely exploit elastic dumbbell models such as Oldroyd-B and FENE-P for a continuum description of viscoelastic fluid flows. However, these constitutive equations fail to accurately capture some characteristics of realistic polymers, such as the steady extension in simple shear and extensional flows, thus questioning the ability of continuum-level modeling to predict the hydrodynamic behavior of viscoelastic fluids in more complex flows. Here, we present seven elastic dumbbell models, which include different microstructurally inspired terms, i.e., (i) the finite polymer extensibility, (ii) the conformation-dependent friction coefficient, and (iii) the conformation-dependent non-affine deformation. We provide the expressions for the steady dumbbell extension in shear and extensional flows and the corresponding viscosities for various elastic dumbbell models incorporating different microscopic features. We show the necessity of including these microscopic features in a constitutive equation to reproduce the experimentally observed polymer extension in shear and extensional flows, highlighting their potential significance in accurately modeling viscoelastic channel flow with mixed kinematics.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0