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Hemodynamic Flow in a Vertical Cylinder with Heat Transfer
Farhad Ali,Anees Imtiaz,Ilyas Khan,Nadeem Ahmad Sheikh,Dennis Ling Chuan Ching 한국자기학회 2018 Journal of Magnetics Vol.23 No.2
In blood, the concentration of red blood cells varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the centre of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non-uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. The present article analyzes the heat transfer effects on the two-phase model of the unsteady blood flow when it flows through the stenosed artery under an external pressure gradient. The direction of the artery is assumed to be vertical and the magnetic field is applied along the radial direction of the artery. Blood is considered as a non-Newtonian Casson fluid with uniformly distributed magnetic particles. Both the blood and magnetic particles are moving with distinct velocities. This two-phase problem is modelled using the Caputo-Fabrizio derivative approach and then solved for an exact solution using joint Laplace & Hankel transforms. Effects of pertinent parameters such as Grashoff number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field on blood velocity and particle velocity have been shown graphically for both large and small values of time. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field and Prandtl number. The behaviour of temperature is studied for different values of the fractional parameter.
A Report of Generalized Blood Flow Model with Heat Conduction Between Blood and Particles
Farhad Ali,Fazli Haq,Naveed Khan,Hessah Alqahtani,Anees Imtiaz,Ilyas Khan 한국자기학회 2022 Journal of Magnetics Vol.27 No.2
This paper examines the magneto hydrodynamic two-phase blood (Casson fluid) flow in a vessel with heat conduction between blood and particles. The temperature of both phases is also considered. The model for the flow under consideration is formulated in terms of partial differential equations. Then the classical model is generalized by utilizing the Caputo fractional order derivative. The generalized equations are then non-dimensionalized by using appropriate dimensionless variables. The exact dimensionless solutions are obtained via the joint application of Laplace & Hankel integral transforms. The influence of various embedded parameters on both the velocities (blood and magnetic particles) and the temperature distribution are presented graphically. It is worth noting that the particle and blood velocities decrease for increasing the values of magnetic parameter (H) which is useful to control the blood flow during magnetic therapy (for treating pain, such as the back, foot, or joint pain) and surgeries. It is worth noting that fractional model better describes the flow behavior than classical model by providing virous integral curves as shown in Fig.
CERTAIN RESULTS INVOLVING FRACTIONAL OPERATORS AND SPECIAL FUNCTIONS
Aghili, Arman The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.
Parveen Lata,Iqbal Kaur 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.6
The present investigation has focus on the study of deformation due to thermomechanical sources in a thick circular plate. The thick circular plate is homogeneous, transversely isotropic with two temperatures and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of stresses, conductive temperature and displacement components are computed in the transformed domain. However, the resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are illustrated graphically. The effects of two temperatures by considering different values of temperature parameters are shown on the various components. Some particular cases are also figured out from the present investigation.
Parveen Lata,Harpreet Kaur Techno-Press 2023 Coupled systems mechanics Vol.12 No.3
This article is an application of new modified couple stress thermoelasticity without energy dissipation in association with two-temperature theory. The upper and lower surfaces of the plate are subjected to an axisymmetric heat supply. The solution is found by using Laplace and Hankel transform techniques. The analytical expressions of displacement components, conductive temperature, stress components and couple stress are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of two temperature is shown on the various components.
Lata, Parveen,Kaur, Harpreet Techno-Press 2019 Coupled systems mechanics Vol.8 No.6
The present study is concerned with the thermoelastic interactions in a two dimensional axisymmetric problem in transversely isotropic thermoelastic solid using new modified couple stress theory without energy dissipation and with two temperatures. The Laplace and Hankel transforms have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region, concentrated thermal source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. The effect of two temperature varying by taking different values for the two temperature on the components of normal stress, tangential stress, conductive temperature and couple stress are depicted graphically.
The deformation of a free surface due to the impact of a water droplet
Kwon, Sun-Hong,Park, Chang-Woo,Lee, Seung-Hun,Shin, Jae-Young,Choi, Young-Myung,Chung, Jang-Young,Isshiki, Hiroshi Korean Society of Ocean Engineers 2011 International journal of ocean system engineering Vol.1 No.1
An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.
Transversely isotropic thin circular plate with multi-dual-phase lag heat transfer
Parveen Lata,Iqbal Kaur,Kulvinder Singh 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.35 No.3
The present research deals with the multi-dual-phase-lags thermoelasticity theory for thermoelastic behavior of transversely isotropic thermoelastic thin circular plate The Laplace and Hankel transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution are computed in the transformed domain with the radial distance and further determined in the physical domain using numerical inversion techniques. The effect of rotation and two temperature are depicted graphically on the resulting quantities.
Lata, Parveen,Kaur, Harpreet Techno-Press 2022 Coupled systems mechanics Vol.11 No.3
The present paper deals with the axisymmetric deformation in homogeneousisotropic thermoelastic solid with two temperatures, with and without energy dissipation using modified couple stresstheory. The effect of energy dissipation and two temperature isstudied due to the concentrated normalforce, normalforce overthe circularregion, thermal pointsource and thermalsource over the circular region. The Laplace and Hankel transform techniques have been used to find the solution to the problem. The displacement components, conductive temperature distribution, stress components and couple stress are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. Effects of two temperature and energy dissipation on the conductive temperature,stress components and couple stress are depicted graphically.