Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

In this study, we delve into the magnetohydrodynamic heat and mass transfer flow of a Casson nanofluid over specifically chosen linear and nonlinear stretching surfaces embedded in a porous medium to understand their distinct effects on fluid behavior. By focusing on the influences of Brownian motion, thermophoresis, thermal radiation, and chemical reactions, we transformed nonlinear partial differential equations into ordinary differential equations, leveraging the Runge-Kutta method and Shooting Techniques for numerical solutions of momentum, temperature, and concentration profiles under predetermined boundary conditions. Our results, depicted in both graphical and tabular forms, shed light on how various parameters, including the Casson fluid characteristics, magnetic fields, buoyancy ratio, and mixed convection effects, influence fluid dynamics. A notable finding is that an increase in the Brownian motion parameter intensifies the fluid velocity and temperature profiles, but reduces its concentration profile, unveiling complex interactions within the nanofluid dynamics. This investigation underscores the importance of linear and nonlinear stretching surfaces in mimicking practical industrial scenarios, thereby providing insights that are crucial for optimizing processes such as coating, cooling of electronic devices, and in the manufacturing of thin plastic films, where precise control over heat and mass transfer is essential.

Fog computing is paving the way for catering latency stringent applications (e.g., augmented reality and virtual reality) at the customer premises. Fog computing nodes are located between the end user devices and remote cloud. They are lightweight and small-scale storage and processing system deployed closer to the data source, allowing faster processing as well as providing privacy and security of the data. We have been witnessing a growing number of solutions that integrate Passive Optical Network (PON) with the fog computing. Along this research line, there are some solutions considering fog computing nodes are co-located with the Optical Line Terminal (OLT), the central intelligence of a PON system, and Optical Network Unit (ONU), a customer premises equipment. There are some solutions, on the other hand, that propose to embed computing and storage functionality within PON equipment itself. In this paper, we particularly focus on the later approach. Here, we propose an energy conserving solution for a PON system with fog computing enabled ONUs, i.e., the ONUs are equipped with additional Computing and Storage Units (CSUs). Our solution aims at minimizing energy consumption of a PON system by keeping only the required number of CSUs active and allowing the ONUs to move into sleep mode (whenever possible) by taking into account task arrival rate and task completion deadline.

Haemodynamics is a branch of fluid mechanics which investigates the features of blood when it flows not only via blood vessels of smaller/larger diameter, but also under normal as well as abnormal flow states, such as in the presence of stenosis, aneurysm, and thrombosis. This review aims to discuss the rheological properties of blood, geometry of constrictions, dilations and the emergence of single-layered fluid to four-layered fluid models. To discuss further the influence of the aforesaid parameters on the physiologically important flow quantities, the mathematical formulation and solution methodology of the two-layered and four layered arterial blood flow problems studied by the authors (Afiqah and Sankar in ARPN J Eng Appl Sci 15:1129--1143, 2020, Comput Methods Programs Biomed 199:105907, 2021. https://doi.org/10.1016/j.cmpb.2020.105907 ) are recalled. It should be pointed out that the increasing resistive impedance to flow in three distinct states encompassing healthy, anaemic, and diabetic demonstrates that the greater the restriction in the artery, very few blood is carried to the pathetic organs, leading to subjects’ death. It is also discovered that the pulsatile nature of blood movement produces a dynamic environment that poses a slew of intriguing and unstable fluid mechanical state. It is hoped that the intriguing results gathered from this literature survey and review conducted may help the medical practitioners to forecast blood behaviour mobility in stenotic arteries. Furthermore, the physiological information gathered from the available clinical data from the literature on patients diagnosed with diabetes and anaemia may be beneficial to doctors in deciding the therapeutic procedure for treating some particular cardiovascular disease.

Understanding potential disease causation due to stenosis and thrombosis and its treatment by utilising catheters and magnetic field has gained increasing attention from experts worldwide. Endothelial injury or plaque rupture can trigger thrombosis, which can cut off the supply of blood to the heart or brain, causing stroke or a myocardial infarction. In the regions of stenosis, narrowing of lumen of arteries and high shear rate generate conditions that increase platelet build-up and blockage. Treatment like catheters and magnetic field are famously being implemented in modern medicine as a way of removing blood clots inside a constricted artery in light to improve the blood circulation inside a human body. This article reviews the impact of the simultaneous presence of stenosis and thrombosis on rheological properties of blood flow and the effects of using catheter in clearing the obstructions in the inner wall of blood vessel. We also introduce significant recent development on blood flow modelling relating to the subject matter. A sample mathematical model is considered from the literature to explain the influence of aforesaid arterial constrictions and clinical therapy for future directions in the medical field. Based on the collected literature, we note that the angioplasty catheter greatly increases blood flow as compared to infusion and guidewire catheters because it uses a balloon-tipped catheter to remove occlusions in the artery lumen. This comprehensive review and the proposed mathematical model together with the clinical data may offer directions for further studies, especially on one specific type of catheter for balloon angioplasty as the best treatment for clearing the occlusions in the diseased artery.

This mathematical model studies the dynamics of tumor growth, one of the most complex dynamics problems that relates several interrelated processes over multiple ranges of spatial and temporal scales. In order to construct a tumor growth model, an angiogenesis model is used with focus on controlling the tumor volume, preventing new establishment, dissemination, and growth. The lattice Boltzmann method (LBM) is effectively applied to Navier-Stokes equation for obtaining the numerical simulation of blood flow through vasculature. It is observed that the flow features are extremely sensitive to stenosis severity, even at small strains and stresses, and that a severe effect on flow patterns and wall shear stresses is noticed in the tumor blood vessels. It is noted that based on the nonlinear deformation of the blood vessel's wall, the flow rate conditions became unstable or distorted and affect the complex blood vessel's geometry and it changes the blood flow pattern. When the blood flows inside the stenotic artery, depending on the presence of moderate or severe stenosis, it can lead to insufficient blood supply to the tissues in the downstream. Consequently, the highly disturbed flow occurs in the downstream of the stenosed artery, or even plaque ruptures happen when the flow pattern becomes very irregular and complex as it transits to turbulent which cannot be described without assumptions on the geometry. The results predicted by LBM-based code surpassed the expectations, and thus, the numerical results are found to be in great accord with the relevant established results of others.

This study analyses the rheological characteristics of non-Newtonian Carreau fluid model for nanoparticles suspended flow of blood through constricted arteries in the presence of stenosis, thrombosis and catheters. Analytical expressions, such as, velocity distribution, temperature, pressure gradient, wall shear stress and resistive impedance to flow are obtained by implementing the perturbation method and through the extensive use of MATLAB and MATHEMATICA programming tools, the results are presented graphically and tabularly. It is found that temperature of the fluid lessens with the increase in stenosis shape parameter and depth of stenosis which results in the reduction of flow of blood in the artery. It is discovered that a rise in Weissenberg number results in the decrease of fluid’s velocity and skin friction. The magnitude of resistance to blood flow reduces with the upsurge of flow rate and stenosis shape parameter and the reverse character is recognized when Weissenberg number, the depth and axial displacement of blood clot increases. When the angioplasty catheter of radius 0.3 is inserted to the clear the constrictions in the artery, the resistance to flow surges considerably in the range of 6.75–8.78 when the stenosis position extends in the axial direction from 0.1 to 0.3. It is also recorded that when the catheter guidewire radius is 0.18, the pressure gradient in blood flow is found to vary in the range of 1.21–1.43 when the axial variable z varies from 0.2 to 0.8 and it decreases from 1.36 to 1.32 when the blood clot position displaces from 0.2 to 0.6.

In this article, the influence of microstructure in the Casson fluid flow through a porous medium is investigated, by extending the Buckingham-Reiner’s one-dimensional model to plane-Poiseuille flow and Hagen-Poiseuille flow geometries. While analyzing the flow characteristics in single-channel/pipes or multiple channels/pipes of different width/radius, four different probability density functions are used to model the pores widths/radii distributions. It is found that when the pressure gradient increases, the Buckingham-Reiner function raises slowly in the plane-Poiseuille flow, whereas in Hagen-Poiseuille flow, it rises rapidly. In all kinds of distribution of pores, the fluid’s mean velocity and porosity of the flow medium are considerably higher in the Hagen-Poiseuille flow than in the plane-Poiseuille flow, and this behavior is reversed for the permeability of the flow medium. The fluid’s mean velocity, porosity, and permeability of the flow medium increases appreciably with the rise of the channel width and pipe radius. The porosity of the flow medium slumps with the rise of the periodof the channels and pipes distribution from 1 to 2, and it decreases very slowly with the further rise of the period H of the channels and pipes from 2 to 11.

In this study, Natural convection of a nanofluid in a porous cavity with activated vertical walls with heated from the right wall is numerically analyzed under the effects of Magnetic field using the Finite Difference technique. The flow in a cavity is performed for various Darcy Number (Da), Hartmann Number (Ha) and Rayleigh Number (Ra). The flow in a cavity is described by streamlines and the isotherms. The heat transfer from the wall are described using the Nusselt numbers. The effect of Magnetic field influences the fluid flow for the higher Darcy number, Da. Also, the results discuss effect of Magnetic field over the flow in a cavity and heat transfer.

The aim of the study is to analyse the axisymmetric free vibration of layered cylindrical shells filled with a quiescent fluid. The fluid is assumed to be incompressible and inviscid. The equations of axisymmetric vibrations of layered cylindrical shell filled with fluid, on the longitudinal and transverse displacement components are obtained using Love’s first approximation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for a frequency parameter and an associated eigenvector of spline coefficients. Two layered shells with three different types of materials under clamped-clamped boundary conditions are considered. Parametric studies are made on the variation of the frequency parameter with respect to length-to-radius ratio and length-to-thickness ratio.

The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.

Acanthaceae is popularly known as acanthus family which belong to mint order – lamiales. They are distributed from tropics to a temperate region such as India, Malaysia, Brunei, Indonesia, Brazil, Central America and Africa. Most members of this family are therapeutically important since they are in the up to date usage by ethnic communities. Andrographis paniculata, Clinacanthus nutans, Graptophyllum pictum, Hemigraphis alternata, Justicia gendarussa and Strobilanthes Crispus are some of the medicinal plants of Acanthaceae family. These plants are recognized for their biopharmaceutical potential usage in traditional medicine. These plants have a plethora of phytochemical compounds such as flavonoids, phenolic compounds, glycosides, terpenoids, benzenoids, quinine, triterpenoids and naphthoquinone present in various parts of the plant that plays a vital role in drug industries. The pharmacological properties of these plants such as anti-bacterial, anti-diabetic, anti-cancer, anti-oxidant, anti-inflammatory, anti-arthritis, hepatoprotective, anti-viral and anti-hypertensive are in general practice as an alternative and complementary medicine in both ethnobotanical and pharmacological fields. This article encompasses not only the comprehensive survey based on the electronic resources, scientific journals but also the books that summarize the botanical, phytochemical properties of these plants and also accentuate their significant role in both ethnobotanical and pharmacological fields. It is felt that this article would provide more insight into the health benefits of some plants of the Acanthaceae family.

Integration of Passive Optical Network (PON) and wireless network technologies can offer a high data rate with ubiquitous Internet access to the end-users. Due to the growing importance of reducing the carbon footprint of telecommunication networks, energy-saving mechanisms are dispensed in the networking equipment. One of the commonly used approaches to reduce energy consumption is the "sleep mode" in which a network equipment periodically turns off some of its components so as to reduce energy consumption. Note that, the current PON and wireless access network technologies have their own power-saving modes. In order to gain power-saving and meet latency of applications in an integrated PON and wireless access network technologies, both optical and wireless access technologies need to have consent on how traffic management (bandwidth allocation, traffic forwarding path), as well as power-saving modes, should be managed in the network. That is, there needs to have synchronization of these two network segments. Otherwise, the end-users would experience longer delay and lower throughput. In this paper, we introduce a Delay-Aware Integrated Sleep Mode (DISM) solution designed considering 5G Heterogeneous Networks (HetNets) architecture which connected with core networks through Time and Wavelength Division Multiplexed Passive Optical Network (TWDM-PON). In particular, we propose a power saving mechanism using sleep mode for TWDM-PON taking into account packet forwarding delay from the optical network termination point to the end-users' mobile terminal so as to maximize energy-saving in TWDM-PON while meeting latency requirements of applications with stringent latency requirements. Results obtained through simulations impart that our proposed scheme can significantly satisfy the delay requirement of the traffic while it can still reduce energy consumption in TWDM-PON. Furthermore, the results provide insights on how power saving mechanism in PON should be managed for such 5G HetNet and optical integrated networks in order to satisfy the latency requirement of the traffic.

A computational model is presented to explore the properties of heat source, chemically reacting radiative, viscous dissipative MHD flow of an incompressible viscous fluid past an upright cone under inhomogeneous mass flux. A numerical study has been carried out to explore the mass flux features with the help of Crank-Nicolson finite difference scheme. This investigation reveals the influence of distinct significant parameters and the obtained outputs for the transient momentum, temperature and concentration distribution near the boundary layer is discussed and portrayed graphically for the active parameters such as the Schmidt number Sc, thermal radiation Rd, viscous dissipation parameter ɛ, chemical reaction parameter λ, MHD parameter M and heat generation parameter Δ. The significant effect of parameters on shear stress, heat and mass transfer rates are also illustrated.

The two-phase flow of blood in a small diameter blood vessel under mild stenotic condition is investigated in this mathematical analysis, modelling the densely concentrated red cells in the inner phase region as Herschel-Bulkley fluid and the plasma with depleted red cells in the peripheral phase region as Newtonian fluid. The analytic solutions for the velocity profile, rate of flow, slip velocity, shear stress at the blood vessel’s wall, resistive impedance to flow and core fluid’s viscosity are obtained. It is found that when the stenosis length ratio and the flow index parameter increase, the slip velocity increases significantly and an opposite behavior is noticed for the core fluid’s viscosity. It is also recorded that the percentage of difference between the core fluid’s viscosity in the two-phase Herschel-Bulkley fluid model and the corresponding experimental values in the blood vessel’s of diameter 40 m  and 66.6 m  are found to be 1.27% and 0.32% respectively and the respective differences observed by Ponalagausamy and Tamil Selvi (2011) in their two-layered Casson fluid model are 3.75% and 6.86% respectively. The estimated slip velocity values of two-phase Herschel-Bulkley fluid model in the blood vessels of diameter 40 m  and 66.6 m  are recoded as 1.202 cm/s and 0.7405 cm/s respectively and these values are in good alignment with the respective values obtained by Ponalagusamy and Tamil Selvi (2011) for two-fluid Casson model. The estimates of the core fluid’s viscosity in two-phase Herschel-Bulkley fluid model increase gradually when the flow index parameter increases in the blood vessels of diameter 40 m  and this behavior is reversed in the blood vessels of diameter 66.6 m  .

Background and objective: This study aims to investigate the haemodynamical factors with the motive to spell out some useful information for better interpretation and treatment of cardiovascular diseases. Numerous researchers theoretically investigated the movement of blood in the vascular system, treating blood as either single-layered or two-layered fluid representation. In this contemporary study, a four-layered fluid model is developed to analyse the rheological elements of blood when it flows via constricted arteries with slight constriction and the arterial wall is considered as porous medium.Methods: The momentum and constitutive equations are solved together with the suitable boundary conditions in an attempt to get the results on the distribution of velocity, volumetric flow rate, pressure gradient, shear stresses at the wall and resistive impedance to flow in which methods of integration and perturbation are utilized. The analytical/numerical solutions and graphical results are obtained by the extensive use of MATLAB software.Results: It is of importance to state that the magnitude of the shear stresses on the wall reduces with the rise of Darcy number, Weissenberg number and power law index. Velocity of blood however, rises with the upsurge in Darcy slip parameter, Weissenberg number and power law index. It is pertinent to record that when the stenosis depth rises from 0 to 0.15, the ratio of increase in the mean velocity of healthy, anemic and diabetic subjects are recorded as 4.58, 2.62 and 22.44 respectively. It is also found that the ratio of increase in the wall shear stress in the aforementioned states of blood are found to be 4.7, 4.27 and 3.62 respectively when the stenosis depth rises from 0 to 0.15.Conclusion: The nature of increased flow resistance in all three different situations such as anemic, healthy, and diabetic shows that the larger the constriction in the artery, the less amount of blood is transported to crucial organs which results in the sudden death of subjects. It is hoped that the outcomes of this study would be useful to medical practitioners and bio-medical engineers in predicting the behavior of blood flow in narrowed blood vessels for a more probable treatment modalities.

The pulsatile two-phase flow of blood in a tapered narrow artery with overlapping stenosis in the presence of magnetic field is analysed, modelling the suspension of all the erythrocytes in the inner phase region as Herschel-Bulkley fluid and the cell depleted plasma in the outer-phase region as Newtonian fluid. Explicit finite difference method is employed to obtain the numerical solution to various flow measurements from the modelled initial boundary value problem. It is found that when the magnetic field parameter increases, the velocity increases and wall shear stress and longitudinal impedance to flow increase. The estimates of the increase in the longitudinal impedance to flow for the two-phase H-B fluid model is higher than that of the single-phase H-B fluid model.

The effect of reversible phase exchange between the flowing fluid and wall tissues of arteries in the unsteady dispersion of solute in blood flow through a narrow artery is analysed mathematically, modelling the blood as Casson fluid. The resulting convective diffusion equation along with the initial and boundary conditions is solved analytically using the derivative series expansion method. The expressions for the negative asymptotic phase exchange, negative asymptotic convection, longitudinal diffusion coefficient and mean concentration are obtained. It is noted that when the solute disperses in blood flow through a narrow artery, the negative exchange coefficient, the negative convection coefficient increase and the longitudinal diffusion coefficient decreases with the increase of the Damköhler number and partition coefficient.