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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.

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.

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.

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.

This theoretical study investigates three types of basic flows of viscous incompressible Herschel-Bulkley fluid such as (i) plane Couette flow, (ii) Poiseuille flow and (iii) generalized Couette flow with slip velocity at the boundary. The analytic solutions to the nonlinear boundary value problems have been obtained. The effects of various physical parameters on the velocity, flow rate, wall shear stress and frictional resistance to flow are analyzed through appropriate graphs. It is observed that in plane Poiseuille flow and generalized Couette flow, the velocity and flow rate of the fluid increase considerably with the increase of the slip parameter, power law index, pressure gradient. The fluid velocity is significantly higher in plane Poiseuille flow than in plane Couette flow. The wall shear stress and frictional resistance to flow decrease considerably with the increase of the power law index and increase significantly with the increase of the yield stress of the fluid. The wall shear stress and frictional resistance to flow are considerably higher in plane Poiseuille flow than in generalized Couette flow.

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.

The pulsatile blood flow in tapered asymmetrically constricted narrow artery is investigated, treating the blood as Carreau fluid model. The expressions obtained by Sankar (2016) for various flow quantities are used to analyze the flow in different arterial geometry. It is found that the wall shear stress and longitudinal impedance to flow decrease with the increase of stenosis shape parameter, amplitude of the pulsatile pressure gradient, flow rate, power law index and Weissenberg number. The estimates of the percentage of increase in the wall shear stress and longitudinal impedance to flow increase with the increase of the angle tapering.

The pulsatile flow of blood in narrow arteries with multiple-stenoses under body acceleration is analyzed mathematically, treating blood as (i) single-phase Herschel-Bulkley fluid model and (ii) two-phase Herschel- Bulkley fluid model. The expressions for various flow quantities obtained by Sankar and Ismail (2010) for single-phase Herschel-Bulkley fluid model and Sankar (2010c) for two-phase Herschel-Bulkley fluid model are used to compute the data for comparing these fluid models in a new flow geometry. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow are marginally lower for two-phase HB fluid model than those of the single-phase H-B fluid model. It is found that the velocity decreases significantly with the increase yield stress of the fluid and the reverse behavior is noticed for longitudinal impedance to flow. It is also noticed that the velocity distribution and flow rate are higher for two-phase Herschel-Bulkley fluid model than those of the single-phase Herschel-Bulkley fluid model. It is also recorded that the estimates of the mean velocity increase with the increase of the body acceleration and this behavior is reversed when the stenosis depth increases.

The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a Herschel-Bulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.

The effect of chemical reaction on the unsteady dispersion of solute in blood flow through a pipe and a channel between two parallel plates is analyzed mathematically, treating the blood as Casson fluid. Generalized dispersion model is applied to solve the convective-diffusion equation. It is seen that the dispersion function at steady state and relative axial diffusivity decrease with the increase of chemical reaction rate while the reverse behavior is shown by dispersion function at unsteady state. The dispersion function increases with the increase of yield stress at the center. The dispersion function is considerably higher when the solute disperses in channel flow than in pipe flow and the reverse behavior is depicted by the relative axial diffusivity.

The peristaltic transport of Casson fluid in a channel and also in an inclined tube is analyzed mathematically, using long wavelength approximation and low Reynolds number assumption. The expressions for the velocity, stream function, flow rate, pressure rise and frictional force at the wall are obtained. It is found that the pressure rise decreases with the increase of the time mean flow rate and angle of inclination and increases with the increase of stress ratio and amplitude ratio. It is also noticed that the frictional force increases with the increase of the stress ratio and decreases with the increase of the angle of inclination. The estimates of the increase in the pressure rise are higher in channel flow compared to that of the inclined tube flow and the estimates of the increase in the frictional force are higher in inclined tube flow compared to that of the channel flow.

This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric stenosis. Blood is modeled as a two-fluid model with the suspension of all the erythrocytes in the core region being treated as Casson fluid and the plasma in the peripheral layer being assumed as Newtonian fluid. Perturbation method is used to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis shape parameter, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius and resistance to flow decrease with the increase of the body acceleration and pressure gradient. It is observed that the velocity and flow rate increase with the increase of the peripheral layer thickness and they decrease with the increase of the stenosis shape parameter. It is recorded that the estimates of the mean flow rate of the two-fluid blood flow model are considerably higher than that of the single-fluid blood flow model. It is also noticed that the presence of body acceleration and peripheral layer influences the mean flow rate by increasing their magnitude significantly in the arteries with different radii.

This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is employed to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of pulsatility, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness. It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.

A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel–Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel–Bulkley material are significantly lower than those of the single-phase Herschel–Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.

Pulsatile flow of blood through mild stenosed narrow arteries is analyzed by treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the coupled implicit system of non-linear differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood on these flow quantities are discussed. It is found that the pressure drop, plug core radius, wall shear stress and resistance to flow increase with the increase of the yield stress or stenosis size while all other parameters held constant. The percentage of increase in the resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with those of the single-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.

Pulsatile flow of a two-fluid model for blood flow through stenosed narrow arteries is studied through a mathematical analysis. Blood is treated as two-phase fluid model with the suspension of all the erythrocytes in the as Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the system of nonlinear partial differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The variations of these flow quantities with stenosis size, yield stress, axial distance, pulsatility and amplitude are analyzed. It is found that pressure drop, plug core radius, wall shear stress and resistance to flow increase as the yield stress or stenosis size increases while all other parameters held constant. It is observed that the percentage of increase in the magnitudes of the wall shear stress and resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with that of the single-fluid model of the Herschel-Bulkley fluid. Thus, the presence of the peripheral layer helps in the functioning of the diseased arterial system.

Steady flow of blood through catheterized arteries is studied by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is modeled as (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress and flow resistance, obtained by Sankar and Lee (2008a, 2008b) for the two-fluid Casson model and two-fluid Herschel-Bulkley model are used to get the data for comparison. It is noticed that the plug flow velocity, velocity distribution and flow rate for the two-fluid H-B model are considerably higher than that of the two-fluid Casson model for a given set of values of the parameters. Further, it is found that the resistance to flow is significantly lower for the two-fluid H-B model than that of the two-fluid Casson model. Thus, the two-fluid H-B model is more useful than the two-fluid Casson model to analyze the blood flow through catheterized arteries.

The pulsatile flow of blood through mild stenosed artery is studied. The effects of pulsatility, stenosis and non-Newtonian behavior of blood, treating the blood as Herschel–Bulkley fluid, are simultaneously considered. A perturbation method is used to analyze the flow. The expressions for the shear stress, velocity, flow rate, wall shear stress, longitudinal impedance and the plug core radius have been obtained. The variations of these flow quantities with different parameters of the fluid have been analyzed. It is found that, the plug core radius, pressure drop and wall shear stress increase with the increase of yield stress or the stenosis height. The velocity and the wall shear stress increase considerably with the increase in the amplitude of the pressure drop. It is clear that for a given value of stenosis height and for the increasing values of the stenosis shape parameter from 3 to 6, there is a sharp increase in the impedance of the flow and also the plots are skewed to the right-hand side. It is observed that the estimates of the increase in the longitudinal impedance increase with the increase of the axial distance or with the increase of the stenosis height. The present study also brings out the effects of asymmetric of the stenosis on the flow quantities.

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The resulting system of the nonlinear implicit system of partial differential equations is solved by perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. The velocity and flow rate are observed to decrease, and the wall shear stress and resistance to flow increase when the yield stress increases. The plug flow velocity and flow rate decrease, and the longitudinal impedance increases when the catheter radius ratio increases. The velocity and flow rate increase while the wall shear stress and longitudinal impedance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the longitudinal impedance are significantly lower for the present two-fluid model than those of the single-fluid model.

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.

The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model.

In this paper the effects catheterization and non-Newtonian nature of blood in small arteries of diameter less than 100 μm, on velocity, flow resistance and wall shear stress are analyzed mathematically by modeling blood as a Herschel–Bulkley fluid with parameters n and θ and the artery and catheter by coaxial rigid circular cylinders. The influence of the catheter radius and the yield stress of the fluid on the yield plane locations, velocity distributions, flow rate, wall shear stress and frictional resistance are investigated assuming the flow to be steady. It is shown that the velocity decreases as the yield stress increases for given values of other parameters. The frictional resistance as well as the wall shear stress increases with increasing yield stress, whereas the frictional resistance increases and the wall shear stress decreases with increasing catheter radius ratio k (catheter radius to vessel radius). For the range of catheter radius ratio 0.3–0.6, in smaller arteries where blood is modeled by Herschel–Bulkley fluid with yield stress θ = 0.1, the resistance increases by a factor 3.98–21.12 for n = 0.95 and by a factor 4.35–25.09 for n = 1.05. When θ = 0.3, these factors are 7.47–124.6 when n = 0.95 and 8.97–247.76 when n = 1.05.

The pulsatile flow of blood through catheterized artery has been studied in this paper by modeling blood as Herschel–Bulkley fluid and the catheter and artery as rigid coaxial circular cylinders. The Herschel–Bulkley fluid has two parameters, the yield stress θ and the power index n . Perturbation method is used to solve the resulting quasi-steady nonlinear coupled implicit system of differential equations. The effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed. The existence of two yield plane locations is investigated and their dependence on yield stress θ , amplitude A , and time t are analyzed. The width of the plug core region increases with increasing value of yield stress at any time. The velocity and flow rate decrease, whereas wall shear stress and longitudinal impedance increase for increasing value of yield stress with other parameters held fixed. On the other hand, the velocity, flow rate and wall shear stress decrease but resistance to flow increases as the catheter radius ratio (ratio of catheter radius to vessel radius) increases with other parameters fixed. The results for power law fluid, Newtonian fluid and Bingham fluid are obtained as special cases from this model.

In this paper, the steady flow of blood through tapered tube has been analyzed assuming blood as (i) Casson fluid and (ii) Herschel–Bulkley fluid. The expressions for pressure drop, wall shear stress and resistance to flow have been obtained. The effects of tapering of the tube and the non-Newtonian nature of the fluid on pressure drop, wall shear stress and resistance to flow are discussed. For all fluids, the pressure drop increases with increasing angle of taper from 0.5° to 1° for a given value of yield stress θ and tapered tube Reynolds number Re ψ . The resistance to flow as well as the wall shear stress increase with increasing yield stress for Herschel–Bulkley fluid and also for Casson’s fluid when the other parameters held constant. Both for Herschel–Bulkley fluid and Casson’s fluid, the wall shear stress as well as the resistance to flow increase with increasing axial distance for a given tapered tube Reynolds number Re ψ , angle of taper ψ and yield stress θ .

Pulsatile flow of a two-phase model for blood flow through arterial stenosis is analyzed through a mathematical analysis. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood, assuming the blood in the core region as a Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid, are discussed. A perturbation method is used to solve the resulting system of non-linear quasi-steady differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. It is noticed that the plug core radius and resistance to flow increase as the stenosis size increases while all other parameters held constant The wall shear stress increases with the increase of yield stress while keeping other parameters as invariables. It is observed that the velocity increases with the axial distance in the stenosed region of the tube upto the maximum projection of the stenosis.

In this paper, the pulsatile flow of blood through stenosed artery is studied. The effects of pulsatility, stenosis and non-Newtonian behavior of blood, assuming the blood to be represented by Herschel–Bulkley fluid, are simultaneously considered. A perturbation method is used to analyze the flow assuming the thickness of plug core region to be non-uniform changing with axial distance. An expression for the variation of plug core radius with time and axial distance is obtained. The variation of pressure gradient with steady flow rate is given. Also the variation of wall shear stress distribution as well as resistance to flow with axial distance for different values of time and for different values of yield stress is given and the results analyzed.

The flow of blood through a narrow artery with bell-shaped stenosis is investigated, treating blood as Casson fluid. Present results are compared with the results of the Herschel-Bulkley fluid model obtained by Misra and Shit (2006) for the same geometry. Resistance to flow and skin friction are normalized in two different ways such as (i) with respect to the same non-Newtonian fluid in a normal artery which gives the effect of a stenosis and (ii) with respect to the Newtonian fluid in the stenosed artery which spells out the non-Newtonian effects of the fluid. It is found that the resistance to flow and skin friction increase with the increase of maximum depth of the stenosis, but these flow quantities (when normalized with non-Newtonian fluid in normal artery) decrease with the increase of the yield stress, as obtained by Misra and Shit (2006). It is also noticed that the resistance to flow and skin friction increase (when normalized with Newtonian fluid in stenosed artery) with the increase of the yield stress.