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In the present work, a new type of nanofluid called the hybrid nanofluid (Al2O3-Cu-water) is used to enhance the heat transfer. The Finite-Volume-Method (FVM) along with the SIMPLE-algorithm has been utilized to study the heat-transfer and, mixed convection fluid-flow of the hybrid nanofluid (Al2O3-Cu-water), placed within the lid-driven rectangular cavity. The bottom and top walls are subjected to constant high temperature (Th) and low temperature (Tc) respectively. The side walls are treated as adiabatic. The top wall moves in the positive x-direction. The effects of Reynolds number and hybrid nanoparticle volume fraction on the flow field have been investigated. It is found that the mean Nusselt number increases with respect to Reynolds numbers and hybrid nanoparticle volume fraction.

The current work analyzes the effects of concentric ballooned catheterization and heat transfer on the hybrid nano blood flow through diseased arterial segment having both stenosis and aneurysm along its boundary. A fractional second-grade fluid model is considered which describes the non-Newtonian characteristics of the blood. Governing equations are linearized under mild stenosis and mild aneurysm assumptions. Precise articulations for various important flow characteristics such as heat transfer, hemodynamic velocity, wall shear stress, and resistance impedance are attained. Graphical portrayals for the impact of the significant parameters on the flow attributes have been devised. The streamlines of blood flow have been examined as well. The present finding is useful for drug conveyance system and biomedicines.

We consider the unsteady flow of Burger fluid within a circular cylindrical tube, driven by a time-dependent pressure gradient, a body acceleration and a magnetic field acting normal to the flow direction. The solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow through arterial walls were obtained via the Laplace transform and the finite Hankel transform. The effects of magnetic field on parameters such as blood temperature and velocity were studied by Caputo time-fractional derivatives. We note that the solutions of many particular models such as fractional Oldroyd-B fluid, fractional Maxwell fluid, fractional second grade fluid and fractional Newtonian fluid models can be recovered from the solutions of the fractional constitutive equations governing the unsteady Burger’s fluid flow by particularizing the material coefficients (i.e. special and limiting cases of the earlier Burger’s fluid model). The numerical computations have been carried out to analyze the effects of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R0 and material parameter λ2 on the blood velocity and temperature. Some interesting flow and temperature characteristics are presented graphically and discussed. The study reveals that blood velocity, temperature and fractional parameters are reduced in the presence of magnetic field. The importance of this study can be found in the application fields of magnetic field control of biotechnological processes, bio magnetic device technology, biomedical engineering, medicine, etc.

This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo-Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems.

Mixed convection heat transfer in cavities is a significant phenomenon in numerous engineering fields, such as nuclear reactors, solar energy storage, and heat exchangers. Despite acknowledging that a square is a basic shape found in these systems, not all the figures are geometrical. Less attention was given to the rectangle cavity even though it could be found in these systems. Various internal reactions could occur inside the systems, especially in geothermal heat exchangers. Therefore, this research aims to analyze the effect of internal heat generation or absorption in a two-dimensional (2D) horizontal cavity to the fluid flow and heat transfer process numerically. The vertical walls are well insulated. Meanwhile, the top and bottom walls are kept at and , respectively, where . The top wall moves at a constant speed from left to right. The finite volume method (FEM) and SIMPLE algorithm are employed to discretize the governing equations. Next, the algebraic equations are solved iteratively using the tri-diagonal matrix algorithm (TDMA). The influences of heat generation or absorption parameters are investigated in terms of the flow, heat transfer, and Nusselt number. The numerical results are plotted in the form of streamlines and isotherms. It is found that the presence of heat generation or absorption has a significant effect on the fluid flow and heat transfer process in the horizontal cavity. Overall, for internal heat generation, the heat transfer rate decreases, while the opposite pattern can be observed for the case of internal heat absorption. However, for Ri = 10.0, as the heat generation's value increases from 2 to 4, the heat transfer rate is the same.

The present paper deals with a weakly nonlinear stability problem under an imposed time-periodic thermal modulation. The temperature has two parts: a constant part and an externally imposed time-dependent part. We focus on stationary convection using the slow time scale and quantify convective amplitude through the real Ginzburg-Landau equation (GLE). We have used the classical fourth order Runge-Kutta method to solve the real Ginzburg-Landau equation. The effect of various parameters on heat transport is discussed through GLE. It is found that heat transport analysis is controlled by suitably adjusting the frequency and amplitude of modulation. The applied magnetic field (effect of Ha) is to diminish the heat transfer in the system. Three different types of modulations thermal, gravity, and magnetic field have been compared. It is concluded that thermal modulation is more effective than gravity and magnetic modulation. The magnetic modulation stabilizes more and gravity modulation stabilizes partially than thermal modulation.

This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems.

We have investigated the study of double diffusive stationary convection in the presence of applied magnetic field and internal heating. A weakly nonlinear stability analysis has been performed using the finite amplitude Ginzburg-Landau model. This finite amplitude of convection is obtained at third order of the system. It is assumed that the buoyancy term has two parts, steady and oscillatory parts. The second part is varying sinusoidally with time and vibrates the system with finite amplitude δ1 and frequency ω. The effects of δ1 and on heat/mass transports have been analysed and depicted graphically. The studies are established that the heat/mass transports can be controlled effectively by gravity modulation. Further, it is found that internal Rayleigh number Ri is to enhance heat transfer and reduces the mass transfer in the system.

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

In this paper a speculative study of an incompressible Newtonian blood flow through a constricted porous channel and pulsatile nature is inspected. Porosity parameter λ is incorporated in the momentum equation. Governing nonlinear differential equations are numerically evaluated by employing the perturbation method technique for a very small perturbation parameter ε 1 such that ε ≠ 0 and with conformable boundary conditions. Numerical results of the flow velocity profile and volumetric flow rate have been derived numerically and detailed graphical analysis for different physical parameters porosity, Reynolds number and stenosis has been presented. It is found that arterial blood velocity is dependent upon all of these factors and that the relationship of fluid velocity and flow is more complex and nonlinear than heretofore generally believe. Furthermore the flow velocity enhanced with Reynolds number, porosity parameter and at maximum position of the stenosis/constriction.

This paper investigates the blood flow in multistenosed porous artery under the influence of external magnetic and electric fields. The blood is modeled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo–Fabrizio derivative without singular kernel. The exact solutions are obtained by using the Laplace and finite Hankel transforms for both blood and magnetic particle velocities. These velocities are graphically presented and analyzed. The velocities increase with respect to the Reynolds number, the Casson parameter, and the electric field. However, the velocity decreases at increasing Hartmann number and porosity. These findings might be beneficial for atherosclerosis therapy.

This paper aims at the heat transfer phenomenon and the effect of magnetic field on the second-grade fluid in a vertical oscillating cylinder. By applying a perpendicular magnetic field, the fluid gets magnetized. Fractional MHD flow was modeled with Caputo-Fabrizio non-integer derivative approach. Exact solution of the governing equations was obtained by Laplace and finite Hankel transforms. Mathematical computations and graphical plots were used to investigate the quantitative effects of emerging dimensionless physical parameters on the second-grade fluid flow, such as magnetic field and Prandtl number.

Effect of heat generation and absorption on mixed convection flows in a sinusoidal heated lid-driven square cavity filled with a porous medium is investigated numerically. Both the vertical walls of the enclosure are insulated while the bottom wall is uniformly heated or cooled. The top wall is moving at a constant speed and is heated sinusoidally. The governing equations and boundary conditions are non-dimensionalized and solved numerically by using finite volume method approach along with SIMPLE algorithm together with non-uniform grid system. The effect of Darcy and heat generation parameters are investigated in terms of the flow, heat transfer, and Nusselt number. The results for stream function and isotherm are plotted and it is found that there have significant influence with the presence of heat generation and porous medium.

The electro-kinetic transport of blood flow mixed with magnetic particles in the circular channel was investigated. The flow was subjected to an external electric and uniform magnetic field. The fluid was driven by pressure gradient and perpendicular magnetic field to the flow direction. Due to the usefulness and suitability of Caputo–Fabrizio fractional order derivative without singular kernel in fluid flow modeling and mass transfer phenomena, the governing equations were modeled as Caputo–Fabrizio time fractional partial differential equations and solved for $$\alpha \in \left( {0,\,1} \right]$$. The analytical solutions for the velocities of blood flow and magnetic particles were obtained by using Laplace, finite Hankel transforms and Robotnov and Hartley’s functions, respectively. Mathematica software was used to simulate the influences of fractional parameter $$\alpha$$, Hartmann number and Reynolds number on the velocities of blood and magnetic particles. The findings are important for controlling bio-liquids in the devices used for analysis and diagnosis in biological and medical applications.

The main theme of this paper is to analyze the effects of concentric catheterization to the diseased arterial segment having both stenosis and aneurysm along its boundary. Fractional second grade hybrid nanofluid model is under consideration. Governing equations are formulated and further linearized for both cases of mild stenosis and aneurysm. Precise articulations for various important flow characteristics heat transfer, hemodynamic velocity, wall shear stress and resistance impedance are attained. Graphical portrayals for the impact of the significant parameters on the flow attributes have been devised and talked about. The worldwide conduct of blood has been examined using an instantaneous streamlines pattern. The present concept plans to be of use in medical regime for the drug conveyance system and biomedicines.

The present theoretical work endeavors to solve the Sutterby nanofluid flow and heat transfer problem over a permeable moving sheet, together with the presence of thermal radiation and magnetohydrodynamics (MHD). The fluid flow and heat transfer features near the stagnation region are considered. A new form of similarity transformations is introduced through scaling group analysis to simplify the governing boundary layer equations, which then eases the computational process in the MATLAB bvp4c function. The variation in the values of the governing parameters yields two different numerical solutions. One of the solutions is stable and physically reliable, while the other solution is unstable and is associated with flow separation. An increased effect of the thermal radiation improves the rate of convective heat transfer past the permeable shrinking sheet.

The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length h is placed in the middle of the left vertical surface in which its temperature is fixed at T h . The temperature of the right vertical surface, however, is maintained at lower temperature T c . The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number R a = 10 3 and 10 5 , number of oscillations: 1 &le, N &le, 4 , angular rotational velocity: &minus, 1000 &le, &Omega, &le, 1000 , and heat source length: 0 . 2 &le, H &le, 0 . 8 . A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder.

The unsteady blood flow in the stenosed porous artery subjected to a magnetic field was studied analytically. Oscillating pressure gradient and periodic body acceleration were imposed on the flow field. The effects of the magnetic field and the permeability of the stenosed artery on the blood velocity were studied. The results showed that the magnetic field affected the flow field significantly which can be beneficial for some practical problems.

A current ideal control issue in the region of financial aspects has numerical properties that do not fall into the standard optimal control problem detailing. In our concern, the state condition at the final time, y(T ) = z, is free and obscure, and furthermore, the integrand is a piecewise consistent capacity of the obscure esteem y(T ). This is not a standard optimal control problem and cannot be settled utilizing Pontryagin’s minimum principle with the standard limit conditions at the final time. In the standard issue, a free final state y(T ) yields an important limit condition p(T ) = 0, where p(t) is the costate. Since the integrand is a component of y(T ), the new fundamental condition is that y(T ) yield is equivalent to a specific necessary consistent capacity of z. We present a continuous approximation of the piecewise consistent integrand function through hyperbolic tangent approach and tackle a case utilizing a C++ shooting method. The limiting free y(T ) value is computed in an external circle emphasis through the golden section method.

This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo–Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo–Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo–Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo–Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological analysis and medical diagnosis.

This study aimed to develop a mathematical model of an unsteady Burgers’ fluid in a circular cylinder with a trapezoidal pressure waveform described by an infinite Fourier series. An analytical solution was obtained for the governing equation using the Bessel transform method together with similarity arguments. The validity of the solution was verified using a numerical inversion method based on Stehfest’s method. Limiting cases were considered to examine the fluid flow performance of different fluids. Our results show that the Newtonian and Oldroyd-B fluids performed similar velocity time variation for the trapezoidal waveform of oscillating motion, whereas the velocity time variation was different for Maxwell and Burger’s fluids. Moreover, it is evident that the material constant of a Burgers’ fluid is another important factor that affects flow performance in an oscillating flow.

Background and Objective Arterial diseases would lead to several serious disorders in the cardiovascular system such as atherosclerosis. These disorders are mainly caused by the presence of fatty deposits, cholesterol and lipoproteins inside blood vessel. This paper deals with the analysis of non-Newtonian magnetic blood flow in an inclined stenosed artery. Methods The Casson fluid was used to model the blood that flows under the influences of uniformly distributed magnetic field and oscillating pressure gradient. The governing fractional differential equations were expressed using the Caputo Fabrizio fractional derivative without singular kernel. Results The analytical solutions of velocities for non-Newtonian model were then calculated by means of Laplace and finite Hankel transforms. These velocities were then presented graphically. The result shows that the velocity increases with respect to Reynolds number and Casson parameter, while decreases when Hartmann number increases. Conclusions Casson blood was treated as the non-Newtonian fluid. The MHD blood flow was accelerated by pressure gradient. These findings are beneficial for studying atherosclerosis therapy, the diagnosis and therapeutic treatment of some medical problems.

In this paper, a study of squeezing unsteady nanofluid flow between two parallel plates was conducted. While the thermal radiation effect along the temperature profile was considered. The homotopy perturbation method (HPM) was used to solve the twodimensional nonlinear momentum and energy equations. The results obtained in the current study were compared with the one obtained using Duan-Rach Approach (DRA) and Least Square Method (LSM). The results are found in understandable agreement with the aforementioned methods.

In the present paper, an unsteady motion of fluid flow in a pulsating pipe is studied to determine the effect of non-sinusoidal waveforms on the heat transfer performance. Three non-sinusoidal waveforms, namely sawtooth, square and triangular waveforms have been considered. Explicit analytical expressions for a periodic laminar flow describing the flow and heat transfer at small and large times with sawtooth and square pressure waveforms have been derived using Bessel transform technique. The heat transfer performance of periodic flow at sawtooth and square pressure waveforms has been compared with the published result for triangular waveform [1] . The temperature performance for a triangular waveform pressure is very different from the sawtooth and square pressure waveforms.