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The objective of this study is to determine the irreversible losses and associated entropy generation within a fluid system, considering the combined effects of magnetic field, convective boundaries, and porous media. It accomplishes this objective by a thorough investigation into the second law analysis and entropy generation of a magnetohydrodynamic (MHD) Eyring–Powell fluid flowing through a symmetric porous medium. To achieve this, the governing equations for the Eyring–Powell fluid are formulated using the conservation laws of mass, momentum, and energy, while incorporating the magnetic field’s effects. In order to account for the porous character of the medium, the equations are coupled with the Darcy model. Using appropriate computational techniques, the resulting system of partial differential equations is numerically solved. The local irreversibility ratio calculates the system’s entropy generation number, revealing its distribution. The Hartmann number and Eyring–Powell fluid parameters are also studied. The primary findings indicate that $A^{\ast }$ enhances velocity and diminishes temperature and entropy, while $B^{\ast }$ has the opposite effect. Entropy is also increased by Hartmann and Brinkman numbers, which are a result of the enhanced heat transfer and stronger magnetic fields. The findings emphasize the need and importance of studying irreversible losses and improving fluid system energy efficiency.

In this article, we considered the peristaltic flow of Newtonian incompressible fluid of chyme in small intestine. The analysis has been performed using an endoscope. The peristaltic flow of chyme is modeled by assuming that the peristaltic wave is formed in non-periodic mode comprising two sinusoidal waves of different wave lengths propagating with same speed along the outer wall of the tube. Heat transfer mechanisms have been taken into account, such that the constant temperature and are assigned to inner and outer tubes, respectively. A complex system of equations has been simplified using long wavelength and low Reynolds number approximation because such assumptions exist in small intestine. Exact solutions have been carried out for velocity temperature and pressure gradient. Graphical results have been discussed for pressure rise, frictional forces, temperature, and velocity profile. Comparison of present results with the results of the existing literature have been presented through figures. Trapping phenomena have been presented at the conclusion of the article.

Analysis has been carried out to examine the heat and mass transfer effects on the magnetohydrodynamics (MHD) peristaltic flow in a channel with compliant walls. An incompressible Maxwell fluid occupies the porous space. Modified Darcy's law and slip conditions are used in the problem formulation. Solutions for small wave number are derived. The effects of emerging parameters in the obtained solutions are displayed and discussed.

In this attempt, simultaneous effects of slip condition and an induced magnetic field on the peristaltic flow of viscous fluid in an asymmetric channel is investigated. The whole analysis have been carried out in the presence of heat and mass transfer characteristics. The resulting mathematical model is solved by exploiting the boundary conditions derived from physical point of view. The expressions of the desired flow quantities of interest are derived and discussed. A comparison with no-slip condition is shown.

Flow and heat transfer of blood under the action of an external magnetic field are analyzed in this paper. The flow is considered to take place in a channel that is bounded by stretchable walls. The surface velocity of the channel is assumed to vary linearly with axial distance. The microrotation of the micro-particles of blood is taken into account by treating blood as a micropolar fluid. The governing partial differential equations are transformed into a system of ordinary differential equations and then solved numerically by developing a suitable finite difference technique. Computational work has been carried out in order to have an estimate of the velocity, microrotation, and the temperature of the fluid for different values of various physical parameters of interest in the present study of blood flow dynamics. Different physiological aspects are discussed via graphical presentation of the computed results.

The temperature rise of the hand palm has been measured with infrared thermography under the influence of an external infrared radiation source. The temperature rises could be very well fitted to exponential function, so that the experimental data could be summarized with just two parameters: amplitude and time constant. A simple mathematical model has been set up to explain the experimentally observed phenomena. It was found that the blood perfusion is essential to explain the results. From our measurements, which is essentially a noninvasive technique, several parameters could be found, the numerical values of which, agree with data found in the literature.

A two-phase thermo-hydrodynamic model is presented for transport in the vertical chamber of a porous media blood filtration device. A non-Darcy drag force formulation was employed. The Marble–Drew fluid–particle suspension model was used to simulate the plasma phase and the suspension (erythrocyte) particle phase. The non-dimensional transport equations were solved using a semi-computational procedure known as the homotopy analysis method (HAM). With the judicious use of the auxiliary parameter ℏ, HAM affords a powerful mechanism to adjust and control the convergence region of solution series. This method provides an efficient approximate analytical solution with high accuracy, minimal calculation and avoidance of physically unrealistic assumptions. Detailed computations are presented for the effects of Grashof number (Gr), momentum inverse Stokes number (Sk_m), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (P_L), buoyancy parameter (B) and temperature inverse Stokes number (Sk_T) on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity (U_p), dimensionless fluid phase temperature (Φ) and the dimensionless temperature of particle phase (Φ_p). A Prandtl number of 25 was used to simulate blood at room temperature. Excellent correlation was obtained between the HAM and numerical shooting quadrature solutions. The results indicated that there is a strong decrease in fluid phase velocities with increasing Darcian (first order) drag and second-order Forchheimer drag, and a weaker reduction in particle phase velocity field. Applications of the study include porous media bio-filtration devices and dialysis simulations.

The present investigation deals with a mathematical model representing the response of heat transfer to blood streaming through the arteries under stenotic condition. The flowing blood is represented as the suspension of all erythrocytes assumed to be Casson fluid and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell (MAC) method. The necessary checking for numerical stability has been incorporated into the algorithm for better precision of the results computed. The quantitative analysis carried out finally includes the respective profiles of the flow-field and the temperature along with their individual distributions over the entire arterial segment as well. The key factors like the pressure drop, wall shear stress, flow separation, Nusselt number and streamlines are examined for qualitative insight into the blood flow and heat transport phenomena through arterial stenosis. In conformity with other several existing findings the present simulation predicts that the pressure drop and Nusselt number diminishes with increasing yield stress values, and significant enhancement in values of Nusselt number is observed with increasing severity of the stenosis. However, the effect of the shapes of the stenoses on flow separation cannot be ruled out from the present investigation.

Microfluidics technology has emerged as an attractive approach in physics, chemistry and biomedical science by providing increased analytical accuracy, sensitivity and efficiency in minimized systems. Numerical simulation can improve theoretical understanding, reduce prototyping consumption, and speed up development. In this paper, we setup a 3D model of an integrated microfluidic system and study the multi-physical dynamics of the system via the finite element method (FEM). The fluid–structure interaction (FSI) of fluid and an immobilized single cell within the cell trapping component, and the on-chip thermodynamics have been analyzed. The velocity magnitude and streamline of flow field, the distribution of von Mises stress and Tresca stress on the FSI interface have been studied. In addition, the on-chip heat transfer performance and temperature distribution in the heating zone have been evaluated and analyzed respectively. The presented approach is capable of optimizing microfluidic design, and revealing the complicated mechanism of multi-physical fields. Therefore, it holds the potential for improving microfluidics application in fundamental research and clinical settings.

In the present paper, we have studied the effects of endoscope and heat transfer on the peristaltic flow of second grade fluid through an inclined tube. The endoscope is a solid circular cylinder which is inserted in a peristaltic tube, and the flow takes place through the gap between endoscope and the peristaltic tube. The endoscope is maintained at a temperature $T_1$, while the outer tube has a sinusoidal wave traveling down its wall and is exposed to temperature $T_0$. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The equations governing the flow of second grade fluid are modeled in cylindrical coordinates. Using perturbation method, the solutions are obtained for the stream function, pressure gradient and temperature fields. The pressure difference and frictional force at both the walls are calculated using numerical integration. The graphical results are presented to interpret the effect of various physical parameters of interest. It is found that, velocity increases with an increase in inclination angle and the best pumping rate appear in the vertical tube as compared to the horizontal tube. It is also found that, the heat generation parameter has an increasing effect on the velocity of the fluid.

The present investigation is associated with the contemporary study of viscous flow in a vertical tube with temperature dependent viscosity. The main flow problem has been modeled using cylindrical coordinates and flow equations are simplified to ordinary differential equations using longwave length and low Reynold's number approximation and exact solutions have been obtained for velocity, pressure gradient and temperature. Results acquired are discussed graphically for better understanding. It is seen that with an increment in the Grashof number, the velocity of the governing fluids start to decrease significantly and pressure gradient is higher for pure water as compared to multi-walled carbon nanotubes (MWCNTs) due to low density. As the specific heat is very high for pure water as compared to the multi-wall CNTs, it rise temperature of the muscles for the case of pure water as compared to the MWCNTs. Furthermore, it is noted that the trapped bolus starts to decrease in size as the buoyancy forces are dominant as compared to viscous force.

A precise model is presented to designate the curvature effects in electroosmotic flow classifications to organize flow in a curved micro-vessel. Heat transfer analysis is also considered under the viscous dissipation effect. Lubrication scheme, Debye–Hückel estimation, and suitable boundary conditions have been employed to arising nonlinear system. The coupled nonlinear PDEs are solved numerically using Mathematica software. The obtained numerical results for electric potential, stream function, pressure gradient, axial velocity, temperature and shear stress are displayed through graphical illustrations. Trapping for blood flow under the effects of physical parameter is also discussed. The annotations also demonstrate the silent features of the micro-mixer peristaltic pumps and chip devices which may additionally be exploited in hemodialysis and judgement of samples respectively.

This work aims at the investigation of 2D, steady, laminar, viscous, incompressible boundary layer and heat transfer flow of a biomagnetic fluid over a convectively heated moving horizontal plate in the presence of a magnetic dipole. It is assumed that the fluid viscosity is the inverse linear function of temperature and the temperature at the wall varies as power law function. The governing equations involve a system of coupled PDEs (momentum and energy equations) which are converted into a system of nonlinear ODEs by utilizing similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by adopting a finite difference algorithm. The physical effects of the governing parameters (i.e., ferrohydrodynamic interaction parameter, buoyancy force parameter, viscosity-temperature parameter, wall parameter) on the flow fields along with the skin friction and heat transfer rate are presented. Verification of this work has been done by comparing former published results and acceptable agreement is found. It has been analyzed theoretically by using suitable transformations, that the ferrohydrodynamic interaction parameter, has a great enhancement effect on biomagnetic fluid rather than that on a regular fluid. It has been discovered that the inclusion of certain intensity of magnetic field along with the consideration of the variable viscosity and temperature, has significant effects on the flow and heat transfer mechanism. These outcomes could be of interest in medical as well as bioengineering implementations, like magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries and treating cancer by producing magnetic hyperthermia.

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Hydrocephalus is an asymmetric and unusual cerebrospinal fluid flow in the lateral ventricular portions. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. Mathematical models of transport in the hydrocephalus, which constitutes an excess of fluid in the cavities deep within the brain, enable a better perspective of how this condition contributes to disturbances of the CSF flow in the hollow places of the brain. Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Thermophysical and mass transfer effects are therefore addressed in this paper to quantify the transport phenomena in pulsatile hydrocephalus CSF transport with oscillating pressure variations that characterize general neurological activity and transitions from one functional state to another. A new mathematical model is developed which includes porous media drag for brain tissue and solutal diffusion (concentration) effects. A classical Laplace transform method is deployed to solve the dimensionless model derived with appropriate boundary conditions. The analysis reveals that with increasing permeability of the subarachnoid space, the CSF velocity is increased, and a significant fluid flux enhancement arises through the brain parenchyma as the pressure of the fluid escalates drastically due to hydrocephalus disorder. Stronger thermal buoyancy (Grashof number) also results in deceleration in the flow. CSF temperature is reduced with progression in time. Particle (e.g. ion) concentration is suppressed with increasing Schmidt number. As heat conduction parameter increases, there is a substantial depletion in CSF velocity with respect to time. Increasing Womersley parameter displaces the CSF velocity peaks and troughs. The present effects are beneficial in determining the thermo-fluidic transport mechanism of the pathological disorder hydrocephalus. Also, the present results are compared with those clinical studies for some cases. We have confirmed that our validity provides a decent justification with the neurological studies.

A two-dimensional (2D) steady boundary layer flow along with heat transfer of a self-similar biomagnetic fluid over a permeable moving flat plate has been taken into consideration in this work. The flow is contemplated to be embedded by a magnetic dipole of sufficient magnetic strength. Transpiration as well as movement along the wall is also regarded. By imposing the appropriate similarity technique, the governing equations are converted into a system of coupled nondimensional equations. An efficient numerical technique has been incorporated to solve these dimensionless coupled nonlinear ordinary differential equations. The existence of dual solutions along with their stability has been established with the consideration of stability analysis. We discovered from our analysis that two solutions exist (one stable and another unstable) for the arbitrary values of transpiration, movement velocity and biomagnetic interaction parameters on flow and physical parameters. The attained results are demonstrated graphically and in tabular form. For the validity of our numerical scheme, we compared our findings with others previously published and found significant agreement.

The movement of bile inside ducts in a diseased state is investigated using a mathematical model that takes into account heat transport and chemical interactions. Bile is considered as a viscous fluid, geometry of ducts is assumed as finite length asymmetric channel and the flow is induced by peristaltic wave along the length of channel walls. Under the presumption of a long wave length and a low Reynolds number, the formulas for axial velocity, pressure gradient, volume flow rate, stream function, pressure increase, shear stress, and heat transfer coefficient are produced. In the end, a plot and discussion are made of how different emergent factors affect the relevant physical quantities.