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This paper aims to investigate the flow of two-layered non-Newtonian fluids with different viscosities in an axisymmetric elastic tube.

A mathematical model was considered for this study to describe the flow characteristics of two-layered non- Newtonian Jeffrey fluids in an elastic tube. Because Jeffrey fluid model is a better model for the description of physiological fluid motion. Further, this model is a significant generalization of Newtonian fluid model. Analytical expressions for flux, stream functions, velocities and interface velocity have been derived in terms of elastic parameters, inlet, outlet and external pressures. The effects of various pertinent parameters on the flow behavior have been studied.

The volumetric flow rate was calculated by different models of Mazumdar (1992) and Rubinow and Keller (1972); from this it was found that the flux of Jeffrey fluid is more in the case of Rubinow and Keller model than Mazumdar. A comparative study is made between single-fluid and two-fluid models of Jeffrey fluid flows and it was observed that more flux and higher velocities were observed in the case of two-fluid model rather than single-fluid model. Furthermore, when both the Jeffrey parameter tends to zero and ratios of viscosities and radii are unity, the results in this study agree with those of Rubinow and Keller (1972).

To describe the fluid flow in an elastic tube with two-layered systems, the models and solutions developed here are very important. These results will be highly suitable in analyzing the rheological characteristics of blood flow in a small blood vessel because of their elastic nature.

A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation.

Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool.

The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number.

Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.

The aim of the present paper is to investigate the homogeneous and heterogeneous reactions on Prandtl fluid flow at a stretching sheet with an induced magnetic field and slip boundary conditions.

The governing equations include the continuity, induced magnetic field, momentum, energy and homogeneous–heterogeneous equations. Initially, with suitable similarity variables, the governing partial differential equations and converted into a system of ordinary differential equations. Then, the nonlinear ordinary differential equations are solved by a shooting technique with the help of the BVC5C Matlab package.

The results of the present investigation are presented through graphs for different values of the various parameters. The authors observed that the large values of the stretching ratio and the induced magnetic parameters are moderate magnetic field, velocity and temperature primarily. Also, the authors found the more velocity and temperatures by boosting the slip parameters.

In addition, the values of the skin friction and the rate of heat transfer for various values of physical parameters are tabulated and deliberated in detail.

The main purpose of this numerical work is to study free convection of Casson fluid in a square differentially heated cavity taking into account the effects of thermal radiation and viscous dissipation.

The cavity is heated from the left vertical wall and cooled from the right vertical wall while horizontal walls are insulated. The governing partial differential equations invoking Rosseland approximation for thermal radiation with corresponding boundary conditions have been solved by finite difference method of the second-order accuracy using dimensionless variables stream function, vorticity and temperature. The governing parameters are Rayleigh number (Ra = 10⁵), Prandtl number (Pr = 0.1, 0.7, 7.0), Casson parameter (γ = 0.1-5.0), radiation parameter (R_d = 0-10), Eckert number (Ec = 0-1.0).

It is found that an increase in Casson parameter leads to the heat transfer enhancement and fluid flow intensification. While a growth of Eckert number illustrates the heat transfer suppression.

The originality of this work is to analyze for the first-time natural convective fluid flow and heat transfer of a Casson fluid within a differentially heated square cavity under the effects of thermal radiation and viscous dissipation. The results would benefit scientists and engineers to become familiar with the flow behavior of such non-Newtonian fluids, and the way to predict the properties of this flow for possibility of using this specific fluid in various engineering and industrial processes, such as chyme movement in intestine, blood flows, lubrication processes with grease and heavy oils, glass blowing, electronic chips, food stuff, slurries, etc.

The purpose of this paper is to study the three dimensional, steady and incompressible flow of non-Newtonian rate type Maxwell fluid, for stagnation point flow toward an off-centered rotating disk.

The governing partial differential equations are transformed to a system of non-linear ordinary differential equations by conventional similarity transformations. The non-perturbation technique, homotopy analysis method (HAM) is employed for the computation of solutions. And, the solution is computed by using the well-known software Mathematica 10.

The effects of rotational parameter and Deborah number on radial, azimuthal and induced velocity functions are investigated. The results are presented in graphical form. The convergence control parameter is also plotted for velocity profiles. The comparison with the previous results is also tabulated. The skin friction coefficients are also computed for different values of Deborah number.

This paper studies the effect of rotation and Deborah number on off-centered rotating disk has been observed and presented graphically.

This study aims to evaluate the amount of entropy generation around the NACA 0012 airfoil. This study takes place in four angles of attack of 0°, 5°, 10° and 16° and turbulent regime. Also, the variation in the amount of generated entropy by the changes in temperature and Mach number is investigated.

The governing equations are solved using computational fluid dynamics techniques. The continuity, momentum and energy equations and the equations of the SST k-ω turbulence model are solved. The entropy generation at different angles of attack is calculated and compared. The effect of various parameters in the generation of entropy is presented.

Results show that the major part of the entropy generation is at the tip of the airfoil. Also, increasing the angle of attack will increase the entropy generation. Also, results show that with increasing the temperature of air colliding with the airfoil, the production of entropy decreases.

Entropy generation is investigated in the NACA 0012 airfoil at various angles of attack and turbulent flow using the SST turbulence model. Also, the effects of temperature and Mach number on the entropy generation are investigated.

The purpose of this paper is to theoretically study the problem of the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct under the effects of Hall and ion slip. An incompressible and magnetohydrodynamics fluid is also taken into account. The governing equations are modelled under the constraints of low Reynolds number and long wave length. Recent development in biomedical engineering has enabled the use of the periastic flow in modern drug delivery systems with great utility.

Numerical integration is used to analyse the novel features of volumetric flow rate, average volume flow rate, instantaneous flux and the pressure gradient. The impact of physical parameters is depicted with the help of graphs. The trapping phenomenon is presented through stream lines.

The results of Newtonian fluid model can be obtained by taking out the effects of Jeffrey parameter from this model. No-slip case is a special case of the present work. The results obtained for the flow of Jeffrey fluid reveal many interesting behaviours that warrant further study on the non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress.

The results of this paper are new and original.

The present work explores the influence of Hall and Ohmic heating effects on the convective peristaltic flow of a conducting Jeffrey nanofluid in an inclined porous asymmetric channel with slip. Also, the authors investigated the impact of viscous dissipation, thermal radiation, heat generation/absorption and cross diffusion effects on the flow. Peristaltic flow has many industrial and physiological applications and most of the biofluids show the non-Newtonian fluid behaviour. Further, in a living body, several biofluids flow through different kinds of systems that are not symmetric, horizontal or vertical. The purpose of this paper is to address these issues.

The authors considered the flow of Jeffrey fluid which is generated by a sinusoidal wave propagating on the walls of an inclined asymmetric channel. The flow model is developed from the fixed frame to the wave frame. Finally, yield the nonlinear governing equations by applying the non-dimensional quantities with the assumptions of lengthy wave and negligible Reynolds number. The exact solution has been computed for the velocity and pressure gradient. The solutions for temperature and concentration are obtained by the regular perturbation technique.

Graphical analysis is made for the present results for different values of emerging parameters and explained clearly. It is noticed that the magnetic field enriches the temperature where it drops the fluid velocity. This work describes that the temperature field is decreasing due to the radiation but it is a rising function of temperature slip parameter. The temperature profile declines for growing values of the Hall parameter. The flow velocity diminishes for boosting values of the Darcy parameter. Further, the authors perceived that the concentration field reduces for large values of the chemical reaction parameter.

The authors validated and compared the results with the existing literature. This investigation will help to study some physiological systems, and heat transfer in peristaltic transport plays key role in medical treatments, so we ensure that these results are applicable in medical treatments like cancer therapy, drug delivery, etc.

This article aims to describe the effect of an endoscope and heat transfer on the peristaltic flow of a Jeffrey fluid through the gap between concentric uniform tubes.

The mathematical model of the present problem is carried out under long wavelength and low Reynolds number approximations. Analytical solutions for the velocity, temperature profiles, pressure gradient and volume flow rate are obtained.

The results indicate that the effect of the wave amplitude, radius ratio, Grashof number, the ratio of relaxation to retardation times and the radius are very pronounced in the phenomena. Also, a comparison of obtaining an analytical solution against previous literatures shows satisfactory agreement.

Analytical solutions for the velocity, temperature profiles, pressure gradient and volume flow rate are obtained. Numerical integration is performed to analyze the pressure rise and frictional forces on the inner and outer tubes.

This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues.

The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined.

It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting process enhances the fluid velocity. An opposite effect of melting heat process is noticed on velocity and skin friction.

The boundary layer flow in non-Newtonian fluids is very important in many applications including polymer and food processing, transpiration cooling, drag reduction, thermal oil recovery and ice and magma flows. Further, the thermal diffusion effect is employed for isotope separation and in mixtures between gases with very light and medium molecular weight.

Very scarce literature is available on thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet with melting heat transfer. Series solution is developed using HAM. Further, the authors compare the present results with the existing in literature and found excellent agreement.