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Ohmic heating generates temperature with the help of electrical current and resists the flow of electricity. Also, it generates heat rapidly and uniformly in the liquid matrix. Electrically conducting biofluid flows with Ohmic heating have many biomedical and industrial applications. The purpose of this study is to provide the significance of the effects of Ohmic heating and viscous dissipation on electrically conducting Casson nanofluid flow driven by peristaltic pumping through a vertical porous channel.

In this analysis, the non-Newtonian properties of fluid will be characterized by the Casson fluid model. The long wavelength approach reduces the complexity of the governing system of coupled partial differential equations with non-linear components. Using a regular perturbation approach, the solutions for the flow quantities are established. The fascinating and essential characteristics of flow parameters such as the thermal Grashof number, nanoparticle Grashof number, magnetic parameter, Brinkmann number, permeability parameter, Reynolds number, Casson fluid parameter, thermophoresis parameter and Brownian movement parameter on the convective peristaltic pumping are presented and thoroughly addressed. Furthermore, the phenomenon of trapping is illustrated visually.

The findings indicate that intensifying the permeability and Casson fluid parameters boosts the temperature distribution. It is observed that the velocity profile is elevated by enhancing the thermal Grashof number and perturbation parameter, whereas it reduces as a function of the magnetic parameter and Reynolds number. Moreover, trapped bolus size upsurges for greater values of nanoparticle Grashof number and magnetic parameter.

There are some interesting studies in the literature to explain the nature of the peristaltic flow of non-Newtonian nanofluids under various assumptions. It is observed that there is no study in the literature as investigated in this paper.

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 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.

The current paper investigates the bioconvective third-grade nanofluid flow containing gyrotactic organisms with Copper-blood nanoparticles in permeable walls.

The equations governing the flow are solved by adopting the Adomian decomposition method.

The results show that the biconvection Peclet number decreases the density of motile microorganisms, and the Rayleigh number also decreases the velocity profile.

The present study can be applied to design the higher generation microsystems.

To the best of the authors’ knowledge, no such investigation has been carried out in the literature.

Particular attention is given to the viscous damping force parameter, stiffness parameter, rigidity parameter, and Brinkman number and plotted their graph for thermal distribution, momentum profile and concentration profile.

In the field of engineering, biologically inspired propulsion systems are getting the utmost importance. Keeping in view their developmental progress, the present study was made. The theoretical analysis explores the effect of heat and mass transfer on non-Newtonian Sisko fluid with slip effects and transverse magnetic field in symmetric compliant channel. Using low Reynolds number, so that the authors neglect inertial forces and for keeping the pressure constant during the flow, channel height is used largely as compared to the ratio of wavelength. The governing equations of fluid flow problem are solved using the perturbation analysis.

Results are considered for thickening, thinning and viscous nature of fluid models. It is found that the velocity distribution profile is boosted for increasing values of the Sisko fluid parameter and porous effect, while thermal profile is reducing for Brinkman number (viscous dissipation effects) for all cases. Moreover, shear-thicken and shear-thinning behavior of non-Newtonian Sisko fluid is also explained through the graphs.

Hear-thicken and shear-thinning behavior of non-Newtonian Sisko fluid is also explained through the graphs.

objective of the present investigation is to examine the influence of Hall on the peristaltic mechanism of Johnson-Segalman fluid in a heated channel with elastic walls. The transmission of heat is carried out. Relevant equations are computed for heat transfer coefficient, temperature and velocity. Low Reynolds number assumptions and long wavelength are employed. The interpretation of various parameters is analyzed. The results indicate that the heat transfer coefficient, temperature and velocity are larger for viscous material in comparison with Johnson-Segalman material.

The transmission of heat is carried out. Relevant equations are computed for heat transfer coefficient, temperature and velocity. Low Reynolds number assumptions and long wavelength are employed. The interpretation of various parameters is analyzed. The results indicate that the heat transfer coefficient, temperature and velocity are larger for viscous material in comparison with Johnson-Segalman material.

The formulation of paper is executed as follows. Section 2 comprises problem summary and mathematical design. Solution methodology is discussed, and expressions for temperature, velocity and coefficient of heat transfer are derived in Section 3. Graphical outcomes for the parameters are reported in Section 4. Conclusions are outlined in Section 5.

Peristaltic phenomenon of fluids has a definite role in many physiological, industrial and engineering processes. The mechanical devices for instance finger and roller pumps operate via this process, and it is quite significant for vasomotion of blood vessels, consumption of food via esophagus, chyme flow in gastrointestinal zone, toxic liquid flow in nuclear industry and transport of corrosive fluids.

Literature review witnesses that information about peristalsis of conducting fluid in a heated channel with flexible walls and Hall effect is scarce. So, our goal is to discuss the peristaltic activity of non-Newtonian fluids in flexible channel. Johnson-Segalman fluid is taken into account. This model is used to allow non-affine deformations. Experimentalists relate “spurt” with wall slip. That is why the work presented is original.

The purpose of this paper is to emphasize the peristaltic mechanism of power-law fluid in an elastic porous tube under the influence of slip and convective conditions. The effects of different waveforms on the peristaltic mechanism are taken into account.

The governing equations are rendered dimensionless using the suitable similarity transformations. The analytical solutions are obtained by using the long wavelength and small Reynold’s number approximations. The expressions for velocity, flow rate, temperature and streamlines are obtained and analyzed graphically. Furthermore, an application to flow through an artery is determined by using a tensile expression given by Rubinow and Keller.

The principal findings from the present model are as follows. The axial velocity increases with an expansion in the estimation of velocity slip parameter and fluid behavior index, and it diminishes for a larger value of the porous parameter. The magnitude of temperature diminishes with an expansion in the Biot number. The flux is maximum for trapezoidal wave and minimum for the triangular wave when compared with other considered waveforms. The flow rate in an elastic tube increases with an expansion in the porous parameter, and it diminishes with an increment in the slip parameter. The volume of tapered bolus enhances with increasing values of the porous parameter.

The current study finds the application in designing the heart-lung machine and dialysis machine. The investigation further gives a superior comprehension of the peristaltic system associated with the gastrointestinal tract and the stream of blood in small or microvessels.

This paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.

The governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.

The analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.

In practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.

Although many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.

The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.

The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.

A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

The purpose of this paper is to perform a numerical analysis on the static and dynamic behaviors of beams made up of functionally graded carbon nanotube (FG-CNT) reinforced polymer and hybrid laminated composite containing the layers of carbon reinforced polymer with CNT. Conventional fibers have higher density as compared to carbon nanotubes (CNTs), thus insertion of FG-CNT reinforced polymer layer in fiber reinforced composite (FRC) structures makes them sustainable candidate for weight critical applications.

In this context, stress and strain formulations of a multi-layer composite system is determined with the help of Timoshenko hypothesis and then the principle of virtual work is employed to derive the governing equations of motion. Herein, extended rule of mixture and conventional micromechanics relations are used to evaluate the material properties of carbon nanotube reinforced composite (CNTRC) layer and FRC layer, respectively. A generalized eigenvalue problem is formulated using finite element approach and is solved for single layer FG-CNTRC beam and multi-layer laminated hybrid composite beam by a user-interactive MATLAB code.

First, the natural frequencies of FG-CNTRC beam are computed and compared with previously available results as well as with Ritz approximation outcomes. Further, free vibration, bending, and buckling analysis is carried out for FG-CNTRC beam to interpret the effect of different CNT volume fraction, number of walls in nanotube, distribution profiles, boundary conditions, and beam-slenderness ratios.

A free vibration analysis of hybrid laminated composite beam with two different layer stacking sequence is performed to present the advantages of hybrid laminated beam over the conventional FRC beam.