Nanofluids are potential heat transfer fluids with improved thermophysical properties and heat transfer performance. Double diffusion convection plays an important role in natural processes and technical applications. The effect of double convection by diffusion is not limited to oceanography, but is also evident in geology, astrophysics, and metallurgy. For such a vital role of such factors in applications, the authors have presented the analytical solutions of pumping flow of third-grade nanofluid and described the effects of double diffusion convection through a compliant curved channel. The model used for the third-grade nanofluid includes the presence of Brownian motion and thermophoresis. Additionally, thermal energy expressions suggest regular diffusion and cross-diffusion terms. The governing equations have been constructed for incompressible laminar flow of the non-Newtonian nanofluid along with the assumption of long wavelength. The obtained analytical expressions for velocity, temperature, and nanoparticle concentration have been sketched for various considerable parameters. The effects of regular buoyancy ratio, buoyancy parameter, modified Dufour parameter, and Dufour-solutal Lewis number have been analyzed along with wall properties and pumping characteristics. This study concludes that fluid becomes hotter with increase in regular buoyancy ratio and a modified Dufour parameter, but a decrease in temperature is observed for the buoyancy parameter. Moreover, the solutal concentration is behaving inversely against the Defour-Solutal Lewis number.

In this article, we discuss the entropy generation on the asymmetric peristaltic propulsion of non-Newtonian fluid with convective boundary conditions. The Williamson fluid model is considered for the analysis of flow properties. The current fluid model has the ability to reveal Newtonian and non-Newtonian behavior. The present model is formulated via momentum, entropy, and energy equations, under the approximation of small Reynolds number and long wavelength of the peristaltic wave. A regular perturbation scheme is employed to obtain the series solutions up to third-order approximation. All the leading parameters are discussed with the help of graphs for entropy and temperature profiles. The irreversibility process is also discussed with the help of Bejan number. Streamlines are plotted to examine the trapping phenomena. Results obtained provide an excellent benchmark for further study on the entropy production with mass transfer and peristaltic pumping mechanism.

In this manuscript, the authors developed the mathematical model for entropy generation analysis during the peristaltic propulsion of Jeffrey nanofluids passing in a midst of two eccentric asymmetric annuli. The model was structured by implementation of lubrication perspective and dimensionless strategy. Entropy generation caused by the irreversible influence of heat and mass transfer of nanofluid and viscous dissipation of the considered liquid was taken into consideration. The governing equations were handled by a powerful analytical technique (HPM). The comparison of total entropy with the partial entropy was also invoked by discussing Bejan number results. The influence of various associated variables on the profiles of velocity, temperature, nanoparticle concentration, entropy generation and Bejan number was formulated by portraying the figures. Mainly from graphical observations, we analyzed that, in the matter of thermophoresis parameter and Brownian motion parameter, entropy generation is thoroughly enhanced while inverse readings were reported for the temperature difference parameter and the ratio of temperature to concentration parameters.

The proposed model of drug delivery has been developed as a medication methodology for the direct treatment of diseased body tissues. The mathematical model is built upon the particulate peristaltic transport of an electrical conducting Jeffrey fluid within an asymmetric duct. The flow takes place under the action of slip effects due to the occurrence of magnetohydrodynamics, which is generally known as electrical resistance and the energy released by charged particles as they make collisions with other particles. Transportation of drug particles along with Jeffry fluid due to peristaltic pumping in a rectangular duct is demonstrated. Magnetic force is utilized for the control of the process of pumping to the flow path at the right position. Taking into consideration the flow conditions and assumptions, the derivation of the system of partial differential equations of the flow is described. The eigenfunction expansion method is used to establish the solutions, and then the data are graphically displayed to imagine the effects of different parameters. It can be professed that the velocity component for Jeffrey fluid flow is decreased because of magnetic force, volume fraction size, and wall compliance. Heat and mass transfer with nanoparticles of different shapes of particles to extend this work.

In this study, a novel model of entropy generation effects measured in the Cu-blood flow of a nanofluid under the effect of ciliary-oriented motion is proposed. The effects of viscous dissipation are also taken into account. The physical model was composed with the incorporation of a low Reynolds number and long-wavelength phenomena. The exact solutions for the axial velocity, temperature and pressure gradient distribution were achieved successfully. Key findings are presented through a strategy of plotting the significant factors affecting the physical quantities of the stream. It was found that the heat absorption parameter and Brownian motion accounted for the large thermal transfer rate, while the effect of entropy was minimal compared to these factors in the center of the flow but increased on the walls in the case of Cu-blood flow. It can also be added that a more intense flow gave rise to the entropy effects. This study may be helpful in medical science as cilia play vital roles, which include cell migration and external fluid transport, in human tissues and some key organs. Moreover, the considered annulus-shaped geometry gives vital readings that are used in medical equipment such as endoscopes.