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In this paper, we developed a mathematical model to simulate virus transport through a viscous background flow driven by the natural pumping mechanism. Two types of respiratory pathogens viruses (SARS-Cov-2 and Influenza-A) are considered in this model. The Eulerian-Lagrangian approach is adopted to examine the virus spread in axial and transverse directions. The Basset-Boussinesq-Oseen equation is considered to study the effects of gravity, virtual mass, Basset force, and drag forces on the viruses transport velocity. The results indicate that forces acting on the spherical and non-spherical particles during the motion play a significant role in the transmission process of the viruses. It is observed that high viscosity is responsible for slowing the virus transport dynamics. Small sizes of viruses are found to be highly dangerous and propagate rapidly through the blood vessels. Furthermore, the present mathematical model can help to better understand the viruses spread dynamics in a blood flow.

Electroosmotic flow (electric field induces fluid flow) has modernized the fluid dynamics by enabling precise control over fluid flow at the microscale and explored the new domain of technology i.e., microfluidics-based technology or lab-on-chip devices. This paper studies the membrane pumping-driven electroosmotic flow of non-Newtonian fluids in inclined microchannels where the non-Newtonian nature of fluid is defined by the Casson fluid model. The propagating membrane exhibits rhythmic contractions and relaxations over time. The governing equations are simplified using the lubrication approach, low Reynolds number approximation, and Debye–Hückel linearization, and derived the analytical solutions with the appropriate boundary conditions. The velocity profile, pressure gradient, pumping characteristics, wall shear stress, and stream function are analyzed with respect to key parameters, including the inclination angle, Casson fluid parameter, Helmholtz–Smoluchowski velocity, electroosmotic parameter, zeta potential, Reynolds number, and Froude number. The results reveal that the axial velocity and the pressure difference increase with the Casson fluid parameter, inclination angle, electroosmotic forces, and membrane shape, but decrease with Froude number. Conversely, the pressure gradient enhances with Froude number and declines with other parameters. Stream function magnitude intensifies with increasing inclination angle, Casson fluid parameter, Helmholtz-Smoluchowski velocity, zeta potential, and Reynolds number. These findings enhance the understanding of electroosmotic transport in complex fluids and support the design of efficient microfluidic systems for biomedical, chemical, and micro/nano-technological applications requiring precise flow control.

We explore the physical influence of magnetic field on double-diffusive convection in complex biomimetic (peristaltic) propulsion of nanofluid through a two-dimensional divergent channel. Additionally, porosity effects along with rheological properties of the fluid are also retained in the analysis. The mathematical model is developed by equations of continuity, momentum, energy, and mass concentration. First, scaling analysis is introduced to simplify the rheological equations in the wave frame of reference and then get the final form of equations after applying the low Reynolds number and lubrication approach. The obtained equations are solved analytically by using integration method. Physical interpretation of velocity, pressure gradient, pumping phenomena, trapping phenomena, heat, and mass transfer mechanisms are discussed in detail under magnetic and porous environment. The magnitude of velocity profile is reduced by increasing Grashof parameter. The bolus circulations disappeared from trapping phenomena for larger strength of magnetic and porosity medium. The magnitude of temperature profile and mass concentration are increasing by enhancing the Brownian motion parameter. This study can be productive in manufacturing non-uniform and divergent shapes of micro-lab-chip devices for thermal engineering, industrial, and medical technologies.

Gold-based metal nanoparticles serve a key role in diagnosing and treating important illnesses such as cancer and infectious diseases. In consideration of this, the current work develops a mathematical model for viscoelastic nanofluid flow in the peristaltic microchannel. Nanofluid is considered as blood-based fluid suspended with gold nanoparticles. In the investigated geometry, various parametric effects such as Joule heating, magnetohydrodynamics, electroosmosis, and thermal radiation have been imposed. The governing equations of the model are analytically solved by using the lubrication theory where the wavelength of the channel is considered large and viscous force is considered more dominant as compared to the inertia force relating the applications in biological transport phenomena. The graphical findings for relevant parameters of interest are given. In the current analysis, the ranges of the parameters have been considered as: 0 < κ < 6 , 0 < λ 1 < 0 . 6 , 2 < M < 8 , 0 < ζ 1 < 3 , 0 < ζ 2 < 3 , 0 . 1 < ϕ 1 < 0 . 4 , 0 < B r < 3 , 0 < β < 3 , 0 < R n < 0 . 3 and 0 < ϕ < π / 2 . The current results reveal that, A stronger magnetic field leads the enhancement in nanoparticle temperature and shear stress, and it reduces the velocity and trapping bolus. The nanoparticle temperature rises with the increasing parameters such as Brinkman number and Joule heating parameter.

SignificanceValveless membrane contractions-driven pumping has emerged as a promising mechanism for efficient fluid transport in microfluidic and biomedical systems. Particularly when handling electrically conducting and shear-dependent biological fluids. Understanding the significance of nonlinear rheology, slip effects, and magnetic fields together influencing such transport is essential for designing next-generation microscale pumping devices.Problem statementExisting studies on membrane contraction-driven flows rarely integrate Ree-Eyring shear-thinning behaviour, multi-slip boundary effects, magnetohydrodynamic forcing, and coupled with heat-mass transport effects. As a result, the collective influence of these mechanisms on membrane-driven micro-pumping remains unexplored.Aim of the studyA comprehensive mathematical framework is developed to analyse MHD flow of a Ree-Eyring fluid in a deformable membrane microchannel, incorporating velocity, thermal, and concentration slip, along with heat and mass transfer effetcs.MethodologyThe governing equations are formulated from the Navier–Stokes, energy, and species transport laws and reduced to dimensionless form using long-wavelength and low-Reynolds-number approximations. The analytical solutions are derived for velocity, temperature, concentration, shear stress, stream function, and volumetric flow. A parametric analysis is conducted using MATLAB R2024b to quantify the influences of the Ree-Eyring parameter, Hartmann number, and multi-slip conditions.ConclusionsThis study demonstrates that shear-thinning rheology, magnetic damping, and interfacial slip provide effective control over pumping performance, thermal regulation, and solute transport in membrane-driven microchannels. These insights provide useful strategies for optimising such microfluidic pumping, thermal management, and biomedical transport processes in electrically conducting non-Newtonian fluids.

Tree-based systems in arid region of India are an integral part of livelihood and environment security. Traditionally, the maintenance of scattered trees on farm to reap several tangible and intangible benefits is a way of life. Presently, these systems are often known as low-hanging fruit and become a key weapon to fight climate change evil by offsetting greenhouse gas (GHG) emission through carbon sequestration. Therefore, to quantify the offsetting potential of GHG emission and area occupied by these tree-based systems in Rajasthan was undertaken. The study was carried out into two major aspects: estimation of agroforestry area using satellite remote sensing data, and to estimate the carbon sequestration potential of existing agroforestry by using dynamic CO2FIXv3.1 model for a simulation period of 30-years in five districts (20% sampling), namely, Bikaner, Dausa, Jhunjhunu, Pali and Sikar from Rajasthan, India. The estimated area under agroforestry in Rajasthan was 1.49 million ha. The findings revealed that the major tree species existing on farmer’s field were Prosopis cineraria, Tecomella undulata , Capparis decidua, Acacia tortilis , Prosopis juliflora , Azadirachta indica and Ziziphus mauritiana with an observed number of trees in selected districts varied from 1.40 to 14.90 ha −1 (with average tree density of 9.71 ha −1 ). The total biomass (tree + Crop) varied from 2.22 to 19.19 Mg ha −1 , whereas the total biomass carbon ranged from 1.00 to 8.64 Mg C ha −1 . The soil organic carbon ranged from 4.51 to 16.50 Mg C ha −1 . The average estimated carbon sequestration and mitigation potential of the agroforestry were 0.26 Mg C ha −1  year −1 and 0.95 Mg CO 2 eq ha −1  year −1 on farmers' field of Rajasthan. At the state level, the reduction of GHG emission potential of agroforestry was found to be 1.42 million tonnes annually, which helps to cut carbon footprint and achieve targets of Paris agreement.

The present paper investigates the peristaltic flow of Newtonian fluids through the porous medium. The effects of electroosmosis mechanism on peristaltic pumping are also considered. An analytical solution is obtained under lubrication approach. Poisson Boltzmann equations are also simplified using Debye linearization. The effects of permeability parameter, electrical double layer thickness and electro-osmotic parameter on the flow characteristics, pressure distribution and shear stress distributions are computed. Numerical computations reveal that electroosmosis and permeability play vital role in peristaltic pumping. The findings of present study may be applicable in biomedical engineering and chemical engineering where peristaltic micropumps may be designed.

The present investigation deals with a theoretical study of the peristaltic hemodynamic flow of couple-stress fluids through a porous medium under the influence of wall slip condition. This study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for axial velocity, pressure gradient, frictional force, stream function and mechanical efficiency are obtained. Effects of different physical parameters reflecting couple-stress parameter, permeability parameter, slip parameter, as well as amplitude ratio on pumping characteristics and frictional force, streamlines pattern and trapping of peristaltic flow pattern are studied with particular emphasis. The computational results are presented in graphical form. This study puts forward an important observation that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the amplitude ratio.

In this work, the combined impacts of electroosmosis and peristaltic processes are investigated to better understand the behavior of fluid flow in a symmetric channel. The Poisson–Boltzmann equation is included into the Navier–Stokes equations to account for the electrokinetic effects in micropolar fluid model. The fluid motion caused by electric fields is effectively described by incorporating electrokinetic variables in these equations. Under the premise of a low Reynolds number and small amplitude, the linearized equations are resolved. Partial differential equations are solved to yield analytical formulations for the velocity and pressure fields. As opposed to earlier research, our analysis explores the combined impacts of electroosmosis and peristaltic motion in symmetric channels. By considering these mechanisms together, we gain a comprehensive understanding of fluid movement and manipulation in microchannels. According to research on modifying the properties of fluid flow, zeta potential, applied voltage, and channel shape all affect the velocity of electroosmotic flow. In addition, the flow rate is impacted by the peristaltic motion-induced periodic pressure changes. In addition, the combined effects of peristalsis and electroosmosis show promise for accurate and efficient regulation of fluid flow in microchannels. The study reveals that the micropolar parameter modifications (0–100) have little effect whereas adjusting the coupling parameter (0–1) modifies electroosmotic peristaltic flow. Center streamlines are trapped and then aligned in a length-dependent way by the interaction of electric fields. Several microfluidic applications, including mixing, pumping, and particle manipulation, are affected by the findings of this research. The electroosmosis and peristaltic processes may be understood and used to create sophisticated microfluidic devices and lab-on-a-chip systems. This development has the potential to greatly improve performance and functionality in industries like chemical analysis, biomedical engineering, and other areas needing precise fluid control at the microscale.

The flow analysis of electrolyte solution in microchannel/capillary is essential in various applications of health care such as dialysis and diagnosis processes of biological fluids/samples. To investigate the flow analysis in a homogeneous and isotropic porous microchannel with two membranes fitted at the upper wall surface, a novel biophysical model is presented mathematically. The lower wall surface is kept stationary and negatively charged to analyse the influence of the electroosmosis mechanism. The membranes have a self-propagating pumping process with varying amplitude and phase lag. The continuity and momentum equations are considered to describe the fluid flow and the Poisson–Boltzmann equation is taken to analyse the distribution of the electric potential for the electrolyte solution in the normal direction to a charged surface. To derive the governing equations, we have considered the approximation of low Reynolds number and Debye-Hückel linearization. Using MATLAB coding, key results like velocity, pressure difference, skin friction, volumetric flow rate, and stream function are computed under the influence of significant parameters. Present study finds that the movement of the electrolyte solution can be driven by membrane-based pumping at a small scale and further regulated by electroosmosis. The resistance due to the porous medium impacts the velocity and volumetric flow rate but this resistance can be mitigated by increasing the strength of the external electric field. This analysis is potentially useful for developing membrane-based microfluidic devices to analyse the biological flow at the micro-scale.