Thermal and physical impact of viscoplastic nanoparticles in a complex divergent channel due to peristalsis phenomenon: Heat generation and multiple slip effects.

In the advance studies, researchers have performed productive research contributions in the field of nanofluid mechanics under various biological assumptions. These contributions are fruitful to understand the applications of nanofluids in the various fields such as hybrid-powered engine, heart-diagnose, to prevent numerous diseases, heat exchanger, pharmaceutical processes, etc. The current analysis explores the combined effects of heat generation and chemical reaction on the peristaltic flow of viscoplastic nanofluid through a non-uniform (divergent) channel. The physical effects of second-order velocity slip, thermal slip and mass slip parameters on the rheological characteristics are also considered. To describe non-Newtonian effects, the Casson fluid is deployed. The greater wavelength assumption and low Reynolds number theory are used to attain the rheological equations. Numerical solutions of these governing equations associated with suitable boundary conditions are obtained via Mathematica symbolic software. The velocity magnitude of Casson fluid is higher than associated with Newtonian fluid. Radiation parameter has a vigorous impact in the reduction (enhancement) of temperature (mass concentration) profile. The porous parameter has a remarkable impact in reduction of temperature and velocity profile. Thermal enhancement is perceived by intensifying the chemical reaction parameter, and opposite inclination is noticed in mass concentration. Temperature has been demonstrated to be increased by increasing the Darcy number. The magnitudes of both axial velocity and temperature distribution are smaller in the presence of second-order velocity slip parameters effect as compared with no-slip condition. The magnitudes of axial velocity and mass (or, nanoparticle) concentration are augmented by accumulating the Prandtl number. A rise in Brownian parameter is noticed to depress the mass concentration. The present study has been used in bio-mechanical processes, nanomaterial devices, heat transfer enhancement, radiators, and electronics cooling systems.

The Impact of Different Arrangements of Molecular Chains in Terms of Low and High Shear Rate's Viscosities on Heat and Mass Flow of Nonnewtonian Shear thinning Fluids.

BACKGROUND: Non-newtonian fluids, especially shear thinning fluids, have several applications in the polymer industry, food industry, and even everyday life. The viscosity of shear thinning fluids is decreased by two or three orders of magnitude due to the alignment of the molecules in order when the shear rate is increased, and it cannot be ignored in the case of polymer processing and lubrication problems. OBJECTIVE: So, the effects of viscosities at the low and high shear rates on the heat and mass boundary layer flow of shear thinning fluid over moving belts are investigated in this study. For this purpose the generalized Carreau model of viscosity relate to shear rate is used in the momentum equation. The Carreau model contains the five parameters: low shear rate viscosity, high shear rate viscosity, viscosity curvature, consistency index, and flow behavior index. For the heat flow, the expression of the thermal conductivity model similar to the viscosity equation due to the non-Newtonian nature of the fluid is used in the energy equation. METHODS: On the mathematical model of the problem, boundary layer approximations are applied and then simplified by applying the similarity transformations to get the solution. The solution of the simplified equations is obtained by numerical technique RK-shooting method. The results are compared with existing results for limited cases and found good agreement. RESULTS: The results in the form of velocity and temperature profiles under the impact of all the viscosity's parameters are obtained and displayed in graphical form. Moreover, the boundary layer parameters such as the thickness of the regions, momentum thickness, and displacement thickness are calculated to understand the structure of the boundary layer flow of fluid. CONCLUSION: The velocity and temperature of the fluid are decreased and increased respectively by all viscosity's parameters of the model. So, the results of the boundary layer fluid flow under rheological parameters will not only help engineers to design superior chemical equipment but also help improve the economy and efficiency of the overall process.

Double-diffusion convective biomimetic flow of nanofluid in a complex divergent porous wavy medium under magnetic effects.

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.

Cilia-assisted flow of viscoelastic fluid in a divergent channel under porosity effects.

Cilia-driven laminar flow of an incompressible viscoelastic fluid in a divergent channel has been conducted numerically using the BVP4C technique. The non-Newtonian Jeffrey rheological model is utilized to characterize the fluid. The flow equations are formulated in a curvilinear coordinate system, and the porosity effects are simulated with a body force term in the Navier-Stokes equation. The flow equations are transformed into a wave frame from a fixed frame of reference using a linear mathematical relationship. A biological approximation of creeping phenomena and the long-wavelength assumption is used in the flow analysis. The flow analysis is carried out by using a complex (wavy) propulsion of cilia beating. The two-dimensional flow is controlled by physical parameters-Darcy's number, curvature parameter, viscoelastic parameter, phase difference, cilia length, and divergent parameter. They also examined the ciliated pumping and bolus trapping in their flow analysis. The boundary layer phenomena in the velocity profile are noticed under more significant porosity and time relaxation effects. The bolus circulations are reduced for a larger porosity medium and larger numeric values of the time relaxation parameter.

Double diffusive convection and Hall effect in creeping flow of viscous nanofluid through a convergent microchannel: a biotechnological applications.

Current analysis presents the mathematical modeling for peristaltic transport of nanofluid with applications of double-diffusive convection and Hall features. The flow has been induced by a convergent channel due to peristaltic propulsion. These rheological equations are transformed from fixed to wave frames by using a linear mathematical relation between these two frames. The dimensionless variables are used to transform these rheological equations into nondimensional forms. The flow analysis is carried out under two distinct scientific biological assumptions, one is known as long wavelength and the second one is low Reynolds number. The analytical solutions of these rheological equations are obtained with the help of a rigorous analytical method known as integration in the term of stream function. The physical effects of magnetic and Hall devices, respectively, on the flow features are also considered in the present analysis. The physical influences of dominant hydro-mechanical parameters on the axial velocity, pressure gradient, trapping, volumetric fraction of nanofluid, heat and mass transfer phenomena are studied. The complex scenario of biomimetic propulsions are considered in boundary walls to boost the proficiency of peristaltic micropumps.

Peristaltic activity for electro-kinetic complex driven cilia transportation through a non-uniform channel.

MOTIVATIONS: Now-a-days in medical science, the transport study of biological fluids through non-uniform vessels are going to increase due to their close relation to the reality. Motivated through such type of complex transportation, the current study is presented of cilia hydro-dynamics of an aqueous electrolytic viscous fluid through a non-uniform channel under an applied axial electric field. Mathematical Formulations: Because of the complexity shape and nature of flow channel, we have used curvilinear coordinates in the derivation of continuity and momentum equationsin a fixed frame of reference. A linear transformation is used to renovate the flow system of equations from fixed (laboratory) to moving (wave) frame. For further simplification, the dimensionless variables are introduced to make the flow system of equations into the dimensionless form and at last convert these equations in term of stream function by using the mathematical terminologies of streamlines. The whole analysis is performed under (low Reynolds number) creeping phenomena and long wavelength approximation, respectively. Additionally, small ionic Peclet number and Debye-Huckel linearization are used to simplify the Nernst-Planck and Poisson-Boltzmann equations. The BVP4C technique is used to obtain the numerical solution for velocity distribution, pressure gradient, pressure rise and stream function through MATLAB. MAIN OUTCOMES: The amplitude of velocity distribution is increased (decreased) at larger values of non-uniform parameter (cilia length). The non-uniform parameter played a vital role not only in the enhancement of circulation at the upper half of the channel but also the length of bolus increased. Results of straight channel are gained for larger value of the dimensionless radius of curvature parameter as well as cilia length.

A theoretical analysis of Biorheological fluid flowing through a complex wavy convergent channel under porosity and electro-magneto-hydrodynamics Effects.

BACKGROUND AND OBJECTIVE: Flow generated via peristaltic waves in naturally occurring physical phenomenon inside human body. Its combination with electric and magnetic forces makes it even more versatile in biomedical engineering applications. The results presented in this article are useful in designing artificial tubes, lab-on-a-chip devices for cell manipulation, drug design, flow amalgamation, micro-scale pumps and micro-bots which can be externally controlled by electric and magnetic sensors. Motivated by the aforesaid facts the current investigation is based on the transportation of a couple stress bio-fluid by peristalsis through a convergent channel under the postulates of creeping phenomena and long wavelength, respectively METHODS: A closed form solution is acquired for the axial velocity profile, volumetric flow rate and streamlines, respectively. The physical influence of involved parameters on the rheological characteristics are argued analytically with the help of Mathematica software 12.0.1 in detail. Additionally, the flow system is considered to take place under the both porosity and electro-magneto-hydrodynamics effects, respectively. The amplitude of axial velocity across one wavelength is strongly affected at the larger values of numerous embedded parameters: Darcy number, Hartmann number, Electro-osmotic velocity parameter and non-Newtonian (couple stress) parameter. RESULTS: We have observed remarkable effects of embedded parameters on velocity distribution, flow rate and trapping phenomena under porous and electro-osmotic (combination of both magnetic and electric) effects. The circulation of boluses and number of streamlines are reduced/enhanced for larger Hartmann number/Darcy number due strong magnetic/porosity effects. This research study additionally tells us how to control the transportation phenomena of biological fluids by appropriate adjusting the porosity effects (the effects of porous media) and electro-osmotic influences. Moreover, in order to enhance the performance of a peristaltic pump at the micro-scale level, we have used complex peristaltic wave scenario in the boundary walls of the convergent micro-channel.

Bio-inspired propulsion of micro-swimmers within a passive cervix filled with couple stress mucus.

BACKGROUND AND OBJECTIVE: The swimming mechanism of self-propelling organisms has been imitated by biomedical engineers to design the mechanical micro bots. The interaction of these swimmers with surrounding environment is another important aspect. The present swimming problem integrates Taylor sheet model with couple stress fluid model. The thin passage containing micro-swimmers and mucus is approximated as a rigid (passive) two-dimensional channel. The spermatozoa forms a pack quite similar as a complex wavy sheet. METHODS: Swimming problem with couple stress cervical liquid (at low Reynolds number) leads to a linear sixth order differential equation. The boundary value problem (BVP) is solved analytically with two unknowns i.e. speed of complex wavy sheet and flow rate of couple stress mucus. After utilizing this solution into equilibrium conditions these unknowns can be computed via Newton-Raphson algorithm. Furthermore, the pairs of numerically calculated organism speed and flow rate are utilized in the expression of power dissipation. RESULTS: This work describes that the speed of micro-swimmers can be enhanced by suitable rheology of the surrounding liquid. The usage of couple stress fluid as compared to Newtonian fluid enhances the energy dissipation and reduces the flow rate. On the other hand complex wavy surface also aids the organisms to swim faster.