A mathematical model for the flow of a Casson fluid due to metachronal beating of cilia in a tube

Understanding locomotion in trilobites by means of three-dimensional models

Trilobites were one of the first animals on Earth to leave their imprints on the seafloor. Such imprints represent behavioral traces related to feeding or protection, in both cases implying different types of locomotion. Modeling how trilobites moved is essential to understand their evolutionary history and ecological impact on marine substrates. Herein, locomotion in trilobites is approached by means of three-dimensional models, which yielded two main gait types. These two gaits reflect basic behaviors: burrowing and walking. This model reveals that trilobites could change their gait and consequently increase rapidly their speed varying the amplitude of the metachronal wave, a change independent from their biological structure. Fast increases in speed enhanced the protection of trilobites against predators and sudden environmental crises. The trilobite body pattern constrained their gaits, controlled by the distance between the pair of legs and between legs in a same segment.

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.

Mucociliary clearance affected by mucus-periciliary interface stimulations using analytical solution during cough and sneeze

Assessment of mucus velocity variations under different conditions including viscosity variation and boundary conditions is useful to develop mucosal-based medical treatments. This paper deals with the analytical investigation of mucus-periciliary velocities under mucus-periciliary interface movements and mucus viscosity variations. The results for mucus velocity show that there is no difference between the two cases under the free-slip condition. Therefore, power-law mucus can be substituted with a high viscosity Newtonian fluid since the upper boundary of the mucus layer is exposed to the free-slip condition. However, when the upper boundary of the mucus layer is under nonzero shear stress levels, including cough or sneeze, the assumption of a high viscosity Newtonian mucus layer is invalid. Moreover, mucus viscosity variations are investigated for both Newtonian and power-law mucus layers under sneeze and cough to propose a mucosal-based medical treatment. The results indicate by varying mucus viscosity up to a critical value, the direction of mucus movement changes. The critical values of viscosity in sneezing and coughing for Newtonian and power-law mucus layers are 10^-4 and 5 × 10^-5 and 0.0263 and 006.024 m² s^-1, respectively. Therefore, the pathogen entry into the respiratory system can be prevented by varying mucus viscosity during sneeze and cough.

Residual time of sinusoidal metachronal ciliary flow of non-Newtonian fluid through ciliated walls: fertilization and implantation

The monitoring of the ciliated walls in the uterine tube has supreme importance in enhancing the sperm to reach the egg (capacitation processes), and at peristaltic ciliary flow has a more favorable residual time along the canal when compared to the peristaltic flow. Based on the importance of this study, a mathematical simulation of this process has been carried out by studying the behavior of a non-Newtonian magnetized fluid with a Darcy flow model with an oscillating wall having an internal ciliated surface. The governing equation is formed with Eyring-Powell fluid (tubal fallopian fluid) without using any approximations and solved using the Adomian analysis method. Using the vorticity formula, the components of the velocity function, pressure gradient, and stream function are obtained. The influence of relevant parameters is explained through diagramming and discussion. We also analyzed the residue time effects on the flow parameters. The results indicate that peristaltic ciliary flow has a more favorable residual time along the canal when compared to peristaltic flow.

MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model.