In this article, the intra-uterine flow with small suspended particles under the impact of heat transfer is investigated. Intra-uterine fluid motion occurs in a non-pregnant uterus which is essential for examining the embryo movement in a uterus. It also plays a key role in assisting sperm movement to the fallopian tube. The Jeffrey fluid through a tapered channel with compliant boundary walls is taken into account. The proposed Jeffrey fluid model has the following features. It is electrically conducting, incompressible, irrotational with constant density, etc. The mathematical formulation is conducted under the lubrication approach for both fluid and particulate phases. The formulated equations are linearly coupled, which are solved with the help of computational software, and the exact solutions for temperature and velocity profile are presented. The influence of key parameters for velocity, and thermal profiles is illustrated graphically. It is observed that the graphical results are in accordance with the physical expectations. The presented analysis is believed to aid in reducing the risk of miscarriages and fetal withering. The obtained results are helpful in examining the embryo transfer and hydrosalpinx.

Intra-uterine particle–fluid motion through a compliant asymmetric tapered channel with heat transfer

In this study, the time-dependent incompressible 3D solid–liquid Williamson non-Newtonian fluid for momentum and heat flow is evaluated. Flow is generated through a sheet in both x and y directions and effected by MHD, dust particles and nonlinear thermal radiations. Problem controlling partial differential equations are converted into ordinary differential equations by using appropriate transformations. The finalized mathematical model is evaluated by ‘bvp4c method’. Numerical results are compared with already published data. Non-dimensional parameters such as first- and second-ordered radiation parameter, the interaction parameter between fluid and particles, the unsteadiness parameter, the stretching parameter, and others are discussed that how they affect the velocity and heat distribution. Physical quantities nusselt number and skin friction are also analyzed numerically as well as graphically.

Numerical analysis of unsteady flow of three-dimensional Williamson fluid-particle suspension with MHD and nonlinear thermal radiations

Combined effects of Joule heating and non-uniform heat source/sink on unsteady MHD mixed convective flow over a vertical stretching surface embedded in a Darcy-Forchheimer porous medium

Abstract Little is known on the significance of fluid–particle interaction for velocity and temperature as in the case of centrifuge for separating particles of different types, launching of rockets, and motion of space shuttle through the air when there exist chemical reactions between the flow and the wall. The aim of this study is not only to explore the significance of quartic autocatalytic chemical reaction on the flow of dusty fluid in which the transmission of energy in form of electromagnetic is nonlinear but also to unravel the effects of buoyancy on the velocity of the dust and temperature of the dust. The nonlinear partial differential equations that model the transport phenomenon was transformed, nondimensionalised, and parameterised using suitable variables. The corresponding boundary value problems were converted to an initial value problem using the method of superposition and solved numerically. The outcome of the study indicates that enhancement of buoyancy is a yardstick to increase the vertical velocity, horizontal velocity, and shear stress within the fluid domain; increase the velocity of the dust particles; increase the temperature distribution across the flow of dusty fluid; increase the concentration of dusty fluid; and decrease the concentration of the catalyst. It is worth noticing that utmost velocity of the dust occurs at a minimum value of fluid–particle interaction for velocity in the flow over a larger thickness of paraboloid of revolution.

A Note on the Significance of Quartic Autocatalysis Chemical Reaction on the Motion of Air Conveying Dust Particles

The present paper considers suction/injection, constant and variable thermophysical influence in squeezing flow of magnetized blood rheological (Casson) fluid model between two parallel disks subjected to nonlinear convection process, slip and convective surface conditions. The unsteady, squeezing, magnetized, and chemically reacting dissipative fluid flowing between parallel disks is modeled and non-dimensionalized via an applicable similarity transformation. An approximate solution of the flow distributions is sought by employing the Chebyshev Collocation Approach (CCA). In the limiting scenario, an excellent agreement in the present results with the existing literature is obtained. The analysis reveals the dominance of constant thermophysical effect over the variable thermo-properties on velocities and temperature field. Higher thermal/solutal Biot number highlighted the dominance of positive squeezing number while its minimal values showcase the dominance of negative squeezing number on flow and energy field. Therein, the squeezing effect remains invariant for some range values of thermal/solutal Biot number, while a rise in velocity slip and suction parameter enhanced the fluid velocities and concentration profiles respectively. Moreover, the current analysis is applicable in moving engines such as in parallel disk gate valve, locomotion of piston in ring where oil is viewed as Casson fluid, thermoforming, injection molding, biomedical use among others.

Thermophysical impact on the squeezing motion of non-Newtonian fluid with quadratic convection, velocity slip, and convective surface conditions between parallel disks

K.R. Madhura

Papers

Impact of temperature-dependant viscosity and thermal conductivity on MHD boundary layer flow of two-phase dusty fluid through permeable medium

Magnetohydrodynamic boundary layer flow of hybrid nanofluid with the thermophoresis and Brownian motion in an irregular channel: A numerical approach