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Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature.

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the impact of variable thermal conductivity on the mixed convective cilia beating transport of viscous fluid in a curved channel in the presence of radial magnetic field. The energy equation is also modulated with heat source/sink and viscous dissipation impacts. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). The numerical results concerning the impacts of various physical parameters on the velocity, temperature, pumping phenomena, and streamlines are graphed and explained. The obtained results indicate that as the Hartman number upsurges, fluid velocity reduces, and the Brickman number shows stronger viscous dissipation effects, leading to an increase in the fluid temperature. [ABSTRACT FROM AUTHOR]

Micropolar fluid flow in a channel with variable viscosity, variable thermal conductivity and activation energy is examined numerically using the Runge–Kutta Fehlberg method in this article. Two different boundary conditions are postulated in this study namely Prescribed Surface Temperature (PST) and Newtonian Heating (NH). The numerical outcomes are compared to check the precision of the suggested problem. Significant metrics like Reynolds number, Peclet number for heat and mass transfer, Schmidt number, Activation energy and chemical reaction parameter are graphically described. The influence of the parameters like spin gradient viscosity, vortex viscosity, micro-inertia density on the flow fields are discussed and shown. According to the graphic data, the velocity increases as the viscosity parameter increases whereas the temperature decays for larger values of variable thermal conductivity and also, activation energy enhances the concentration profile. The variation in viscosity parameter shows a significant effect on thermal distribution. The viscosity variation parameter enhances the shear stress and the couple stress. The Peclet number for heat transmission displays a changing effect for high and low Biot numbers regardless of the effect of variable thermal conductivity. This analysis tabulates the link between Nusselt number and Sherwood number over a Peclet number for heat and mass transfer. The skin friction coefficient increases with the viscosity parameter ∊ whereas enhancement in the thermal conductivity parameter decreases the Nusselt number. Furthermore, sensitivity analysis is carried here by developing RSM in order to identify the variations in the input values for the parameters Peh,Pem and N1. The response surface equation is created by using the software package MINITAB-16 by design of experiments. The regression model’s quality of fit is assessed by using the Analysis of Variance.

Micropolar fluid flow in a channel with variable viscosity, variable thermal conductivity and activation energy is examined numerically using the Runge–Kutta Fehlberg method in this article. Two different boundary conditions are postulated in this study namely Prescribed Surface Temperature (PST) and Newtonian Heating (NH). The numerical outcomes are compared to check the precision of the suggested problem. Significant metrics like Reynolds number, Peclet number for heat and mass transfer, Schmidt number, Activation energy and chemical reaction parameter are graphically described. The influence of the parameters like spin gradient viscosity, vortex viscosity, micro-inertia density on the flow fields are discussed and shown. According to the graphic data, the velocity increases as the viscosity parameter increases whereas the temperature decays for larger values of variable thermal conductivity and also, activation energy enhances the concentration profile. The variation in viscosity parameter shows a significant effect on thermal distribution. The viscosity variation parameter enhances the shear stress and the couple stress. The Peclet number for heat transmission displays a changing effect for high and low Biot numbers regardless of the effect of variable thermal conductivity. This analysis tabulates the link between Nusselt number and Sherwood number over a Peclet number for heat and mass transfer. The skin friction coefficient increases with the viscosity parameter ∊ whereas enhancement in the thermal conductivity parameter decreases the Nusselt number. Furthermore, sensitivity analysis is carried here by developing RSM in order to identify the variations in the input values for the parameters Pe h , Pe m and N 1 . The response surface equation is created by using the software package MINITAB-16 by design of experiments. The regression model's quality of fit is assessed by using the Analysis of Variance. [ABSTRACT FROM AUTHOR]

The current research article explores the bio-convection magnetized Carreau-nanofluid flow utilizing activation energy and magnetic dipole. Magnetic nanomaterials have significant effect on the magnetized behavior of ferrofluids which leads to robust the changes in fluid viscosity and thermophysical characteristics. Darcy-Forchheimer flow model is also present. Thermal conductivity of nanofluid is dependent on the temperature. Brownian motion and thermophoresis aspects are also accounted. The PDEs are reduced to set of ODEs via appropriate functions. Numerical solutions are achieved with the help of the famous bvp4c solver a built-in function in MATLAB. Numerous flow parameters are graphically and numerically presented with physical significance. The proposed findings could be useful for applications of extrusion systems, organic compounds, improved energy generation and improved manufacturing techniques.

The current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by Jeffrey fluid through a compliant-walled channel. In order to make realistic approximations for the flow characteristics of blood, the channel is considered to be inclined and porous. Furthermore, convective boundary conditions and concentration slip have been employed in the analysis. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution is obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity, whereas exact solution is found for the concentration field. The impact of various parameters included in the study is displayed graphically. A rise in the parameter for variable viscosity is found to accelerate the fluid flow, hence resulting in an increased bolus size. For variable thermal conductivity, a similar influence on the heat transfer was observed. The behaviour of the skin-friction coefficient, Nusselt and Sherwood numbers have also been plotted for the pertinent parameters.

The current research article explores the bio-convection magnetized Carreau-nanofluid flow utilizing activation energy and magnetic dipole. Magnetic nanomaterials have significant effect on the magnetized behavior of ferrofluids which leads to robust the changes in fluid viscosity and thermophysical characteristics. Darcy-Forchheimer flow model is also present. Thermal conductivity of nanofluid is dependent on the temperature. Brownian motion and thermophoresis aspects are also accounted. The PDEs are reduced to set of ODEs via appropriate functions. Numerical solutions are achieved with the help of the famous bvp4c solver a built-in function in MATLAB. Numerous flow parameters are graphically and numerically presented with physical significance. The proposed findings could be useful for applications of extrusion systems, organic compounds, improved energy generation and improved manufacturing techniques. [ABSTRACT FROM AUTHOR]

The current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by Jeffrey fluid through a compliant-walled channel. In order to make realistic approximations for the flow characteristics of blood, the channel is considered to be inclined and porous. Furthermore, convective boundary conditions and concentration slip have been employed in the analysis. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution is obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity, whereas exact solution is found for the concentration field. The impact of various parameters included in the study is displayed graphically. A rise in the parameter for variable viscosity is found to accelerate the fluid flow, hence resulting in an increased bolus size. For variable thermal conductivity, a similar influence on the heat transfer was observed. The behaviour of the skin-friction coefficient, Nusselt and Sherwood numbers have also been plotted for the pertinent parameters. [ABSTRACT FROM AUTHOR]

This article is concerned with the two-dimensional flow of Powell–Eyring fluid with variable thermal conductivity. The flow is caused due to a stretching cylinder. Temperature dependent thermal conductivity is considered. Both numerical and analytic solutions are obtained and compared. Analytic solution is found by homotopy analysis method. Numerical solution by shooting technique is presented. Discussion to different physical parameters for the velocity and temperature is assigned. It is observed that the velocity profile enhances for larger magnetic parameter. It is also further noted that for increasing the value of Prandtl number temperature profile decreases.

This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6].

Abstract The effect of nanofluid and thermal radiation on MHD Williamson fluid over a stretching cylinder in the presence of convective boundary conditions is analyzed. The variable thermal conductivity is considered during the formulation of energy equation. Nonlinear ordinary differential equations are attained by proposing relevant similarity transformations on partial differential equations. These non-dimensional ordinary differential equations are then converted to the system of first order ODEs and solved numerically by shooting method. Results are further compared by using bvp 4 c , a MATLAB built-in function. The results obtained from MATLAB codes are compared with previously published results of the same nature in limiting case. Numerical results of skin-friction coefficient, local Nusselt and Sherwood numbers are systematized in the form of tables. The effect of prominent parameters on velocity, temperature and concentration is displayed by using graphs. It is observed that velocity profile diminishes for the higher values of Weissenberg number but a reverse relation is noticed for the temperature profile. [ABSTRACT FROM AUTHOR]

The temperament of stream characteristic, heat and mass transfer of MHD forced convective flow over a linearly expanding porous medium has been scrutinized in the progress exploration. The germane possessions of the liquid like viscosity along with thermal conductivity are believed to be variable in nature, directly influenced by the temperature of flow. As soon as gaining the system of leading equations of the stream, Lie symmetric group transformations have been employed to come across the fitting parallel conversions to alter the central PDEs into a suit of ODEs. The renovated system of ODE with appropriate boundary conditions is numerically solved with the assistance of illustrative software MAPLE 17. The consequences of the relevant factors of the system have been exemplified through charts and graphs. An analogous qualified survey has been prepared among present inquiry and subsisting reads and achieved an admirable accord between them. The variable viscosity parameter has more significant effect on nanofluid velocity than regular fluid and temporal profile as well as nanoparticle concentration is also influenced with variable viscosity. [ABSTRACT FROM AUTHOR]

This article is concerned with the two-dimensional flow of Powell–Eyring fluid with variable thermal conductivity. The flow is caused due to a stretching cylinder. Temperature dependent thermal conductivity is considered. Both numerical and analytic solutions are obtained and compared. Analytic solution is found by homotopy analysis method. Numerical solution by shooting technique is presented. Discussion to different physical parameters for the velocity and temperature is assigned. It is observed that the velocity profile enhances for larger magnetic parameter. It is also further noted that for increasing the value of Prandtl number temperature profile decreases. [ABSTRACT FROM AUTHOR]

This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6]. [ABSTRACT FROM AUTHOR]

The present paper focuses on the analysis of thermophoretic hydromagnetic slip flow over a permeable flat plate with convective surface heat flux at the boundary and temperature dependent fluid properties in the presence of non-uniform heat source/sink. The transverse magnetic field is assumed to be a function of the distance from the origin. Also it is assumed that the liquid viscosity and the thermal conductivity vary as an inverse function and a linear function of temperature, respectively. The shooting method is employed to yield the numerical solutions for the model. Results show that the thermal boundary layer thickness reduces with increase of surface convection parameter whereas reverse effect occurs for viscosity parameter. It is also observed that the thermophoretic parameter decreases the concentration distribution across the boundary layer. [ABSTRACT FROM AUTHOR]