Stability analysis of unsteady stagnation-point gyrotactic bioconvection flow and heat transfer towards the moving sheet in a nanofluid

The present work investigated the unsteady stagnation-point flow and heat transfer of a nanofluid containing gyrotactic microorganisms past a permeable moving surface. The similarity transformations produced the mathematical model in the simpler form, which is in the form of ordinary differential equations, and the collocation method solved it numerically. The dual solutions are observable when the governing parameters vary. The decelerating flow and weak effect of suction at the shrinking sheet delays the boundary layer separation. Stability analysis showed that the upper branch solution is a solution with the stabilizing feature while the lower branch solution is an unstable solution which implies the flow with separation. This theoretical study is significantly relevant to microscopic biological propulsion integrated with the nano-based system.     

Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis

This research presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in the presence of distinct thermal features. The novel aspects of various features, such as Joule heating, porous medium, dissipation features, and radiative mechanism are addressed. In order to improve thermal transportation systems based on nanomaterials, convective boundary conditions are introduced. The thermal viscoelastic nanofluid model is expressed in terms of differential equations. The problem is presented via nonlinear differential equations for which analytical expressions are obtained by using the homotopy analysis method (HAM). The accuracy of solution is ensured. The effective outcomes of all physical parameters associated with the flow model are carefully examined and underlined through various curves. The observations summarized from current analysis reveal that the presence of a permeability parameter offers resistance to the flow. A monotonic decrement in local Nusselt number is noted with Hartmann number and Prandtl number. Moreover, entropy generation and Bejan number increases with radiation parameter and fluid parameter.     

Effect of thermal stratification on free convection in a square porous cavity filled with a nanofluid using Tiwari and Das' nanofluid model

Natural convection in a square porous cavity filled with a nanofluid in conditions of thermal stratification has been numerically studied. The mathematical model has been formulated in terms of the dimensionless stream function and temperature using the Darcy–Boussinesq approximation and Tiwari and Das' nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids. Formulated partial differential equations along with the corresponding boundary conditions have been solved by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, thermal stratification parameter, porosity of the porous medium, solid volume fraction parameter of nanoparticles, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It has been observed an essential effect of thermal stratification parameter on heat and fluid flow fields.     

FEM for Blood-Based SWCNTs Flow Through a Circular Cylinder in a Porous Medium with Electromagnetic Radiation

This work aims to study magnetohydrodynamic flow through a circular cylinder in a horizontal position of SWCNTs in blood as a base fluid in the existence of non-linear thermal radiation and heat source/sink. Three kinds of nanoparticles shapes are considered. The study is employed the finite element technique to explore and enhance the influences of essential parameters on temperature profiles and is debated the heat transport within blood injects with SWCNTs and exposes to electromagnetic radiation. The treatment with thermal analysis and heat transfer rate being a better substitute more than surgery and chemotherapy for cancer therapy. Utilizing of nanoparticles thermal features is a mounting area of nanomedicine field because of the probable for purposeful demolition of cancer cells.This remedy is relied on many parameters, including nanofluid thermal conductivity, nanoparticles volume fraction,thermal radiation and power and heat source. The numerical solutions for flow and heat transfer features are assessed for diverse governing parameters values. The obtained results are substantiated against the relevant numerical results in the published researches. Results show that both flow velocity and temperature increase for larger values of thermal radiation, heat source and SWCNTs volume fraction with lamina and cylinder shapes. Also, spherical shape of SWCNTs occurs high disturbances in velocity and temperature distribution in the case of cooled cylinder.     

Simultaneous investigation of MHD and convective phenomena on time-dependent flow of Carreau nanofluid with variable properties: Dual solutions

In countless applications, there is a thoughtful necessity for augmenting the poor thermal conductivity of conventional liquids to improve effectual heat transfer liquids. Nanofluids are fluids interruptions of nanoparticles and broad scrutiny have been presented on nanoliquid solicitations in heat transfer progressions. The intention of this exertion is to scrutinize the dual nature solutions of unsteady magnetite Carreau nanofluid influenced by porous stretching/shrinking surface. The phenomena of heat and mass transfer have been established in the manifestation of combined convective conditions with heat sink/source and variable thermal conductivity. By utilizing compatible conversions to rehabilitate the structure of nonlinear partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs) which were then elucidated numerically via bvp4c. Under the impact of diverse somatic parameters the graphical depiction of all the probable dual solutions of velocity, temperature, concentration, skin-friction coefficient, local Nusselt and Sherwood numbers are scrutinized. These outcomes specify that the liquid velocity display similar tendency for both upper and lower solutions and decline for unsteadiness parameter, while it enhance for Weissenberg number.     

Nanofluid MHD natural convection through a porous complex shaped cavity considering thermal radiation

Control volume based finite element method (CVFEM) is applied to simulate H₂O based nanofluid radiative and convective heat transfer inside a porous medium. Non-Darcy model is employed for porous media. Influences of Hartmann number, nanofluid volume fraction, radiation parameter, Darcy number, number of undulations and Rayleigh number on nanofluid behavior were demonstrated. Thermal conductivity of nanofluid is estimated by means of previous experimental correlation. Results show that Nusselt number enhances with augment of permeability of porous media. Effect of Hartmann number on rate of heat transfer is opposite of radiation parameter.     

Entropy analysis on unsteady MHD biviscosity nanofluid flow with convective heat transfer in a permeable radiative stretchable rotating disk

We examine the entropy analysis in three-dimensional hydromagnetic flow and convective heat transport of a biviscosity nanofluid over a rotating porous disk with a time-dependent stretching rate in the direction of the radius of the circular disk. We also examine the influence of thermal radiation and viscous dissipation due to nanoparticles and applied magnetic field. We invoked suitable self-similar transformations to covert the modeled coupled nonlinear PDEs into a set of nonlinear ODEs. The transformed system of equations is then worked out numerically by a well-known shooting technique and the fourth-order Runge–Kutta–Fehlberge method. The rotating phenomenon yields an additional parameter known as a rotation parameter, which controls the disk’s rotation. The study shows that the fluid motion is accelerated along the radial and cross-radial directions with an increase in the rotation of the disk. The skin-friction and the heat transfer rate at the disk strongly depend on the rotation of the disk, permeability of the porous medium, thermal radiation, and nanoparticle size. The Bejan number quantifies the entropy production of the system. It has a considerable impact on the magnetic field, rotation of the disk, thermal radiation, and Biot number. The efficient performance of the system is possible by a suitable choice of the physical parameters discussed in this article.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.     

Natural Convection of Fe_3O_4-Ethylene Glycol Nanofluid under the Impact of Electric Field in a Porous Enclosure

Free convection of Fe_3O_4-Ethylene glycol nanofluid in existence of Coulomb forces is studied. Effect of thermal radiation is taken into account. Properties of nanofluid are varied with supplied voltage and shape of nanoparticles. The bottom wall is considered as positive electrode. Control Volume based Finite Element Method is used to obtain the results, which are the roles of Darcy number(Da), radiation parameter(Rd), Rayleigh number(Ra), nanofluid volume fraction(φ), and supplied voltage(?φ). Results indicate that Nusselt number is an enhancing function of supplied voltage and Darcy number. Maximum values for temperature gradient are occurred for platelet shape nanoparticles.     

Simultaneous features of Wu's slip,nonlinear thermal radiation and activation energy in unsteady bio-convective flow of Maxwell nanofluid configured by a stretching cylinder

This continuation deals with the bioconvection flow of magnetized Maxwell nanofluid over a stretched cylinder in presence of slip effects. The novel features of activation energy and thermal radiation are also encountered to analyze the flow. The higher order slip relations are introduced to inspect the thermal flow problem. The flow model is developed in terms of dimensionless equations via appropriate variables. The numerical simulations are presented with shooting scheme by using MATLAB software. The physical outcomes of interesting parameters are visualized. The observations show that velocity profile reduces with unsteady parameter, curvature constant and second order slip factor. The temperature profile enhanced with first order velocity slip parameter and curvature constant. Moreover, nanofluid concentration reduces with Lewis number and Brownian constant.     

Free convection flow of nanofluid over infinite vertical plate with damped thermal flux

In this article, the unsteady free convection flow and heat transfer of nanofluid past over an infinite vertical plate is considered. The fractional generalized Fourier's law with Caputo time derivatives with power-law model to describe the influence of memory on the nanofluid behavior. The analytical solutions for dimensionless temperature and velocity fields and dimensionless thermal flux are obtained by means of Laplace transformation. The fluid is water based nanofluid containing nanoparticles of CuO or Ag. The effects of fractional and physical parameters are discussed graphically.     

Convective heat transfer flow of nanofluid in a porous medium over wavy surface

In this letter, water base nanofluid flow over wavy surface in a porous medium of spherical packing beds is investigated. The copper oxides particles are taken into account. These properties are rehabilitated when fluid interacts with porous walls. For porous medium, Dupuit–Forchheimer model; an extension of Darcy's law model is utilized. The natures of velocity and temperature profiles of nanofluid are discussed graphically whereas the values of convection heat transfer coefficient in the presence of different nanoparticles concentrations in porous medium is presented in tabular form. The obtained results illustrate that convection heat transfer is improved by nanoparticles concentration but reduces when fluid attract to pores structured medium. On the other hand, when particles are added in fluid, convection heat transfer rate is improved but flow velocity is declined.     

Thermo-physical characteristics during the flow and heat transfer analysis of GO-nanoparticles adjacent to a continuously moving thin needle

Nanofluids have shown significant promise in thermal enhancement of many industrial systems and they have been used extensively in energy applications during recent years. Keeping such applications in mind, the present work exhibits a two-dimensional numerical simulation for the boundary layer flow of Graphene oxide (GO)-nanofluids adjacent to a thin needle along with heat transfer. Influence of heat generation/absorption and viscous dissipation have been included to explore the heat transport analysis. The nanofluid flow is generated due to a continuously moving horizontal thin needle. The non-linear expressions governing the flow and heat transfer analysis are changed into dimensionless form by introducing new dimensionless variables. The novelty of current study is to predict the multiple numerical solutions for dimensionless velocity and temperature fields. Numerical computations and graphical delineations were done with the assistance of MATLAB software. This study explores the impacts of several dimensionless key parameters, like, magnetic parameter, Prandtl number, nanoparticles volume fraction and ratio of needle's velocities on the flow and thermal distributions. The computational results have proved that the fluid temperature enhances for higher values of nanoparticles volume fraction while an opposite is true for velocity distributions. In addition, the computed outcomes revealed that for the case of upper branch solution, significant reduction in skin-friction coefficient is seen for higher magnetic parameter.     

Convective heat and zero-mass flux conditions in the time-dependent second-grade nanofluid flow by unsteady bidirectional surface movement

In this paper, a theoretical model is developed for the deliberation of time-dependent 3D magnetohydrodynamics second-grade (SG) nanofluid with radiation effects past an unsteady stretched surface. The work is carried out by involving the physical effects of thermophoresis and Brownian movement. To find the desired solutions, more practical boundary conditions are introduced familiar as the Robin and zero-mass diffusion conditions. The derived model of partial differential form is reframed into the structure of ordinary differential expressions by implementing the dimensionless variables which are reported numerically through the Runge-Kutta-Fehlberg (RKF) scheme with shooting procedure. Numerically determined skin-friction data and energy transportation rate are also addressed with appropriate analysis. Solutions are performed for nanofluid velocity, concentration of nanoparticles and nanofluid temperature. The analysis of dissimilar parametric values on liquid velocity, concentration of nanoparticles and temperature is reported using plots and tabulated data. The presence of Hartman and Biot numbers demonstrated the higher temperature curves. The nanoparticle concentration and temperature distributions reduced for larger unsteady parameter values. A comparison is also provided for limiting cases to authenticate our obtained results.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption in a Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption.Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method(HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N _b, thermophoresis parameter N _t, radiation parameter N _r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Theoretical solution of impulsively started vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation

An analysis is performed to study the free convective flow over a moving vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation. The fluid considered here is a gray, absorbing-emitting radiation, but a nonscattering medium. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature, skin friction and Nusselt number are studied for different parameters like the radiation parameter, Grashof number, Prandtl number, magnetic field parameter, permeability parameter, and time. It is observed that the velocity decreases with increasing radiation parameter.     

Flow and heat transfer of a hybrid nanofluid past a permeable moving surface

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al₂O₃) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.