Free Convection Flow Of Nanofluid Research Articles

The Newtonian heating effect on MHD free convective boundary layer flow of magnetic nanofluids past a moving inclined plate

The effect of magnetic strength on the MHD free convection flow of nanofluids over a moving inclined plate with Newtonian heating is analyzed. The governing partial differential equations with Newtonian heating boundary conditions are transformed into a system of nonlinear coupled ordinary differential equations (ODEs) by using similarity transformations. The Keller Box method was used as a solvation method for ODEs. The skin friction and Nusselt number are evaluated analytically as well as numerically in a tabular form. Numerical results for velocity and temperature are shown graphically for various parameters of interest, and the physics of the problem is well explored. The significant findings of this study are promoting an angle of an aligned magnetic field, magnetic strength parameter, the angle of inclination parameter, local Grashof number, the volume fraction of nanoparticles, and Newtonian heating parameter. The result shows that the moving inclined plate in the same direction increases the skin friction coefficient and reduces the Nusselt number. It is also observed that the velocity of moving an inclined plate with the flow is higher compared to the velocity of moving an inclined plate against the flow. The temperature of a moving inclined plate with the flow is decreased much quicker than the temperature of a moving inclined plate against the flow. The other noteworthy observation of this study demonstrates that the Nusselt number in the Newtonian heating parameter shows that Fe3O4-kerosene is better than Fe3O4-water.

Dual Stratification on the Double Diffusive Magnetohydrodynamics Flow of Nanofluids with Dissipation Effects-Revised Buongiorno Model

We analyze the effects of double stratification and dissipation on the hydro magnetic free convection flow of nanofluids over a vertical plate in this work. Considered two different kinds of nanofluids, such as copper and alumina–water nanofluids. By employing the similarity transformation, partial differential equations are converted into non-linear ordinary differential equations, which can be numerically computed with MATLAB. In practical situations where the heat and mass transfer mechanisms run simultaneously, the analysis of natural convection in the influence of double stratification is a fundamentally interesting and important problem, because of its broad range of engineering applications. These applications include the rejection of heat into the environment, such as lakes, rivers, and seas; the storage of thermal energy, such as solar ponds; and the transmission of heat from thermal sources, such as the condensers of power plants. To highlight the impact of double stratification and dissipation on the hydromagnetic free convective flow of nanofluid over a vertical plate, a wide variety of parameter values are used. The numerical outcomes for the different parameters of velocity, temperature, volume fraction, and concentration are obtained and displayed graphically. The skin friction coefficient and reduced Nusselt number are also determined numerically and tabulated.

Magnetohydrodynamic stagnation point flow and heat transfer effects of Al2O3-Cu/water hybrid nanofluid over a porous stretching surface

In this article, the heat transfer analysis of an unsteady free convection flow of a hybrid nanofluid over a porous stretching sheet subjected to a uniform magnetic field is investigated. The effects of radiation and heat source/sink are taken into consideration. Two different types of nanoparticles namely, aluminum oxide (Al2O3) and copper (Cu) are considered. The unsteady free convection flow of nanofluids over a stretching surface has vast applications in heat exchanger technology, next-generation solar film collectors, geothermal energy storage, etc. In view of this, we considered the time-dependent governing equations. The set of non-linear equations (PDEs) is changed into ordinary differential equations with the help of similarity transformations. The transformed equations are solved by using the MATLAB bvp4c shooting technique. The obtained results are presented and analyzed through graphs and tables. From the results, it is noticed that the free convection parameter enhanced the fluid velocity and temperature in both nanofluid and hybrid nanofluid cases. It is noticed that the hybrid nanofluid has the highest temperature distribution than the nanofluid. It is further observed that the fluid flow is substantially influenced by the variations in the unsteadiness parameter.

Modeling and computation of nanofluid for thermo-dynamical analysis between vertical plates

It is well fact that the computational complexity of unsteady and viscoelastic nanofluid can be measured by mathematical modeling that allows the suitable performance for variations from specific to particular rheological parameters. This manuscript addresses the fractionalized mathematical modeling of an unsteady incompressible Maxwell transient free convection flow of nanofluids in the existence of radiation as well as damped thermal flux by using the Caputo time-fractional derivative. The integral transform technique is invoked on the fractionalized governing equations to find the exact solution. The numerical solution to the problem is also attained by utilizing Stehfest and Tzou algorithms. Finally, for the sake of graphical illustration, the comparative analysis for validating both algorithms on velocity and temperature profiles is performed numerically. The temperature and velocity curves are reduced by growing α for small time, and behavior is contrary for large time. By growing values of [Formula: see text] declines the velocity profiles. Velocity is linearly proportional to relaxation time λ, and the boundary layer difference is decreased by increasing the time. Our achieved solutions via two different numerical methods, that is, Stehfest and Tzou are equal.

Effect of generalized thermal transport on MHD free convection flows of nanofluids: A generalized Atangana-Baleanu derivative model

The purpose of this article is to analyse the influence of a the generalized thermal transport on the free convection flow of a viscous nanofluid inside a cylindrical tube. The generalized Atangana-Baleanu time-fractional differential operator is used to generalized the heat transport equation. The effect of transverse magnetic field is also considered. The close form solutions are found by use of integral transformations, more precisely Laplace and finite Hankel transformations. The graphs depict the influence of fractional and other physical characteristics. Tables illustrate the effect of the volume fraction parameter. It has found that the heat flux given by the fractional equation influence heat transfer because the values of the temperature gradient are attenuated by the weight function in the heat flux expression. The temperature in the nanofluid has a different evolution concerning the fractional parameter.

RETRACTED: Investigation of dynamics of SWCNTs and MWCNTs nanoparticles in blood flow using the Atangana–Baleanu time fractional derivative with ramped temperature

This analysis deals with the mixed free convection flow of nanofluid in the presence of porous space. Human blood is supposed to be a base fluid for which the heat transfer characteristics are performed by using the single- and multi-wall carbon nanotubes. The leading equations of the problem are obtained in dimensionless form by following the appropriate non-dimensional variables. The semi-analytical solution for the temperature and velocity field, the famous Atangana–Baleanu time-fractional derivative and Laplace transform techniques are utilized. The effects of different parameters are studied with interesting physical explanations. The summarized results show that the temperature and velocity profile decreases by varying the value of the fractional parameter. An increasing change in velocity is observed for the Grashof number. Moreover, the solution simulated via fractional model for velocity and temperature profile is more consistent and scalable for any value of the fractional parameter.

Effects of fractional derivative and heat source/sink on MHD free convection flow of nanofluids in a vertical cylinder: A generalized Fourier's law model

This research looked at the unsteady free convection flows of an incompressible viscous fluid with heat/sink in a vertical cylinder containing a mixture of 47 nm alumina nanoparticles in water. The flow direction is subjected to a perpendicular magnetic field. The generalization entails taking into account a new version of the constitutive equation for thermal flux, known as the generalized Atangana-Baleanu derivative, which is based on the generalized time-fractional derivative with Mittag-Leffler kernel. Using the Laplace transform and the finite Hankel transform, closed forms of analytical solutions for temperature and velocity fields, represented with Bessel and generalized G–function of Lorenzo and Hartley functions, are determined. The generalized solutions are appropriate for particularizations to yield solutions corresponding to fractional derivatives with power-law kernel and exponential kernel. The Mittag-Leffler function is a one-parametric function. It is also possible to acquire the usual situation, which corresponds to classical Fourier's law. To compare models based on generalized Atangana-Baleanu, Atangana-Baleanu, Caputo, and Caputo-Fabrizio time fractional derivatives, numerical simulations produced with the program Mathcad are carried out and visually depicted.

Unsteady Free Convection Flow of Nanofluids between Vertical Oscillating Plates with Mass Diffusion

In this paper, free convection of nanofluids flow with oscillating vertical parallel plates and mass diffusion were considered. Obtained equations were converted into ordinary differential equations with appropriate transformations. Method of Laplace transform was used to find the exact solutions of velocity, temperature and concentration profiles from the dimensionless governing equations. Discussion of graph pertaining to different embedded parameters such as Prandtl number, Schmidt number, Grashof and mass Grashof number, oscillating parameter and nanoparticles volume fraction parameter was also added. Skin friction, Nusselt and Sherwood number were also discussed and deliberated.

Unsteady Free Convection Flow of Nanofluid with Dissipation Effect over a Non-Isothermal Vertical Cone

This paper investigated unsteady free convection flow of nanofluid with dissipation effect over a non-isothermal vertical cone. The dimensional governing equations that consists of continuity, energy and momentum equations are reduced by using appropriate dimensionless variables along with variable wall temperature as its initial and boundary conditions. The case when water is the base fluid has been considered and the effects of the solid volume fraction on the flow and heat transfer characteristics are determined for Silver (Ag), Copper (Cu), Alumina (Al2O3) and Titanium oxide (TiO2) nanofluids. The purpose of the study is to investigate numerically the mathematical model by using the Crank-Nicolson method. The discretization equations were computed, and numerical results were plotted using MATLAB software. It has been shown that when the nanoparticles volume fraction increases, the NuX increases and the velocity profile decreases. Moreover, for Silver(Ag), Copper(Cu) and Titanium oxide (TiO2) nanoparticles, the thermal boundary layer decreases at first but later started to increase at certain values as the nanoparticles volume fraction increases. However, for Alumina (Al2O3) nanoparticles, the temperature profile increases as the nanoparticles volume fraction increases. It has also been found in this problem that the Alumina (Al2O3) nanoparticles have the highest heating performance while Silver (Ag) nanoparticles have the highest cooling performance.

Heat transfer in magnetohydrodynamic free convection flow of generalized ferrofluid with magnetite nanoparticles

This article investigates the effects of magnetite $$ {\text{Fe}}_{3}^{{}} {\text{O}}_{4}^{{}} $$ nanoparticles on free convection flow of nanofluid with magnetohydrodynamics. The magnetite $$ {\text{Fe}}_{3}^{{}} {\text{O}}_{4}^{{}} $$ nanoparticles that have been dispersed in water are taken as a conventional base fluid. In order to compare newly fractional derivatives, the governing equations have been fractionalized via Atangana–Baleanu and Caputo–Fabrizio fractional operators. The resulting partial differential equations are solved by employing Laplace transforms. Exact solutions have been investigated for temperature and velocity field via Atangana–Baleanu and Caputo–Fabrizio fractional operators and then expressed in Mittag–Leffler function $$ {\mathbf{M}}_{{\upbeta,\upgamma}}^{\rm{y}} \left( W \right) $$ and M-function $$ {\mathbf{M}}_{\text{q}}^{\rm{p}} \left( W \right) $$ . The enhancement of heat transfer and effects in the natural convection flows are analyzed graphically by Atangana–Baleanu and Caputo–Fabrizio fractional operators. Graphical comparison has been depicted via Atangana–Baleanu and Caputo–Fabrizio derivatives for four types of models, i.e., (1) fractionalized nanofluid with magnetic field, (2) ordinary nanofluid with magnetic field, (3) fractionalized nanofluid without magnetic field and (4) ordinary nanofluid without magnetic field on fluid flows.

Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag–water nanofluid has higher skin friction and surface temperature than the Cu–water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

G-Jitter Free Convection Flow of Nanofluid in The Three-Dimensional Stagnation Point Region

The three dimensional free convection boundary layer flow near a stagnation point region is embedded in viscous nanofluid with the effect of g-jitter is studied in this paper. Copper (Cu) and aluminium oxide (Al2O3) types of water base nanofluid are cho- sen with the constant Prandtl number, Pr=6.2. Based on Tiwari-Das nanofluid model, the boundary layer equation used is converted into a non-dimensional form by adopting non- dimensional variables and is solved numerically by engaging an implicit finite-difference scheme known as Keller-box method. Behaviors of fluid flow such as skin friction and Nusset number are studied by the controlled parameters including oscillation frequency, amplitude of gravity modulation and nanoparticles volume fraction. The reduced skin friction and Nusset number are presented graphically and discussed for different values of principal curvatures ratio at the nodal point. The numerical results shows that, in- crement occurs in the values of Nusset number with the presence of solid nanoparticles together with the values of the skin friction. It is worth mentioning that for the plane stagnation point there is an absence of reduced skin friction along the y-direction where as for axisymmetric stagnation point, the reduced skin friction for both directions are the same. As nanoparticles volume fraction increased, the skin friction increased as well as the Nusset number. The results, indicated that skin frictions of copper are found higher than aluminium oxide.

Free convection flow of nanofluids between two vertical plates with damped thermal flux

In this article, we consider the transient free convection flow of nanofluids between two vertical parallel plates in the presence of radiation and damped thermal flux. The generalized Fourier's law is considered in thermal flux constitutive equation with a weakly memory. The integral transform technique is used for finding the exact solutions of the fractional governing differential equations for fluid temperature and velocity field. The solutions are presented in the term of the time-fractional derivative of the Wright function and Robotnov and Hartley function. Solutions to the ordinary fluid, corresponding to the fractional parameter equal to unit, are obtained as a particular case of the fractional problem. Numerical calculations are carried out and results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with thermal memory and the ordinary fluid is made.

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.

Unsteady Magnetohydrodynamic Free Convection Flow of Nanofluid Through an Exponentially Accelerated Inclined Plate Embedded in a Porous Medium with Variable Thermal Conductivity in the Presence of Radiation

Unsteady Magnetohydrodynamic Free Convection Flow of Nanofluid Through an Exponentially Accelerated Inclined Plate Embedded in a Porous Medium with Variable Thermal Conductivity in the Presence of Radiation

Numerical solutions of free convection flow of nanofluids along a radiating sinusoidal wavy surface

In this article, our interest is to investigate the free convection boundary-layer flow of a nanofluid past a sinusoidal semi-infinite vertical surface in the non-absorbing medium. The contribution of surface radiative heat flux is employed in the boundary conditions with the help of Stefan-Boltzmann law. Governing equations are transformed into a non-conserved dimensionless system and integrated numerically by means of an implicit finite difference scheme. The accuracy of numerical method is assessed by a comparison of the present results with the earlier published work and it is found that there exists a favorable agreement between the two. Our problem is subject to the influence of a set of parameters, which appear due to the presence of surface radiation, nanoparticles, and transverse curvature of vertical wall. It is noticed that radiative length parameter λ and surface radiation parameter R contribute in a reduction of local skin friction coefficient and local Nusselt number.

English

English

Exact analysis of the transient free convection flow of nanofluids between two vertical parallel plates in the presence of radiation

The transient free convection flow of nanofluids between two long vertical parallel plates has been investigated analytically in the presence of thermal radiation by considering prescribed wall temperature (PWT) and prescribed wall heat flux (PWHF) at one boundary while the other boundary is maintained at the initial fluid temperature. The exact analytical solutions for the nanofluid velocity, temperature, skin friction, and Nusselt number are derived in the form of rapidly converging series with the help of Laplace transform technique. Five different types of water‐based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), titanium oxide (TiO2), and aluminium oxide (Al2O3) are considered in the analysis. The effects of nanoparticle volume fraction, radiation parameter, and temporal variable on the velocity, temperature, skin friction, Nusselt number, volume flow rate, and vertical heat flux have been discussed in detail. Some new heat and fluid flow characteristics of nanofluids have been presented. The present results can be used as a benchmark to validate the numerical solutions of transient free convection flow of nanofluids in a vertical channel for limiting cases. Also, the results are useful in gaining a deeper insight into the relevant practical systems.

Finite element analysis of magnetohydrodynamic transient free convection flow of nanofluid over a vertical cone with thermal radiation

A finite element analysis is performed to study the unsteady natural convection flow of a nanofluid past a vertical cone under the influence of applied magnetic field and thermal radiation. The governing two-dimensional momentum, energy and concentration are highly non-linear coupled partial differential equations. They are solved by finite element method based on Galerkin weighted residual approach. The investigations are conducted for the effects of various physical parameters such as magnetic parameter ( M), Prandtl number ( Pr), radiation parameter ( Rd), Lewis number ( Le), Brownian motion parameter ( Nb), thermophoresis parameter ( Nt), ratio of Grashof numbers and index parameter ( n). The results indicate that the velocity, temperature and concentration fields are significantly dependent on the above-mentioned flow parameters.

Exact solutions for free convection flow of nanofluids with ramped wall temperature

This article aims to study the unsteady convection flow of nanofluids induced by free convection and the oscillating plate condition. The fluid is confined to the region over an infinite vertical flat plate with ramped wall temperature. Five different types of water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina ( Al2O3 and titanium oxide (TiO2 are chosen for this analysis. The Laplace transform technique is applied to obtain exact solutions of velocity and temperature for both cases of ramp and isothermal plate conditions. Ramp and isothermal solutions are compared graphically and it is found that the ramp velocity and the temperature are smaller in magnitude than isothermal velocity and temperature. Corresponding expressions for skin-friction and Nusselt number are also evaluated. The results are plotted for various physical parameters contained in the governing equations and discussed in details. Comparison with earlier results provides an excellent agreement.