Brinkman Type Fluid Research Articles

Mathematical Solution for Free Convection Flow of Brinkman Type Fluid in the Channel with the Effect of Accelerated Plate

The main purpose of this research is to formulate the mathematical models and solution for the effect of accelerated plate on free convection flow in Brinkman type fluid through two vertical channels. Using the appropriate dimensionless variables, the dimensional governing energy and momentum equations are reduced to dimensionless equations subjected to the associated initial boundary conditions. The analytical solutions are obtained by using Laplace transform method. Dimensionless parameters are obtained through dimensionless processes such as Grashof number Gr, Acceleration plate parameter, R, Prandtl number Pr, Brinkman type fluid parameter and time, t. The mathematical findings for velocity and temperature are graphically plotted to investigate the influence of dimensionless variables on profiles. It is observed that fluid velocity increases with increasing of Gr and t whereas it decreases with increasing of , R and Pr. Besides that, it is found that temperature profiles decrease with a high value of Prandtl number, Pr while increase with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and also with numerical Gaver-Stehfest algorithm. Both comparisons show that the solution is to be in a mutual agreement.

Fractional study of radiative Brinkman-type nanofluid flow across a vertical plate with the effect of Lorentz force and Newtonian heating

Contaminant removal from water is accomplished using a variety of technologies, with adsorption being the simplest, successful, cost-effective, and long-term solution. Nanocomposites made from clay minerals and polymers have developed as a new method for cleaning contaminated water in recent years. Therefore, in this paper, clay-based water nanoliquid has been analyzed across a vertical sheet. For flow analysis, Brinkman-type fluid model has been considered along with the consequences of first-order chemical reaction and heat generation/heat absorption. Conditions for Slippage velocity and Newtonian heating also have been taken into account. Using relative constitutive equations, a mathematical model for the flow analysis has been formulated in terms of coupled partial differential equations and then generalized by using constant proportional caputo fractional derivative. The fractional Laplace transform approach was used to solve the problem for exact analytical solutions. The physics of several essential flow constraints vs velocity, thermal energy, and concentration propagation have been addressed graphically using the exact solutions. To check the validity and correctness, the obtained solution is evaluated with the published work. It is worth mentioning that the heat transition rate in the fluid increases by 8.7671% by the accumulation of clay nanoparticulates, while the rate of mass transmission increases by 11.830%.

Ramped heating in CNTS fractional nanofluids

The purpose of this paper is to examine the impact of generalized convective heat transfer through an inclined plate using nanofluids. CNTs (Carbon nanotubes) in both shapes (single wall Carbon nanotubes-SWCNTs and multiple walls carbon nanotubes-MWCNTs) are added to water to improve thermal conductivity and gain a better understanding of nanofluids. Using the Caputo Fabrizio derivative, the constitutive equation of the Brinkman type fluid model exposed to ramped wall boundary conditions is generalized (BC). Laplace transformations are used to extract the precise analytical solutions. The graphs show how fractionality and physical characteristics relate to one another. The fractional parameter causes an increase in the isothermal heat flow however this trend can be reversed by ramping up the heat flux. The Caputo Fabrizio fractional parameter has been discovered to increase isothermal heat flow, albeit this trend is found to be reversible for ramping heat flux. Compared to MWCNTs, SWCNTs have a higher thermal conductivity, which results in a larger heat flux in the SWCNTs nanofluid. As the volume concentration of CNTs nanoparticles increases, the heat transfer rate in CNTs nanofluids increases. Skin friction increases with isothermal heating. An interesting applications of ramped heating system can be seen in luxury apartment projects.

CAPUTO TIME FRACTIONAL MODEL BASED ON GENERALIZED FOURIER’S AND FICK’S LAWS FOR BRINKMAN-TYPE FLUID: EXACT SOLUTION VIA INTEGRAL TRANSFORM

This paper proposes a new method for the development of the Caputo time fractional model. The method relies on generalized Fourier’s and Fick’ laws to describe the flow behavior of Brinkman-type fluids. An analysis of the free convection flow through a channel is carried out using a new transformation method. This transformation affects fluid energy and concentration equations. The specific governing equations are solved using a Laplace transform and Fourier sine transform. We obtain the solutions of the governing partial differential equations (PDEs) in terms of the Mittag–Leffler function. Mathematical software has been used for both graphical and numerical computation in order to examine the effects of embedded parameters. From graphical and tabular analysis, fractional-order solution provides more than one layer for fluid behavior, thermal, and concentration distribution in the channel. Experimentalists and engineers can choose from many best-fitted layers to compare their data and results. A deviation in the velocity profile’s behavior is also seen for larger values of the Brinkman parameter.

A Time- Fractional Model for Brinkman-Type Nanofluid with Variable Heat and Mass Transfer

Nanofluids are used in a variety of thermal applications, including heat exchangers, automobiles and solar power generation among others. Nanofluids are the next generation of fluids, with thermal properties that exceed traditional fluids. In order to inticipate the heat transport characteristics of an inclined solar collector using nanofluids under the influence of a transverse magnetic field, a generalised Brinkman-type fluid model was developed. The effects of thermal radiation and concentration are also addressed. Moreover, in this article we apply the idea of Caputo time fractional derivative by using the generalized Fick's and Fourier's Law??™s to convert classical governing equations to fractional PDEs. The equations of energy and concentration are transformed with the help of new productive transform initial and boundary conditions. The Laplace and Fourier sine transforms are applied together and solve the transformed equations. The current study used a variety of nano-sized solid particles, including SWCNTs, MWCNTs, ? and , and found that adding of MWCNTs to the water (working fluid) can increase the rate of heat transfer up to 34.84 percent, improving the working ability of inclined solar collectors by increasing their solar radiation absorbtion power.

A generalized dusty Brinkman type fluid of MHD free convection two phase flow between parallel plates

Fractional order derivative operators are regarded to be very complex mathematical tools for implementing more realistic solutions in a wide range of physics and engineering problems. Due to significance applications of fractional derivatives, the aim of this article is analyzed the combinational effect of the magnetic field and heat transfer on Magneto hydrodynamic, free convective, two-phase flow of generalized Brinkman type dusty fluid among two parallel plates. The buoyant force causes the flow, which is aided by natural convection to transfer heat. Furthermore, the left plate travels at a constant speed and the right plate remains fixed, and all spherically dust particles are homogeneously dispersed among the fluid. The problem is modeled mathematically via set of partial differential equations. The Caputo-Fabrizio fractional derivative is employed to generalize the derived PDE's. A combination of Laplace and finite sine Fourier transformations is utilized to get the closed form solution of the problem. The impacts of many factors on temperature, Brinkman fluid, and dust particle velocity have also been examined, including a Grashof number, magnetic parameter, Reynold number, Peclet number and Dusty fluid parameter. Mathcad-15 is used to plot the graphical findings for the dusty fluid, Brinkman fluid, and temperature profiles. For various embedded parameters, the Brinkman fluid and dusty fluid behave similarly. It is concluded that the fractional Brinkman type dusty fluid is more realistic feature as compared to the classical one. The rate of heat transfer can be enhance with the passage of time.

Suction effect on MHD flow of Brinkman-type fluid with heat absorption and first-order chemical reaction

Suction/injection is a mechanical effect and used to control the energy losses in the boundary layer region by reducing the drag on the surface. In this study, unsteady MHD flow of Brinkman-type fluid with suction/injection, heat absorption, and chemical reaction is investigated and an analytical solution is established. The corresponding results for temperature, concentration, and velocity fields are obtained with the help of the Laplace transformation method analytically. The physical effects of thermal and mass Grashoff number, Prandtl number, Schmidt number, heat absorption parameter, first-order chemical reaction parameter, suction/injection, Brinkman parameter, and magnetic parameter have been discussed graphically. Finally, it is observed that in the presence of suction effect, fluid’s velocity decreases gradually by increasing the value of suction parameter while show an increasing trend for the increasing value of the injection parameter.

Analysis of Fractional Bioconvection with Hybrid Nanoparticles in Channel Flow

In this paper, MHD Brinkman-type fluid flow containing titanium dioxide and silver nanoparticle hybrid nanoparticles with generalized Mittag–Leffler kernel-based fractional derivative is investigated in the presence of bioconvection. The governing equations with dimensional analysis and fractional approach are obtained by using the fractional Fourier’s law for heat flux and Fick’s law for diffusion. As a result, the bioconvection Rayleigh number, which is responsible for the declining in the fluid velocity and fractional parameters used to control the thermal and momentum boundary layers thickness of fluid properties. The obtained solutions can be beneficial for proper analysis of real data and provide a tool for testing possible approximate solutions where needed.

Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives

The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy’s law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by this law. To overcome this difficulty, Brinkman proposed a new idea of Brinkman-type fluid in highly porous media. In this study, the Brinkman-type fluid flow is analyzed with hybrid nanoparticles (a hybridized mixture of clay and alumina), suspended in water taken as a base fluid under the effect of an applied magnetic field. The fluid motion is taken inside a vertical channel with heated walls. Free convection is induced due to buoyancy. The momentum and energy equations are written in dimensionless form using the non-dimensional variables. The energy equation is modified to fractional differential equations using the generalized Fourier’s law and the Caputo fractional derivatives. The fractional model is solved using the Laplace and Fourier transformation. Variations in velocity and temperature are shown for various fractional parameter values, as well as charts for the classical model. For the volume fractions of nanoparticles, the temperature distribution increases, with maximum values of hybrid nanoparticles with the highest specified volume fractions. Moreover, due to hybrid nanoparticles, the rate of heat transfer is intensified.

Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative

This paper considers a particular fluid model known as the fractional free convection flow of Brinkman-type fluid. We use the Caputo derivative to describe the constructive equations of this model. The main objective of the present investigations will be to propose the exact analytical solutions using the Laplace transformation and its inverse method. After the determination of the exact solutions, the Prandtl (Pr), the Grashof parameters (Gr) and (Gm), the Schmidt parameter (Sc), the Brinkman number for fluid, and the chemical reaction parameter will attract our attention, and their impacts on the modeling will be provided and explained in term of physical viewpoints. Due to the heredity and the memory, the Caputo derivative will impact the mass diffusivity of the considered fluid. Therefore, the velocity and the temperature distributions can increase or decrease depending on the value of the order of the fractional operator. The findings of the paper will be illustrated by graphical representations. Note that in the expression of the exact solutions some well-known functions will be used as the Gaussian error function, the convolution rule, the exponential functions, and many others.

Fractional Model for the Flow of Brinkman-Type Fluid with Mass Transfer

The flow of fluid with mas transfer is an important phenomenon in the industries and nature. A new scheme for formulating the Caputo time fractional model for the flow of Brinkman-type fluid between the plates was introduced using the generalized Fick’s law. Within a channel, the free convection flow of the electrically conducted Brinkman-type fluid was considered. The governing equations were solved by the techniques of Fourier sine and the Laplace transform. In terms of the special function, namely, the Mittag-Leffler function, final solutions were obtained. To explain the conceptual arguments of the embedded parameters, separate plots are represented in figures. It is worth noting that for increasing the values of the Brinkman-type fluid parameter, the velocity profile decreases.

Stokes Problems for Transient Flow of Brinkman Type Fluid between two Side Walls over an Infinite Plate

: The aim of this paper is to study the transient flow of Brinkman type fluid between two side walls and find out the solutions for Stokes problems by using finite and infinite Fourier sine transforms. Exact solutions have been established and these solutions are presented as a sum of transient and steady-state solutions for both Stokes first and second problems. The governing equation satisfy the appropriate boundary and initial conditions. The obtained results are reduced to those well-known solutions which are published in literature and corresponding for the flow over an infinite plate by making

A Nonsingular Fractional Derivative Approach for Heat and Mass Transfer Flow with Hybrid Nanoparticles

This paper deals with the study of MHD Brinkman type fluid flow containing hybrid titanium (TiO2) and silver (Ag) nanoparticles with nonlocal noninteger type Atangana‐Baleanu (ABC) fractional differential operator. The problem is designed for the convective flow restrained in a microchannel. With the Mittag–Leffler kernel, the conventional governing equations are converted into dimensionless form and then generalised with noninteger order fractional operators. The solutions for temperature and velocity fields obtained via Laplace transform method and expressed in the series form. The effect of related parameters is dignified graphically with the help of Mathcad and presented in the graphical section. Finally, the results show that the AB fractional operator exhibited improved memory effect as compared to CF fractional operator. Furthermore, due to increasing the values volume fractional temperature can be enhanced and velocity decreases. In comparison between nanoparticles for different types of based fluid, velocity and temperature of water based (TiO2) and silver (Ag) is higher than other base fluids.

ANALYSIS OF THE FLOW OF BRINKMAN-TYPE NANOFLUID USING GENERALIZED FOURIER’S AND FICK’S LAWS

The enhancement of the working ability of the industrial fluid is the need of the present era; nanofluid is an emerging field in science and technology. In this study, the Brinkman-type fluid model is used and is generalized using the Fourier’s and Fick’s laws. The graphene oxide nanoparticles are dispersed in the base fluid water. The fractional partial differential equations are then solved via the Laplace and Fourier transform method. The obtained solutions for velocity, heat transfer, and mass transfer are plotted in graphs. The results show that velocity profile decreases for Brinkman-type fluid parameter and volume fraction of the nanoparticles. The plot for the fractional parameter shows that different plots can be drawn for a fixed time and other physical parameters, which is the memory effect.

Analysis for Flow of an Incompressible Brinkman-Type Fluid in Thin Medium with Friction

In this paper, we consider the Brinkman equation in the three-dimensional thin domain ℚ ε ⊂ ℝ 3 . The purpose of this paper is to evaluate the asymptotic convergence of a fluid flow in a stationary regime. Firstly, we expose the variational formulation of the posed problem. Then, we presented the problem in transpose form and prove different inequalities for the solution u ε , p ε independently of the parameter ε . Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.

Flow of Brinkman Fluid with Heat Generation and Chemical Reaction

Unsteady magnetohydrodynamics (MHD) flow of fractionalized Brinkman-type fluid over a vertical plate is discussed. In the model of problem, additional effects such as heat generation/absorption and chemical reaction are also considered. The model is solved by using the Caputo fractional derivative. The governing dimensionless equations for velocity, concentration, and temperature profiles are solved using the Laplace transform method and compared graphically. The effects of different parameters like fractional parameter, heat generation/absorption Q , chemical reaction R, and magnetic parameter M are discussed through numerous graphs. Furthermore, comparison among ordinary and fractionalized velocity fields are also drawn. From the figures, it is observed that chemical reaction and magnetic field have decreasing effect on velocity profile, whereas thermal radiation and mass Grashof numbers have increasing effect on the velocity of the fluid.

Generalized Brinkman-Type Fluid Model and Coupled Heat Conductivity Problem

Generalized Brinkman-Type Fluid Model and Coupled Heat Conductivity Problem

Magnetohydrodynamic Blood Flow in a Cylindrical Tube with Magnetic Particles: A Time Fractional Model

The present work theoretically investigates the natural convection blood flow as a Brinkman-type fluid with uniformly distributed magnetic particles in a circular cylindrical tube with the applied external magnetic field. The classical model for the blood flow is generalized by using the definition of Caputo time-fractional derivative. The exact solutions are obtained by using the Laplace and Henkel transforms. Unlike the classical model, the obtained general results are expressed in the form of “Lorenzo and Hartley’s” and “Robotnov and Hartley’s” functions. Graphs are plotted to show the effects of different parameters on the blood flow. Furthermore, the velocity and temperature distributions are discussed in terms of memory. The effect of fractional parameter α for a long and short time has also been observed. It is noticed that blood velocity can be controlled using the fractional parameter. It is also found that, for τ > 0 , fluid and particles motion increased, and reverse behavior is observed for τ < 0 . It has been noticed that increasing values of particle mass parameter P m and magnetic parameter M slow down the motion of blood and magnetic particles. These results are helpful for effective drug delivery and regulating blood flow.

Nanoparticles shape effects on thermal performance of Brinkman-type ferrofluid under heat injection/consumption and thermal radiation: A fractional model with non-singular kernel and non-uniform temperature and velocity conditions

The prime aim of this article is the construction of a fractional model to enhance the heat transfer rate for magnetohydrodynamic (MHD) convectional transport of ferrofluid by applying the time-fractional concept of Caputo-Fabrizio derivative on Brinkman-type fluid model. Kerosene oil and water are considered to serve as carrier fluids for iron oxide (Fe3O4) nanoparticles of various non-spherical shapes (brick, cylinder, platelet, and blade). The non-uniform time-dependent motion of an unbounded upward plate causes to generate the flow of ferrofluid. The supplementary physical phenomena such as ramped heating, thermal radiation, and heat injection/consumption are also analyzed. In addition, the effectiveness of using differently shaped Fe3O4 nanoparticles for heat transfer and ferrofluid flow is evaluated. The exact solutions for non-integer order modeled differential equations are computed by employing the Laplace transform method. The comparative graphical illustrations for ramped and constant (isothermal) velocity and temperature conditions are prepared to scrutinize the impacts of several associated thermal and physical quantities. Besides, the outcomes of numerical simulations of Nusselt number and shear stress are communicated through multiple tables for an in-depth analysis. It is perceived that blade and platelet shaped Fe3O4 nanoparticles are more effective to enhance the thermal efficiency of Brinkman-type ferrofluid in contrast to cylinder and brick shaped nanoparticles. It is interesting to report that an improvement of 13.80% in Nusselt number is observed for water based ferrofluid that significantly advances its thermal properties. The fractional parameter γ produces inverse variations in momentum boundary layer thickness for isothermal and ramped plate cases. Additionally, velocity and temperature curves for ramped plate case are always lower than those of isothermal plate case. This fact highlights the importance of plate ramping in heat and flow control problems.

Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates

In this paper, it has been discussed the fractional model of Brinkman type fluid (BTF) holding hybrid nanoparticles. Titanium dioxide (TiO2) and silver (Ag) nanoparticles were liquefied in water (H2O) (base fluid) to make a hybrid nanofluid. The magnetohydrodynamic (MHD) free convection flow of the nanofluid (Ag-TiO2-H2O) was measured in a bounded microchannel. The BTF model was generalized using constant proportional Caputo fractional operator (CPC) with effective thermophysical properties. By introducing dimensionless variables, the governing equations of the model were solved by Laplace transform method. The testified outcomes are stated as M-function. The impact of associated parameters were measured graphically using Mathcad and offered a comparison with the existing results from the literature. The effect of related parameters was physically discussed. It was concluded that constant proportional Caputo fractional operator (CPC) showed better memory effect than Caputo-Fabrizio fractional operator (CF) (Saqib et al., 2020).