Heat Transfer Of Micropolar Fluid Research Articles

Performance of Heat Transfer in Micropolar Fluid with Isothermal and Isoflux Boundary Conditions Using Supervised Neural Networks

The current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. Generally, the explicit or analytical solutions for such nonlinear problems are hard to calculate. Therefore, we have designed a computer or artificial intelligence-based numerical technique. The reliability of neural networks using the machine learning (ML) approach is used with a local optimization technique to investigate the behaviours of different material parameters such as the Prandtl number, micropolar parameters, Reynolds number, heat index parameter, injection/suction parameter on the temperature profile, fluid speed, and spin/rotational behaviour of the microstructures. The approximate solutions determined by the efficient machine learning approach are compared with the classical Runge–Kutta fourth-order method and generalized finite difference approximation on a quasi-uniform mesh. The accuracy of the errors lies around 10−8 to 10−10 between the traditional analytical solutions and machine learning strategy. ML-based techniques solve different problems without discretization or computational work, and are not subject to the continuity or differentiability of the governing model. Moreover, the results are illustrated briefly to help implement microfluids in drug administering, elegans immobilization, and pH controlling processes.

Study of MHD Mixed Convention Flow and Heat Transfer Through Porous Media

In this present paper, the effects of chemical reaction on two-dimensional mixed convection flow and heat transfer of an electrically conducting micropolar fluid in a porous medium between two parallel plates with Soret and Dufour have been considered. The reduced flow field equations are solved using the quasilinearization method. The effects of various parameters such as Hartmann number, inverse Darcy's parameter, Schmidt number, Prandtl number, chemical reaction rate, Soret and Dufour numbers on the velocity components, microrotation, temperature distribution, and concentration are studied in detail and presented in the form of graphs. The flow through porous boundaries has many applications in science and technology such as water waves over a shallow beach, mechanics of the cochlea in the human ear, aerodynamic heating, flow of blood in the arteries, and petroleum industry. Several authors have studied theoretically the laminar flow in porous channels. Berman [1] considered the viscous fluid and analyzed the flow characteristics when it passed through the porous walls. Later the same problem for different permeability was studied by Terril and Shrestha [2]. The theory of micropolar fluids was introduced by Eringen [3] which are considered as an extension of generalized viscous fluids with microstructure. Examples for micropolar fluids include lubricants, colloidal suspensions, porous rocks, aerogels, polymer blends, and microemulsions. The same Berman problem with micropolar fluid was discussed by Sastry and Rama Mohan Rao [4]. The flow and heat transfer of micropolar fluid between two porous parallel plates was analyzed by Ojjela and Naresh Kumar [5]. Srinivasacharya et al. [6] obtained an analytical solution for the unsteady Stokes flow of micropolar fluid between two parallel plates. The effect of buoyancy parameter on flow and heat transfer of micropolar fluid between two vertical parallel plates was investigated by Maiti [7].

Steady Magnetohydrodynamic Micropolar Casson Fluid of Brownian Motion Over a Solid Sphere with Thermophoretic and Buoyancy Forces: Numerical Analysis

The impact of heat transfer in micropolar fluid may be developed due to its various promising applications in engineering, bio-medical sciences, geo-thermal progression, spherical storage tanks, nuclear power plants, automobile sectors etc. Motivated by such significance, the current study is to expound the influences of micropolar Casson fluid flow over a solid sphere with Brownian motion, thermophoretic force and buoyancy force surrounded by porous medium. The adopted model having complex PDE’s are reduced to dimensionless ODE’s by utilizing proper similarity solutions. A numerical approach have been carried out for velocity, micro rotation, temperature and concentration, the solutions are procured by Matlab Bvp4c code and plotted graphs for diverse involved parameters. An adequate result is acquired by an assessment with earlier available work. The effects of key parameters on surface drag coefficient, surface thermal flux and particles concentration flux are examined and displayed in tabular form. Grash of number raises the profiles of thermal flux and concentration flux where the buoyancy force is more dominant. Further, the obtained results indicate that the angular velocity is elevated near the surface of the sphere, and they behaves asymptotically far away from the surface due to the effect of micropolar parameter. Moreover, temperature and molar species concentration are enriched with upper values of micropolar factor. It is perceived that, augmented values of Casson parameter amplifies the velocity outline.

3D flow and heat transfer of micropolar fluid suspended with mixture of nanoparticles (Ag-CuO/H2O) driven by an exponentially stretching surface

PurposeThe purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H2O) nanofluid past rapid moving surface, where porous medium has been considered.Design/methodology/approachThe model of problem was represented by highly partial differential equations which were deduced by using suitable approximations (boundary layer). Then, the governing model was converted into five combined ordinary differential equations applying proper similarity transformations. Therefore, the eminent iterative Runge–Kutta–Fehlberg method (RKF45) has been applied to solve the resulting equations.FindingsHigher values of vortex viscosity, spin gradient viscosity and micro-inertia density parameters are reduced in horizontal direction, whereas opposite behaviour is noticed for vertical direction.Originality/valueThe work has not been done in the area of hybrid micropolar nanofluid. Hence, this article culminates to probe how to improve the thermal conduction and fluid flow in 3D boundary layer flow of micropolar mixture of nanoparticles driven by rapidly moving plate with convective boundary condition.

Hydromagnetic squeezing flow and heat transfer of micropolar fluid between porous parallel plates

Hydromagnetic squeezing flow and heat transfer of micropolar fluid between porous parallel plates

Numerical simulation for Jeffery-Hamel flow and heat transfer of micropolar fluid based on differential evolution algorithm

This article explores the Jeffery-Hamel flow of an incompressible non-Newtonian fluid inside non-parallel walls and observes the influence of heat transfer in the flow field. The fluid is considered to be micropolar fluid that flows in a convergent/divergent channel. The governing nonlinear partial differential equations (PDEs) are converted to nonlinear coupled ordinary differential equations (ODEs) with the help of a suitable similarity transformation. The resulting nonlinear analysis is determined analytically with the utilization of the Taylor optimization method based on differential evolution (DE) algorithm. In order to understand the flow field, the effects of pertinent parameters such as the coupling parameter, spin gradient viscosity parameter and the Reynolds number have been examined on velocity and temperature profiles. It concedes that the good results can be attained by an implementation of the proposed method. Ultimately, the accuracy of the method is confirmed by comparing the present results with the results obtained by Runge-Kutta method.

Influence of electrical-conductivity of walls on magnetohydrodynamic flow and heat transfer of micropolar fluid

In this paper, flow and heat transfer in a horizontal channel with isothermal walls has been investigated. The upper and lower plate have been kept at the two constant different temperatures, micropolar fluid is electrically conducting, while the channel plates have arbitrary electrical-conductivity. Applied magnetic field is perpendicular to the flow and the full MHD model is investigated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ODE and closed-form solutions are obtained. The profiles of velocity, microrotation, induced magnetic and temperature fields in function of electrical-conductivity and the coupling parameter and the spin-gradient viscosity parameter together with electrical-conductivity, are graphically shown and discussed.

Effect of Nonlinear Thermal Radiation on MHD Boundary Layer Flow and Melting Heat Transfer of Micro-Polar Fluid over a Stretching Surface with Fluid Particles Suspension

A comprehensive numerical study is conducted to investigate effect of nonlinear thermal radiation on MHD boundary layer flow and melting heat transfer of micro polar fluid over a stretching surface with fluid particles suspension. Using suitable transformations, the governing equations of the problem are transformed in to a set of coupled nonlinear ordinary differential equations and then they are solved numerically using the Runge–Kutta–Fehlberg-45 method with the help of shooting technique. Authentication of the current method is proved by having compared with established results with limiting solution. The impact of the various stimulating parameters on the flow and heat transfer is analyzed and deliberated through plotted graphs in detail. We found that the velocity, angular velocity and temperature fields increase with an increase in the melting process of the stretching sheet. Also it is visualize that the shear stress factor is lower for micro polar fluids as compared to Newtonian fluids, which may be beneficial in flow and heat control of polymeric processing.

Convective heat transfer of micropolar fluid in a horizontal wavy channel under the local heating

A numerical analysis of laminar mixed convection of micropolar fluid in a horizontal wavy channel with a local heater has been carried out. Governing equations formulated in dimensionless stream function, vorticity and temperature have been solved by finite difference method. Effects of Rayleigh number, Reynolds number, Prandtl number, vortex viscosity parameter and undulation number on streamlines, isotherms, vorticity isolines as well as horizontal velocity and temperature profiles with average Nusselt number at the heater have been studied. It has been found that the average Nusselt number is an increasing function of Rayleigh, Reynolds and Prandtl numbers and a decreasing function of undulation number while an influence of vortex viscosity parameter is non-monotonic.

Effect of heat generation on transient flow of micropolar fluid in a porous vertical channel

The present work is performed to study the effect of heat generation on fully developed flow and heat transfer of micropolar fluid between two parallel vertical plates. The rigid plates are assumed to exchange heat with an external fluid by convection. The governing equations are solved by using Crank–Nicolson implicit finite difference method. The effects of governing parameters such as transient, heat generation, micropolar parameter, Prandtl number, Biot number, and Reynolds number on the velocity and temperature profiles are discussed. It is found that the presence of heat generation enhances the velocity and temperature of the micropolar fluid at the middle of the channel.

MHD boundary layer flow and heat transfer of micropolar fluid past a stretching sheet with second order slip

The intention of this article is to examine a second order slip flow and magnetic field on boundary layer flow of micropolar fluid past a stretching sheet. Employing appropriate similarly transformation and non-dimensional variables, the governing non-linear boundary-value problems were reduced into coupled higher order non-linear ordinary differential equation. Then, solution for velocity, microrotation and temperature has been obtained numerically. The equations were numerically solved using the function bvp4c from the matlab for different values of governing parameters. Numerical results have been discussed for non-dimensional velocity, temperature, microrotation, the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient $$ C_{\text {f}}$$ increases as the values of slip parameter $$\gamma $$ increase. However, the local Nusselt number $$-\theta '(0)$$ decreases as both slip parameter $$\gamma $$ and $$\delta $$ increase. A comparison with previous studies available in the literature has been done and an excellent agreement is obtained.

MHD Unsteady Flow and Heat Transfer of Micropolar Fluid through Porous Channel with Expanding or Contracting Walls

MHD Unsteady Flow and Heat Transfer of Micropolar Fluid through Porous Channel with Expanding or Contracting Walls

Unsteady MHD flow and heat transfer of micropolar fluid in a porous medium between parallel plates

This paper presents an incompressible two-dimensional MHD flow and heat transfer of an electrically conducting micropolar fluid between parallel porous plates. The flow is generated by periodic injection or suction at the plates. The non-uniform temperature of the plates is assumed to vary periodically with time. The governing equations are reduced to nonlinear ordinary differential equations by using similarity transformations, then solved numerically using the quasilinearization technique. The profiles of velocity components, microrotatoion, and temperature distribution are studied for different fluid and geometric parameters.

Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder

The current paper offers an analysis of the steady boundary layer flow and heat transfer of a non-Newtonian micropolar fluid flowing through a vertical exponentially stretching cylinder along its axial axis. The obtained system of nonlinear partial differential equations along with the appropriate boundary conditions is abridged to dimensionless form by means of the boundary layer estimates and a suitable similarity transformation. The subsequent nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved numerically with the help of Keller-box method. The effects of the involved parameters are presented through graphs. The allied physical features for the flow and heat transfer characteristics that is the skinfriction coefficient and Nusselt numbers are presented for different parameters.

Flow and heat transfer of a micropolar fluid in a porous channel with expanding or contracting walls

Considering the influence of the viscous dissipation in the energy equation, we investigate the flow and heat transfer of an incompressible micropolar fluid in a channel with expanding or contracting walls. By introducing suitable similarity transformations, the nonlinear partial differential equations are reduced to a system of ordinary differential equations. Homotopy analysis method (HAM) is employed to obtain the series solutions for the velocity, microrotation and temperature distribution. In order to analyze the influence of the micropolar parameter, the Reynolds number and the deformation of the wall, the graphs for velocity components, microrotation, temperature, couple stress and shear stress in the channel are presented and discussed in detail.

The effect of reduced heat transfer in a micropolar fluid in natural convection

Abstract This paper presents the numerical solution to the unsteady natural convection problem in micropolar fluid in the vicinity of a vertical plate, heat flux of which rises suddenly at a given moment. In order to solve this problem the method of finite differences was applied. The numerical results have been presented for a range of values of the dimensionless material properties and fluid Prandtl number. The analysis of the results shows that the intensity of the heat transfer in micropolar fluid is lower compared to the Newtonian fluid.

Numerical Study of Stagnation Point Flow and Heat Transfer of Micropolar Fluid towards a Surface with Viscous Dissipation Effects

In this paper, we present numerical investigation of the problem of steady laminar two dimensional boundary layer stagnation point flow and heat transfer of a Micropolar fluid towards a heated surface in the presence of viscous dissipation. The governing boundary layer partial differential equations are reduced to a set of ordinary ones using similarity transformations. The solutions for different values of Eckert number, Micropolar parameters and Prandtl number are computed, analyzed and discussed. The study reveals that the reverse flow of heat near the surface may occur due to viscous dissipation which may further be enhanced by the increasing values of the Prandtl number. It may be recommended that the viscous dissipation should not be simply ignored while studying the boundary layer stagnation point flows.

Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet

A boundary layer analysis is presented for the flow and radiative heat transfer of an incompressible micropolar fluid over stretching/shrinking sheet with power-law surface velocity and temperature distributions. Dual solutions are analytically obtained firstly by homotopy analysis method (HAM). It is found that dual solutions not only exist for the shrinking flow as reported in the previous literatures, but also exist for the stretching flow. The special case of the first branch (K=0, classical Newtonian fluid) is compared with the existing numerical results of stretching flow in good agreement. Our results show that both solutions are physically meaningful (two solutions are closely related to each other), unlike the results previously reported that only one solution is acceptable. Moreover, the effects of the material parameter K, the radiative Prandtl number Prn, the velocity exponent parameter m and the temperature exponent parameter λ on the flow and heat transfer characteristics are analyzed in detail.

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.

Thermal stratification and suction/injection effects on flow and heat transfer of micropolar fluid due to stretching cylinder

SUMMARYIn this paper, a numerical solution of flow and heat transfer in micropolar fluid outside a stretching permeable cylinder with thermal stratification and suction/injection effects. The governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved using numerical technique. The cases of strong concentration of microelement and weak concentration of microelement were considered. Our purpose from this study is to investigate the effects of the governing parameters, namely the suction/injection parameter, thermal stratification parameter, Prandtl number, vortex viscosity parameter and Reynolds number on the velocity profiles, pressure distributions, angular velocity profiles and temperature profiles as well as the skin friction coefficient, dimensionless wall couple stress and the Nusselt number. The numerical results are validated by favorable comparisons with previously published results. The results are shown graphically. The values of the skin friction coefficient, dimensionless wall couple stress and the Nusselt number are presented in tables. Copyright © 2011 John Wiley & Sons, Ltd.