Micropolar Boundary Layer Research Articles

Magnetohydrodynamics Micropolar Boundary Layer Flow Past a Stretching Sheet with Microstructural Slip Heat Generation with Convective Boundary Condition

The formulation depicting the magnetohydrodynamics MHD boundary layer of a micropolar fluid on a moving sheet with heat generation and convective boundary conditions in its rectangular form is presented. The PDEs formulated are transformed into nonlinear ODEs via the stream functions and appropriate similarity variables. The solution to the nonlinear coupled equations were presented in decomposed form. The comparison of skin friction values with literatures for validation were carried out and an agreement depicted. The implications of dimensionless physical parameters that appear in this work are graphically studied in the presence of microstructural slip. Physical parameters such as Biot number and heat generation parameters are found to enhance the fluid temperature profile.

Characterization of the Induced Magnetic Field on Third-Grade Micropolar Fluid Flow Across an Exponentially Stretched Sheet

The current research article discusses the two-dimensional, laminar, steady, and incompressible third-grade viscoelastic micropolar fluid flow along with thermal radiation caused by an exponentially stretched sheet. The primary goal of this extensive study is to improve thermal transportation. Thermophoresis and Brownian motion are two key causes of nanoparticle migration in nanofluids, and their impacts on the thermophysical properties of nanofluids are significant. Micropolar fluids are investigated due to their micro-motions that are significant in convective thermal and mass transport polymer formation, nanotechnology, and electronics. The consequences of third-grade fluid parameters, thermophoresis and Brownian motion, induced magnetic field, micro-polarity, and micro-inertia density on the stream of an electrically conductive fluid are analyzed. A homogeneous magnetic field is supplied perpendicularly to the surface, and the liquid is believed to be electrically conducting. As the flow has a significant magnetic Reynolds number, the contribution of the evoked magnetic field is properly accounted in the governing equations. A mathematical model in the form of partial differential equations (PDEs) is built under certain assumptions. By invoking the suitable similarity transformation, the non-linear PDEs are modified into dimensionless coupled ordinary differential equations (ODEs). The MATLAB numerical technique bvp4c is employed to settle the subsequent ODEs together with the boundary constraints. The consequences of numerous physical parameters on the non-dimensional concentration, temperature, micropolar, velocity, and induced magnetic field profiles are portrayed in graphs. It is found that the concentration boundary layer, thermal boundary layer, and micropolar boundary layer thickness decelerate with the increment in the micro-polarity of the fluid.

Joule heating in magnetohydrodynamic micropolar boundary layer flow past a stretching sheet with chemical reaction and microstructural slip

In this article, the microstructural slip principle is applied to the flow of micropolar fluid related to the simulation of different physical scenarios. The fluid flow is pickled with different physical parameters like thermal radiation, thermophoresis, Brownian motion, Joule heating and chemical reaction. The nonlinear system of ordinary differential equations (ODEs) is obtained by using suitable similarity transformations. An analytical method called homotopy analysis method (HAM) is applied to solve the modeled system of equations. A convergence analysis of HAM is also presented. The analytical and numerical solutions of the modeled problem are compared with the help of Figures and Table. Also, a comparative analysis is presented which validate the current analysis. The whole phenomenon is analyzed in the absence and presence of microstructural slip condition. The effect of microstructural slip parameter on the fluid flow is presented through Figures and Tables. The couple stress is calculated for three different cases. In the first two cases whenn=0.0andn=0.5, the couple stress factor increases significantly with the increasing microstructural slip factor. However, for the third case whenn=1.0, a declining influence in couple stress is depicted. A similar impact is depicted on the micro-rotation distribution. Furthermore, the skin friction, Nusselt number, and Sherwood number are calculated through Tables.

On Behavioral Response of Microstructural Slip on the Development of Magnetohydrodynamic Micropolar Boundary Layer Flow

In this paper, the concept of microstructural slip is introduced in the flow of micropolar fluids pertinent to model various physical situations. The flow is modeled by a set of PDEs which are transformed to a nonlinear system of ODEs by employing boundary layer transformations. The system of governing equations is implemented using MATLAB bvp4c function along with the initial-boundary conditions. The code is validated by comparing the computed results in the limiting case with the available literature. Influence of microstructural slip on the skin friction coefficient and Nusselt number along with hydrodynamic and thermal boundary layer profiles is studied and discussed. It is found that, in the presence of microstructural slip, the microrotational velocity boundary layer thickness decreases up to a maximum of 37.5% in its value, in comparison to the case where there is no microstructural slip effect. The results predict that, in the presence of first-order translational slip, the microrotations have shown counterrotational phenomena in comparison to the case where there is no translational slip effect. Moreover, second-order translational slip results in declining the microrotational velocity and associated layer thickness.

Exact and Asymptotic solution of a steady two dimensional boundary layer of a Micropolar fluid flow past a moving wedge

In this paper, we propose an analytic solution of a boundary value problem which models a steady, laminar, two dimensional, boundary layer flow of an incompressible and viscous micropolar fluid over a moving wedge. The governing non-linear partial differential equations are converted into highly non-linear ordinary differential equations using similarity transformations. An analytical exact solution obtained for particular values of parameters are then extended to obtain an exact solution for more general values of the parameters involved. We also propose asymptotic solution of the Micropolar boundary layer flow. The results thus obtained are compared with those of direct numerical solutions, which show a good agreement. The results are discussed in terms of velocity profiles and wall shear stresses for various physical parameters.

Scaling group analysis of bioconvective micropolar fluid flow and heat transfer in a porous medium

The current and potential applications of bioconvection renewed drive for theoretical research on synthesis and process control in biofuel cells and bioreactors. Thus, this work devoted to solving the problem of free convection in micropolar boundary layer fluid flow and heat transfer past a vertical flat stretching plate within a porous medium. Scaling group of transformation was performed to achieve the appropriate similarity solutions, which was later applied to modify the governing boundary layer system to a nonlinear ordinary differential equations system. The Runge–Kutta method in association with the shooting technique in the Maple software exercised to attain the numerical solutions. There is a strong dependence of momentum transportation on the increment of the Darcy number, the suction/injection parameter and the Grashof number, respectively. The temperature distribution within the thermal boundary layer aided by augmenting the magnitude of the microrotation density.

Transient Free Convection Flow of a Micropolar Fluid Over a Vertical Surface

In recent years, the dynamics of micropolar fluids, originated from the theory of Eringen, has been a popular area of research. As the fluids consist of randomly oriented molecules, and as each volume element of the fluid has translational as well as rotational motions, the analysis of physical problems in these fluids has revealed several interesting phenomena, which are not found in Newtonian fluids. The present study presents a numerical study for transient natural convection heat transfer of a micropolar boundary layer flow near a vertical isothermal surface. The governing equations are formulated and solved numerically using the MackCormak’s technique. A comparison with previously published results on special cases of the problem shows excellent agreement. Representative results for the velocity, micro-rotation and temperature profiles are shown graphically for different values of material parameters. In general, it is found that the temperature increases inside the boundary layer for the micropolar flows as compared to the Newtonian flows.

Numerical study of heat transfer characteristics of the micropolar boundary layer near a stagnation point on a moving wall

The present paper presents a numerical study of heat transfer of a micropolar boundary layer flow near a stagnation point on a moving wall. The governing differential equations are solved numerically and the temperature profiles are shown graphically for different values of material parameters and wall velocity. The heat transfer rate has been obtained for both the isothermal and the adiabatic case. It is concluded that the temperature in the boundary layer increases for the micropolar flows, as compared to the Newtonian flows.

Unsteady mixed convection in micropolar boundary layer flow on a vertical plate

By the use of the theory of micropolar fluids due to Eringen, boundary layer solutions are presented to study an unsteady combined convection of a micropolar fluid among a vertical plate. The unsteadiness arises and a result of time-varying nature of the free stream velocity as well as the wall temperature. Numerical results are obatained for the velocity, angular velocity and temperature fields. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress. Micropolar fluids display drag reduction and reduce surface heat transfer rate when compared to Newtonian fluids.

Free convection in the boundary layer flow of a micropolar fluid along a vertical wavy surface

A cubic spline collocation numerical method and a simple transposition theorem have been used to study the free convection in the flow of a micropolar fluid along irregular vertical surfaces. A sinusoidal surface is used to elucidate the amplitude wavelength ratio effects on the free convection in a micropolar boundary layer. The effects of micropolar parameterR and geometries on the velocity and temperature fields have been graphically studied. The skin friction stress on the wall has also been studied and discussed. It is observed that the frequency of the local heat transfer rate is twice that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or micropolar fluid; the same result is also obtained for the skin friction on the wall.

Analysis of a Free-Convection Micropolar Boundary Layer About a Horizontal Permeable Cylinder at a Nonuniform Thermal Condition

Analysis of a Free-Convection Micropolar Boundary Layer About a Horizontal Permeable Cylinder at a Nonuniform Thermal Condition

Combined forced and free convection in micropolar boundary layer flow on a vertical flat plate

Boundary layer solutions are presented to study the combined forced and free convection from a vertical semi-infinite plate to a micropolar fluid. The boundary conditions of isothermal wall and constant surface heat flux are considered. Numerical results are obtained for the velocity and temperature distribution and the missing wall values of the velocity and thermal functions. Micropolar fluids display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids.

Effects of Microstructure on the Conjugated Mixed Forced and Free Convection-Conduction Analysis of Heat Transfer in a Vertical Plate Fin

A conjugated convection-conduction analysis has been made for a vertical plate fin which exchanges heat with its micropolar fluid environment by mixed forced and free convection. The analysis is based on a one-dimensional model for the plate fin whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, angular momentum, and energy in the micropolar fluid boundary layer adjacent to the fin. The local heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. Numerical results of the overall heat transfer rate, the local heat transfer coefficient, the local heat flux, and the fin temperature distribution for Pr = 5 are presented for various values of Δ (dimensionless material parameter), Nc (conjugated convection-conduction parameter), and Ω (buoyancy parameter).

Heat transfer from continuous moving fibers in a micropolar fluid

The laminar micropolar boundary layer in axial flow along a continous moving fiber is studied using the theory of micropolar fluids formulated by Eringen. The fiber filament, is taken as a cylindrical cone that moves steadily through an otherwise quiescent environment. The governing equations for momentum angular momentum and energy have been solved numerically. It has been found that the heat transfer rate increases with increasing values of the dimensionless material parameters of the fluid as well as a reduction in the diameter of the filament.

Analysis of forced convection micropolar boundary layer about a permeable sphere

The heat transfer characteristics and local skin friction for forced convection flow of micropolar fluid over an isothermal or a constant-heat-flux surface of sphere with surface mass transfer have been studied. The problem was formulated by applying a suitable variables transformation and the solutions were obtained by an implicit finite difference method. Numerical results were carried out for a wide range of mass transfer parameters as the Prandtl number at 0.7 or 7 with several values of material parameters of the micropolar fluid. The variations of the local friction factor and local Nusselt number are plotted and discussed.

Boundary layer flow of a micropolar fluid on a continuous moving cylinder

The laminar micropolar boundary layer in axial flow along a continuous, moving cylinder is investigated using the theory of micropolar fluids formulated by Eringen. The governing equations for momentum, angular momentum and energy have been solved numerically by power series approach. Missing values of the velocity, angular velocity, and thermal functions are tabulated for a wide range of the material parameters, transverse curvature parameter and Prandtl number of the fluid.

Heat transfer in micropolar boundary layer flow near a stagnation point

Using the micropolar theory, a set of boundary layer equations are obtained for the two dimensional flow of an incompressible micropolar fluid near a stagnation point. The boundary conditions of isothermal and insulated wall are taken with VISCOUS DISSIPATION effects. Numerical results for the temperature distribution has been shown graphically for different values of the material parameters and Prandtl number.

The axisymmetric micropolar boundary layer on a long thin cylinder

The laminar micropolar boundary layer in axial flow along a long, thin cylinder is investigated using the theory of micropolar fluids due to Eringen. The governing equations are solved numerically by expanding the velocity and angular velocity functions in the form of power series. Wall values of the momentum and angular momentum functions are tabulated for a wide range of values of the material parameters and the transverse curvature parameter.

Heat transfer characteristics of a micropolar boundary layer in a crossflow over a non-isothermal circular cylinder

A boundary layer analysis has been presented for the heat transfer characteristics of a micropolar fluid flowing past a circular cylindrical surface with non-isothermal boundary conditions. The solution of the energy equation is obtained in the form of a power series of the distance measured from the stagnation point. The results for the Nusselt number have been obtained for several values of the material parameters of the fluid. A discussion has been provided for the effect of non-isothermal wall on the heat transfer rate.

Heat transfer in micropolar boundary layer flow over a flat plate

Boundary layer solutions are presented to study the steady state heat transfer from a semi-infinite flat plate to a micropolar fluid. The boundary conditions of isothermal wall, constant surface heat flux and insulated wall with viscous dissipation effects have been treated in this paper. Numerical results for the temperature distribution and the missing wall values of the thermal functions have been given. The range of Prandtl numbers investigated was from 10 to 1000 while the dimensionless grouping of the material properties was allowed to vary over a wide range.