Micropolar flow over a porous stretching sheet with strong suction or injection

We consider self-similar boundary layer flow of a micropolar fluid driven by a porous stretching sheet. For the limiting cases of large suction or injection, an order of magnitude analysis is used to obtain analytic results for the shear stress and the microrotation at the surface. Our analysis reveals how the wall shear stress is significantly affected by two of the parameters in the micropolar model and we indicate how our findings may be of use in technological applications involving micropolar flow.     

Fully Developed Free Convection Heat and Mass Transfer of a Micropolar Fluid Between Porous Vertical Plates

In this article, we consider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid between porous vertical plates with asymmetric wall temperatures and concentrations. The resulting boundary-value problem is solved analytically by the homotopy analysis method (HAM). Profiles for velocity and microrotation are presented for a range of values of the Reynolds number and the micropolar parameter.     

Effects of Newtonian heating and thermal radiation on micropolar ferrofluid flow past a stretching surface: Spectral quasi‐linearization method

This study article addressesthe flow and heat transfer characteristics of a magnetite Fe₃O₄ micropolar ferrofluid flow past a stretching sheet. For practical interest, thermal radiation, Newtonian heating, and a heat source or sink are considered in this investigation. A useful Tiwari‐Das nanofluid model is considered to analyze the microstructure and inertial characteristics of the water‐based nanofluids containing iron oxide. The dimensionless nonlinear ordinary differential equations are solved by employing suitable similarity variables. The resulting nonlinear system is solved by the spectral quasi‐linearization method. The effects of different nondimensional parameters on various profiles are shown graphically and explored in detail. It is found that the micropolar ferrofluid exhibits a higher energy distribution than that of a classical micropolar fluid. Compared to the classical micropolar liquid, local skin‐friction is more significant for the micropolar magnetite ferrofluid. In the presence of Newtonian heating, the thermal behavior of the micropolar nanofluid is remarkably better than that of the classical micropolar fluid.     

Application of differential transformation and Hermite wavelet methods for micropolar flow through a permeable channel

In this study, micropolar fluid flow in a porous channel is investigated using the differential transform method (DTM) and the Hermite wavelet method (HWM). By exploiting Berman's similarity transformation, the governing partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations (ODEs). The concepts of DTM and HWM are briefly introduced and employed to derive solutions of nonlinear coupled ODEs. Our results compared with solutions already existing in the literature. When we compare DTM and HWM, HWM is more efficient and also requires less time to maintain a higher level of accuracy. The results are presented to study the velocity and microrotation profiles for various physical parameters such as Reynolds number, coupling parameter, spin-gradient viscosity parameter, and micropolar fluid constant. As an important result, increases in the values of the coupling parameter and micropolar fluid constant have different results in comparison with the spin-gradient viscosity parameter increasing.     

Natural Convection in a Micropolar Fluid with Thermal Dispersion and Internal Heat Generation

A similarity solution is presented for the flow of a micropolar fluid along an isothermal vertical plate with an exponentially decaying heat generation term and thermal dispersion. Numerical solutions are obtained for the governing equations. Results for velocity, angular and thermal functions are displayed for a range of values of the material parameters of micropolar fluid and thermal dispersion parameters.The data for friction factor, Nusselt number and wall couple stress have been tabulated for a range of thermal dispersion parameters s, Prandtl numbers Pr and micropolar parameter.     

Micropolar free convection flowEcoulement micropolaire par convection naturelleMikropolare freie konvektionMикpoпoляpнoe cвoбoднoкoнвeктивнoe тeчeниe

The flow and heat-transfer characteristics of the free convection micropolar flow are described. It is found that decreasing rates of heat-transfer can be achieved by making the Newtonian solvent more and more micropolar. The micropolar characteristics are determined by the two non-dimensional parameters R (an index to microstructure character) and A (an index to substructure character). The effect of R is more pronounced on the flow and temperature fields while that of A is relatively less.     

Exploration of thermal Péclet number,vortex viscosity,and Reynolds number on two-dimensional flow of micropolar fluid through a channel due to mixed convection

The present theoretical investigation is conducted on a micropolar fluid medium channel in the presence of mixed and nonlinear convection with the assumptions of thermal radiation and species reactive agents. The nonlinear governing equations, which describe the micropolar fluid flow and energy, are converted into ordinary differential equations using appropriate similarity variables. With the Runge–Kutta–Fehlberg method, the resultant equations are numerically solved. The physical characteristics of flow restrictions over velocity, microrotation, energy, and concentration profile are plotted and discussed. Further, the impact of several dimensionless parameters on Nusselt and Sherwood numbers is investigated and depicted graphically. In addition to observing flow patterns, contour plots of streamlines are plotted and discussed. It is demonstrated that the dimensionless velocity, temperature, and concentration of micropolar fluid have a maximum value at the center of the channel. However, the microrotation velocity of the micropolar fluid has both maxima and minima. The thermal and solutal properties of micropolar fluid influence heat and mass transport rates, that is, mixed convection and buoyancy parameter boost up the local heat transfer at the surface. Finally, Péclet number and chemically reactive parameters boost up the local mass transfer at the surface.     

Applied theories of thermoelasticity of micropolar thin beams

In the present article, a system of rather general hypotheses is developed, on the basis of which with the account of transverse shears the applied theories of thermoelasticity of bending of micropolar thin beams are introduced: (a) With free fields of displacements and rotations; (b) with constrained rotation; (c) the reduced model. On the basis of the constructed models, specific problems of thermoelastic bending of micropolar beams are studied. Numerical analysis of the studied problems states the effectiveness of the micropolar material from the point of view of the beam rigidity compared with that of the classical case.     

PROPAGATION OF MICROPOLAR THERMOELASTIC WAVES IN AN INFINITE ELASTIC SPACE CONTAINING A CYLINDRICAL BORE

The propagation of waves in an infinite micropolar elastic solid containing a cylindrical cavity and under the influence of temperature is investigated. Waves with axial symmetry with respect to the axis of the cavity are discussed, using the linear theory of micropolar thermoelasticity.     

Forced Convection in Micropolar Fluid Flow through a Wavy-Wall Channel

ABSTRACT

Forced convection of micropolar fluids through a periodic array of wavy-wall channels has been analyzed by using a simple coordinate transformation method and the spline alternating- direction implicit method. The effects of the wavy amplitude, the micropolar parameter, and the Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging-diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and larger wavy amplitudes. For the micropolar fluids, increasing the vortex viscosity causes an increase in the total viscosity of the fluid, thus the skin friction coefficient increases while the Nusselt number decreases. Also, the influence of vortex viscosity on the minimum cross section of the wavy-wall channel and on a tiny change of the maximum cross section is manifest. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, regardless of whether the fluids are Newtonian or micropolar fluids.     

Mathematical Model of Micropolar Thermo-Elasticity of Thin Shells

With the account of qualitative results of the asymptotic method of integration of the boundary-value problem of micropolar thermo-elasticity in three-dimensional thin domain of shell, adequate hypotheses are formulated. On the basis of these hypotheses, general mathematical models of micropolar thermo-elasticity of thin shells are constructed. Based on the constructed theories of thermo-elasticity of micropolar thin shells, main statements on the thermo-elasticity of microplar circular cylindrical shells are made. With the consideration of the irregular heating of axisymmetric thermo-elasticity, for the case of hinged supported edges, numerical results are obtained. Based on the analysis of numerical results, effects of micropolarity of the material are shown.     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Exact solutions of micropolar SWCNTs nanofluid with heat transfer

The present study is aimed to analyze the unsteady micropolar nanofluid flow passing over an oscillating infinite vertical plate. The flow is affected by thermal radiation and Newtonian heating. Single‐walled carbon nanotubes (SWCNTs) are added to enrich the thermal properties of the micropolar fluid. Kerosene is taken as the base liquid to enhance heat transfer. By using dimensional analysis, the governing equations for temperature, velocity, and microrotation are reduced to dimensionless form and after that, these equations have been solved by applying Laplace transform method to get the exact solutions. Finally, we have presented the effects of material and flow parameters and illustrated graphically by the Mathcad software. We found that microrotation, temperature, and velocity are decreasing functions of Prandtl number but have shown increasing behavior for Grashof number. Furthermore, we found that SWCNTs‐water‐based nanofluid has a comparatively higher heat transfer rate than SWCNTs‐kerosene and SWCNTs‐engine oil‐based nanofluids.     

Numerical simulation of the natural convection plume about line heat source in micropolar fluid

This paper analyses the flow and heat transfer characteristics of laminar free convection in the boundary layer flow of micropolar fluids about a line heat source embedded on the edge of a plate. The nonlinear formulation governing equations are initially cast into dimensionless form by a local non-similar transformation and the resulting system of equations is then solved by the cubic spline collocation method and the finite difference scheme. Of particular interest are the effects of the micropolar parameter, Δ, and the Prandtl number on the velocity and temperature fields and on the skin friction coefficient, wall couple stress, and wall temperature. Numerical results are obtained for the velocity and temperature profiles for different values of the Prandtl number and micropolar parameter.     

Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration

This work examines the natural convection heat and mass transfer near a sphere with constant wall temperature and concentration in a micropolar fluid. A coordinate transformation is used to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. For micropolar fluids, higher viscosity tends to retard the flow and thus decreases the natural convection heat and mass transfer rates from the sphere with constant wall temperature and concentration. Moreover, the natural convection heat and mass transfer rates from a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Magnetohydrodynamic flow of a micropolar nanofluid in association with Brownian motion and thermophoresis: Irreversibility analysis

This investigation was carried out with the purpose of presenting the flow of micropolar fluid flowing in the microchannel placed parallel to the ground. The prime aim of the work was to study the behavior of micropolar fluid and the response of the microrotation component when the two significant mechanisms namely Brownian movement and thermophoresis are accounted for, as these effects are mainly concerned with the motion of the particles of nano-dimensions. For the flow of micropolar, we account for the extra kinematics variables combined with the classical continuum mechanics namely microinertia moment tensor and gyration tensor. Magnetic effect and suction/injection of the fluid through the channel walls are also facilitated. The influence on the fluid concentration due to the presence of activation energy was accounted in the present examination. On considering all of these effects, equations are carefully modeled and the solution was attained with the aid of Runge–Kutta Fehlberg 4–5th order method using a shooting scheme. The results have deciphered that the presence of material parameter elevates the microrotation component on the upper half of the channel and depletes it at the lower half. The microinertia parameter shows the opposite behavior of the material parameter. Brownian motion parameter is found to enhance the thermal profile and concentration profile. Lesser entropy was generated when the material parameter was high.     

ENHANCEMENT OF HEAT TRANSFER IN TURBULENT SEPARATED AND REATTACHING FLOW BY LOCAL FORCING

This article presents numerical solutions for solving the problem of a mixed convective micropolar fluid flow and heat transfer along a vertical wavy surface with a discontinuous temperature profile. The overall surface is equally divided into a heated section succeeded by an unheated section alternately. The problems in the present study have been formulated by using a simple transposition theorem and the cubic spline collocation method. Eringen has applied the spline alternating direction implicit (SADI) procedure to solve the governing momentum, angular momentum, and energy equations those formulated. Along the wavy surface, the velocity, temperature, and microrotation profiles are presented. The influences of micropolar parameters R, u , geometry, and Gr/Re 2 number on the skin friction coefficient and Nusselt number have been studied in this work. The results demonstrate that the skin friction coefficient consists of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases, but the skin friction increases. In addition, when the spin gradient viscosity parameter ( u ) increases, the skin friction decreases. Comparisons between a Newtonian fluid and a micropolar fluid are also discussed.     

Micropolar fluid flow with temperature‐dependent transport properties

In the present article, the heat transfer rate and the fluid flow of a micropolar fluid along with temperature‐dependent transport properties are scrutinized in the presence of heat generation. The variability in transport properties leads to a rise in the heat transfer and decreases the skin friction. Furthermore, Fourier's heat flux model is implemented in the analysis of heat transfer, employing a suitable transformation to convert the flow model into nonlinear ordinary differential equations. Numerical solutions are obtained by using the shooting method/bvp4c technique. Physical quantities of interest, such as local skin friction and Nusselt number, are discussed and computed. Skin friction decreases with the micropolar parameter but the Nusselt number shows the opposite behavior for the micropolar parameter.     

Mixed convection plume about a line heat source in micropolar fluid

This paper analyses the flow and heat transfer characteristics of the mixed convection in the boundary layer flow of micropolar fluids about a line heat source embedded on the edge of a plate. The dimensionless forms of boundary layer equations and their associated boundary conditions have been derived and investigated numerically in order to characterize the behaviors of the mixed convection wall plume. The numerical results have been obtained using the method of cubic spline collocation and the finite difference scheme. The micropolar parameter reduces the velocity but increases the temperature in the boundary layer, whereas the effects of buoyancy parameter trend conversely. Furthermore, the micropolar parameter decreases the skin friction parameter and the wall couple stress but increases the wall temperature, whereas the effects of buoyancy parameter trend conversely. Finally, the higher the value of Prandtl number, the greater the skin friction parameter, the wall couple stress and the wall temperature.