Search Results (11)

The mass and heat transfer magnetohydrodynamic (MHD) flows have a substantial use in heat exchangers, electromagnetic casting, X-rays, the cooling of nuclear reactors, mass transportation, magnetic drug treatment, energy systems, fiber coating, etc. The present work numerically explores the mass and heat transportation flow of MHD micropolar fluid with the consideration of a chemical reaction. The flow is taken between the walls of a permeable channel. The quasi-linearization technique is utilized to solve the complex dynamical coupled and nonlinear differential equations. The consequences of the preeminent parameters are portrayed via graphs and tables. A tabular and graphical comparison evidently reveals a correlation of our results with the existing ones. A strong deceleration is found in the concentration due to the effect of a chemical reaction. Furthermore, the impact of the magnetic field force is to devaluate the mass and heat transfer rates not only at the lower but at the upper channel walls, likewise. Full article

Heat and mass transfer due to a magneto micropolar fluid flow along a semi-infinite vertical plate bounded by a porous medium are investigated in presence of induced magnetic field. In case of cooling flow, heat and mass fluxes from the plate are subjected to be constant under the action of a constant heat sink. Mathematical model related to the problem is developed from the basis of studying magnetohydrodynamics (MHD) for both lighter and heavier particles. Dimensionless model of momentum, microrotation, induction, energy and concentration equations are solved simultaneously by the explicit scheme of finite difference technique. According to the obtained stability and convergence criteria of this transient flow, very negligible time step (Δt = 0.002) compared to the existing works has been taken to perform the numerical computation. Quantities of chief physical interest of the flow as shear stress, couple stress, current density, Nusselt number and Sherwood number are also studied here. The numerically computed results are compared with published results of available research works. Interestingly an excellent agreement is found with finite difference solutions in both explicit and implicit schemes. In order to discuss the physical aspects of the problem, the flow variables for different values of associated parameters are illustrated in graphs. Finally, important findings of the study are listed as concluding remarks. Full article

In this research work, our goal is to scrutinize the case, where water-based nanofluids having single-wall and multi-wall carbon nanotubes (CNTs) flow through a vertical cone. The second law of thermodynamic is taken for the aim of scheming effective heat storage units. The body package is layered in convective heat and diluted permeable medium. The effects of Joule heating, rotary microorganisms, heat generation/absorption, chemical reactions, and heat radiation increase the novelty of the established model. By using a local similarity transformation technique, the partial differential equations (PDEs) change into a coupled differential equation. By using the numerical technique, bvp4c, to get the solution of the conservation equations and their relevant boundary conditions. The parameters appearing in the distribution analysis of the alliance are scrutinized in detail, and the consequences are depicted graphically. It can be perceived that in the situation of composed nanotubes, the velocity of fluid decreases as the magnetic field is increased. Full article

Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier–Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important effects, namely, the Brownian motion and the thermophoretic. In addition, the effects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken over a slanted, stretching surface making an inclination with the vertical one. Suitable similarity transformations are applied to develop a nonlinear transformed model in terms of ODEs (ordinary differential equations). For the numerical simulations, an efficient, stable, and reliable scheme of Keller-box is applied to the transformed model. More exactly, the governing system of equations is written in the first order system and then arranged in the forms of a matrix system using the block-tridiagonal factorization. These numerical simulations are then arranged in graphs for various parameters of interest. The physical quantities including skin friction, Nusselt number, and Sherwood number along with different effects involved in the governing equations are also justified through graphs. The consequences reveal that concentration profile increases by increasing chemical reaction parameters. In addition, the Nusselt number and Sherwood number decreases by decreasing the inclination. Full article

The studies dealing with micropolar magnetohydrodynamic (MHD) flows usually ignore the micromagnetorotation (MMR) effect, by assuming that magnetization and magnetic field vectors are parallel. The main objective of the present investigation is to measure the effect of MMR and the possible differences encountered by ignoring it. The MHD planar Couette micropolar flow is solved analytically considering and by ignoring the MMR effect. Subsequently, the influence of MMR on the velocity and microrotation fields as well as skin friction coefficient, is evaluated for various micropolar size and electric effect parameters and Hartmann numbers. It is concluded that depending on the parameters’ combination, as MMR varies, the fluid flow may accelerate, decelerate, or even excite a mixed pattern along the channel height. Thus, the MMR term is a side mechanism, other than the Lorentz force, that transfers or dissipates magnetic energy in the flow direct through microrotation. Acceleration or deceleration of the velocity from 4% to even up to 45% and almost 15% deviation of the skin friction were measured when MMR was considered. The crucial effect of the micromagnetorotation term, which is usually ignored, should be considered for the future design of industrial and bioengineering applications. Full article

A numerical study was carried out to examine the magnetohydrodynamic (MHD) flow of micropolar fluid on a shrinking surface in the presence of both Joule heating and viscous dissipation effects. The governing system of non-linear ordinary differential equations (ODEs) was obtained from the system of partial differential equations (PDEs) by employing exponential transformations. The resultant equations were transformed into initial value problems (IVPs) by shooting technique and then solved by the Runge–Kutta (RK) method. The effects of different parameters on velocity, angular velocity, temperature profiles, skin friction coefficient, and Nusselt number were obtained and demonstrated graphically. We observed that multiple solutions occurred in certain assortments of the parameters for suction on a surface. The stability analysis of solutions was performed, and we noted that the first solution was stable while the remaining two solutions were not. The results also showed that the velocity of the fluid increased as the non-Newtonian parameter rose in all solutions. Furthermore, it was detected that the temperature of fluid rose at higher values of the Eckert number in all solutions. Full article

The main purpose of the present analysis is to report the numerical solution of the thermal radiations and magnetohydrodynamic (MHD) effect on the flow of micropolar nanofluid. Further, the effect of Brownian motion and thermophoresis on the flow field are also elucidated. The combined phenomenon of heat and mass transfer is considered. Compatible similarities are implemented for the conversion of nonlinear ordinary differential equations from nonlinear partial differential equations. The numerical solution of the governing differential equations is obtained via the implicit Keller box technique. This is an efficient scheme based on the finite difference method. Findings demonstrate that the heat and mass exchange reduce with growth of the Brinkman parameter, whereas the wall shear stress enhances with improving the magnitude of the Brinkman factor. The temperature contour enhances when the radiation parameter reaches its peak, which is useful for industrial processes. The heat and mass flow rates decrease against higher magnitudes of inclination. Full article

The main purpose of this study is to investigate the multislip effects on the magneto-hydrodynamic (MHD) mixed convection unsteady flow of micropolar nano-fluids over a stretching/shrinking sheet along with radiation in the presence of a heat source. The consequences of multislip and buoyancy conditions have been integrated. By using the suitable similarity variables are used to solve the governing non-linear partial differential equations into a system of coupled non-linear ordinary differential equations. The transformed equations are solved numerically by using Runge–Kutta fourth-order method with shooting technique. The impacts of the several parameters on the velocity, temperature, micro-rotation, and concentration profiles as well as on the skin friction coefficient, Sherwood number, and Nusselt number are discussed with the help of graphs and tables. Full article

In this article, the intention is to explore the flow of a magneto-hydrodynamic (MHD) bioconvective micro-polar Nanofluid restraining microorganism. The numerical solution of 2-D laminar bioconvective boundary layer flow of micro-polar nanofluids are presented. The phenomena of multi-slip, convective thermal and Solutal boundary conditions have been integrated. A system of non-linear partial differential equations are transformed into the system of coupled nonlinear ordinary differential equations by applying appropriate transformations, the transformed equations are then solved by applying the variational finite element method (FEM). The fascinating features of assorted velocity parameter, microrotation, temperature, microorganism compactness, solutal and nanoparticles concentration have been inspected. The rate of heat transfer, the skin friction coefficient, couple stress and Sherwood number for microorganisms have also been discussed graphically and numerically. The investigations illustrated that increase in material parameters causes a reduction in microorganism compactness, concentration and temperature. As a result of enhancement in the unsteadiness parameter, the fluid velocity, concentration of microorganisms and the temperature are observed to be declines. Energy and microorganism compactness profile affected by the improvement in the buoyancy ratio parameter. As the improvement in results of buoyancy ratio parameter effects on improvement in the energy and the microorganism compactness profile while the velocity profile is condensed. In the end, rationalized convergence of the finite element solution has been inspected; the computations are found out via depreciating the mesh size. Full article

The present study accentuates the magnetohydrodynamics (MHD) flow and heat transfer characteristics of a dual stratified micropolar fluid over a permeable stretching/shrinking sheet. Thermal and solutal buoyancy forces are also included to incorporate with the stratification effect. Similarity, transformation is applied to reduce the governing model (partial differential equations) into a set of nonlinear ordinary differential equations (ODEs) due to its complexity. Using bvp4c solver in the MATLAB software, numerical results for some limiting cases are in favorable agreement with the earlier published results. Both assisting and opposing buoyancy flows have dual similarity solutions within specific range of suction and stretching/shrinking parameters, whereas only a distinctive solution is observed for pure forced convective flow. The micropolar fluid shows a disparate pattern of flow, heat and mass transfer characteristics between stretching and shrinking cases. Unlike the shrinking flow, the surface velocity gradient, local Nusselt and Sherwood numbers for stretching flow intensify with the increment of the material parameter. The result from stability analysis reveals that the first solution is the real solution, whereas the second solution is virtual. Full article

In this paper, the MHD flow of a micropolar nanofluid on an exponential sheet in an Extended-Darcy-Forchheimer porous medium have been considered. Buongiorno’s model is considered in order to formulate a mathematical model with different boundary conditions. The governing partial differential equations (PDEs) of the nanofluid flow are changed into a third order non-linear quasi-ordinary differential equation (ODE), using the pseudo-similarity variable. The resultant ODEs of the boundary value problems (BVPs) are renewed into initial value problems (IVPs) using a shooting method, and then the IVPs are solved by a fourth order Runge-Kutta (RK) method. The effects of various physical parameters on the profiles of velocity, temperature, microrotation velocity, concentration, skin friction, couple stress coefficients, heat, and concentration transfer are demonstrated graphically. The results reveal that triple solutions appear when $S\ge 2.0337$ for $K=0.1$ and $S\ge 2.7148$ for $K=0.2$ . A stability analysis has been performed to show the stability of the solutions; only the first solution is stable and physically possible, whereas the remaining two solutions are not stable. Full article