Microrotation Profiles Research Articles

Unsteady solute dispersion of electro-osmotic flow of micropolar fluid in a rectangular microchannel

This study scrutinizes the two-dimensional concentration distribution for a solute cloud containing a micropolar fluid in a rectangular microchannel under the influence of an applied electric field. The concentration distribution is obtained up to second order approximation using Mei's homogenization method. Analytical formulas are derived for dispersion coefficient, mean and two-dimensional concentration distributions. This study also includes the analytical expressions for electric potential, velocity, and microrotation profiles. This study discusses the impact of coupling number, couple stress parameter, electric double layer thickness, and Péclet number on solute concentration distribution. The results of fluid velocity and dispersion coefficient are validated with available works in the literature. The non-Newtonian parameter and electric double layer thickness are shown to have a significant impact on dispersion. Our study reveals that concentration distribution rises but spreading of solute reduces when the coupling number increases. This is also true when the Debye length decreases. It is also obtained that the solute spreads more in the Newtonian fluid case compared to the micropolar fluid case. Finally, coupling number and electric double layer thickness show a symmetric pattern to the indicator function for the transverse concentration variation rate. The findings of this work have broad implications in deoxyribonucleic acid analysis, chemical mixing, and separation.

A numerical study on MHD micropolar nanofluid flow over a Darcian porous stretching surface: impacts of thermophoretic and Brownian diffusions

This article provides a quantitative analysis of the flow of MHD micropolar fluid through a Darcian permeable medium bounded by a stretched surface. The RK45 method, along with the shooting approach, is employed to perform the analysis. The impacts of Joule heating, thermophoretic, and Brownian diffusions over the fluid flow are particularly, focused in this research work. The study's findings can be applied in nanofluid technology for optimizing heat transfer, porous media engineering for designing efficient systems, and magnetohydrodynamics for applications like magnetic drug targeting and liquid metal cooling in nuclear reactors. The nonlinear partial differential equations (PDEs) that govern the flow are altered into nonlinear ordinary differential equations (ODEs) by using appropriate variable similarity transformations. Displayed the graphical effects of various physical factors over the velocity, angular velocity, concentration, and temperature profiles. Velocity profiles are enhancing as the micropolar fluid and porous factor rises whereas the opposite trend exists for the boosting estimations of the magnetic parameter. Temperature distribution is escalating for the rising estimations of the magnetic, Eckert, Brownian, and thermophoresis parameters but there is an opposite scenario deploys as the Prandtl number upsurges. As Schmidt and Brownian motion parameters increase, the micropolar nanoparticle concentration decelerates and elevates when the thermophoresis parameter is boosted. The micro-rotation profiles are enhanced as the values of the micropolar fluid parameter rise. The drag force was enhanced as the magnetic and micropolar fluid parameters upsurged but diminished when the porous parameter was elevated. The rate of heat flow diminishes with higher estimates of the micropolar fluid parameter but improves when the magnetic and Prandtl number parameters increase. The rate of mass flux escalates for the enhanced values of thermophoresis, Brownian, Schmidt, and chemical reaction parameters. Considerable numerical outcomes have been produced and cross-referenced with the latest study, which unveiled remarkable concurrence.

EMHD micropolar fluid flowing through a micro‐structural slipped surface with heat source/sink and chemical reaction

AbstractThe electromagnetohydrodynamic (EMHD) has a vital role due to its importance in aerospace and plasma physics, including energy transformation systems in which interaction between the liquid and magnetic field is crucial. Further, micropolar fluids with microstructural slip is used in the lubrication and liquid crystals. From this observation, the current study is conducted to express an EMHD flow of liquid on a microstructural slipped surface. The effects of a uniform heat source/sink (HS/S) with homogeneous and heterogeneous chemical reactions have been incorporated in energy and mass profiles. The governing equations are converted to ordinary differential equations using proper similarity variables. The converted equations are computed by the implementation of Runge–Kutta–Fehlberg (RKF) 4th 5th order with shooting technique. A list of the essential dimensionless constraints and graphs showing how they are affected are provided. The outcome of the problem shows that the electric parameter will improve the velocity but decline the microrotation profile. Further, both heterogeneous and homogeneous reactions have a decreasing concentration. While the heat distribution rate increases with greater magnetic and electric fields, the surface drag force decreases.

Non-similar analysis of bioconvection MHD micropolar nanofluid on a stretching sheet with the influences of Soret and Dufour effects

In this study, we investigate the capabilities of magnetohydrodynamic bioconvective micropolar nanofluids, considering the impact of Soret and Dufour effects using a non-similarity analysis. Our objective is to forecast the complex heat and mass transfer phenomena observed in both biological and industrial systems. In recent years, notable progress in energy applications has spurred our inquiry and exploration. To augment thermal conductivity and explore potential biocompatibility, we utilize blood as the base fluid, incorporating silver Ag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left({\ ext{Ag}}\\right)$$\\end{document} and copper oxide (CuO)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{CuO}})$$\\end{document}. This distinctive configuration offers improved control over thermal properties and supports the exploration of advanced applications across various domains. In our analysis, we also consider factors such as viscous dissipation, the influences of Soret and Dufour effects, the existence of a magnetic field, and the occurrence of heat generation. The governing PDEs and their corresponding boundary conditions are transformed into dimensionless form through the use of suitable non-similar transformations. The outcomes generated by the modified model are obtained through the application of a local non-similarity approach, extended up to the second degree of truncation, and integrated with a finite difference code (bvp4c). Furthermore, the effects of different factors on fluid flow, micro-rotation, heat transfer, volume fraction, and microorganism properties in the analyzed flow scenarios are demonstrated and examined through visual representations, following the attainment of satisfactory agreement between the obtained results and those reported in prior studies. The tables are designed to present numerical variations for the drag coefficient and Nusselt number. A comparative analysis is conducted on previously published work, despite certain limitations, in order to evaluate the accuracy of the numerical scheme. It can be shown that the material parameter K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document} has two effects on micropolar fluid dynamics: it increases the micro-rotation profile, which leads to higher fluid stiffness, and it reduces the velocity profile in response to an angled magnetic field. Furthermore, in bio-convective micropolar fluid, greater K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document} values are correlated with an elevated temperature profile, showing enhanced heat transfer efficiency via increased fluid speed and kinetic energy production. The velocity profiles in bioconvective micropolar fluids rise with higher magnetic field values (M)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(M)$$\\end{document}, highlighting the significance of magnetic field orientations for a thorough comprehension of the behavior of fluids in these systems. Increasing the Dufour effect (Du)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{Du}})$$\\end{document} raises the temperature profile, whereas increasing the Soret effect (Sr)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{Sr}})$$\\end{document} lowers the concentration profile. Furthermore, increasing the bio-convective Lewis numbers (Le)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{Le}})$$\\end{document} results in larger concentrations of moving microorganisms, but increasing the Peclet number (Pe)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext{Pe}})$$\\end{document} results in a drop in microbe concentrations. The main focus of our study is to devise unique transformations customized to address the intricacies of the specific problem under investigation. These transformations aim to produce precise and efficient outcomes, offering valuable insights for future research in the realm of nanofluid flows, particularly concerning pressure ulcer problems.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

DARCY FORCHHEIMER FLOW OF WILLIAMSON FLUID PAST A STRETCHING SHEET WITH VARIABLE THERMAL CONDUCTIVITY

The primary objective of this experiment is to examine the motion of molecules of Williamson micropolar fluid moving along a stretchable sheet set in a porous regime with microrotation in presence of magnetic field. The coupled partial differential equations are converted into a system of ODEs using appropriate similarity transformations. To solve the system of ODEs, BVP4C solver has been employed with relative tolerance of . To make sure the present study is stable and convergent, all the outcomes are compared to the earlier findings. The impression of various parameters on velocity, temperature and microrotation profile are illustrated with the help of graph. The graph of entropy generation and skin friction and Nusselt number is also plotted against various governing parameters. Through this investigation it is found that Nusselt number can be increases by regulating the porous parameter and the viscosity of the Williamson fluid. The drag at the surface can be minimized by increasing the strength of magnetic field and Williamson fluid parameter. The implication of this study can be found in industrial field where entropy of the system plays an important role for better performance and stability.

A Novel Approximation Approach for the Analytical Solution of the Flow of Micropolar Fluid Through a Permeable Channel

An attempt is made in this study to investigate the problem of micropolar fluid flow in a porous medium theoretically. Employing the Berman’s similarity solution, the model equations governing the flow is transformed into a set of nonlinear ordinary differential equation and solved using Temimi-Ansari method. Expressions for the velocity and micro-rotation profiles are obtained under the impressions of diverse parameters affecting the flow problem. Using symbolic computation software Mathematica, the nondimensional equations are solved numerically using the Keller Box scheme. Comparison between the analytical solution obtained by TAM and the numerical result are compared with results in literature to observe rapid convergence. Findings from the study showed in the presence of

MAGNETOHYDRODYNAMIC TERNARY HYBRID NANOFLUID FLOW OVER A STRETCHING SURFACE SUBJECT TO THERMAL CONVECTIVE AND ZERO MASS FLUX CONDITIONS

Nanoparticles have the capability to augment the thermal conductivity of nanofluids. For the transmission of heat, the material’s low thermal conductivity is the key problem. Therefore, to increase the thermal conductivity, researchers mixed different nanoparticles in the base fluids. In this field of study, utilizing three different particles is the most recent strategy to form a ternary hybrid nanofluid that gives us better results in terms of heat transfer. The interaction of three different kinds of nanoparticles, i.e. copper, alumina and silver, is considered with water serving as the base fluid to form a ternary hybrid nanofluid. The paper explores the behavior of ternary hybrid nanofluids on heat and mass transportation phenomena of the two-dimensional magnetohydrodynamic (MHD) micropolar flow across a porous extending surface with zero mass flux and convective conditions. The Brownian motion, thermal radiation, heat source and sink, and joule heating are taken into consideration in the temperature equation. The chemical reaction is incorporated into the concentration equation. Appropriate similarity transformations are used to transform the system of partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). The homotopy analysis method (HAM) is used to solve the system of the flow equations. The effects of the nanoparticle’s volume fractions and other different physical parameters on the surface drag force, Nusselt number, velocities, microrotation, temperature and concentration profiles are scrutinized through figures and tables. The outcomes of the present investigation show that the heat transfer rate is augmented with the increasing value of thermophoresis parameter. The magnetic field has augmented temperature while the opposite result is seen in velocity and microrotation profiles. With the escalating values of thermophoresis parameter, the concentration and temperature of ternary hybrid nanofluids are boosted while the increasing Brownian and chemical reaction parameters have decreased the concentration profile. The surface friction coefficient exhibited by the ternary hybrid nanofluid is higher than hybrid and conventional nanofluids.

Numerical Approach to Thermo-Convective Micro-Polar Fluid with Radiation in Permeable Medium

A steady, incompressible and thermo-convective flow of micro-polar fluid over a stretching permeable sheet with heat and mass transfer under effects of radiation, Soret, Schmidt and Dufour numbers has been analyzed. The modeled governing equations, of the classical Navier-Stokes are coupled with micro rotation, temperature and concentration equations, in the form of Partial Differential Equations (PDE’s), along with initial and boundary conditions, are transformed into a system of nonlinear coupled Ordinary Differential Equations (ODE’s) by using an appropriate transformation. The numerical solution is obtained by using the Parametric Continuation Method (PCM). For the validity of the scheme the results are compared with a numerical package bvp4c. It has been observed that both the results are in their best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, temperature and concentration profiles are discussed and depicted graphically. It has been detected that the permeability parameter give rise in micro-rotation profile.

Entropy analysis on EMHD 3D micropolar tri-hybrid nanofluid flow of solar radiative slendering sheet by a machine learning algorithm

The purpose of this paper is to analyze the heat transfer behavior of the electromagnetic 3D micropolar tri-hybrid nanofluid flow of a solar radiative slendering sheet with non-Fourier heat flux model. The conversion of solar radiation into thermal energy is an area of significant interest as the demand for renewable heat and power continues to grow. Due to their enhanced ability to promote heat transmission, nanofluids can significantly contribute to enhancing the efficiency of solar-thermal systems. The combination of silicon oil-based silicon (Si), magnesium oxide (MgO), and titanium (Ti) nanofluids has attracted attention for their ability to improve the performance of solar-thermal systems. The present study discloses a new approach for intelligent numerical computing solving, which utilizes an MLP feed-forward back-propagation ANN and the Levenberg-Marquard algorithm. The collection of data was conducted for the purpose of testing, certifying, and training the ANN model. The Bvp4c solver in MATLAB is utilized to solve the nonlinear equations governing the momentum, temperature, skin-friction coefficient, and Nusselt number. The characteristics of numerous dimensionless parameters such as porosity parameter left(K={0.0,2.0,4.0}right), vortex viscosity parameter left({R}_{1}={0.5,1.0,1.5}right), electric field parameter left(E={0.0,0.1,0.2}right), thermal relaxation time left(Lambda ={0.01,0.10,0.20}right), heat source/sink parameter, left(Q=-{0.3,0.0,0.3}right) thermal radiation parameter left(R={0.5,1}.{0,1.5}right), temperature ratio parameter left({theta }_{w}={0.5,1.0,1.5}right),nanoparticle volume fraction left(phi ={0.00,0.02,0.04}right) on Si + MgO + Ti/silicon oil micropolar tri-hybrid nanofluida are analyzed. The ANN model engages in a process of data selection, network construction, training, and evaluation of its effectiveness through the utilization of mean square error. Tables and graphs are used to show how essential parameters affect fluid transport properties. The velocity profile is decreased by higher values of the porosity parameter, whereas the temperature profile is increased. The temperature profile is inversely proportional to higher values of the electric field parameter. The micro-rotation profiles reduced by expanding values vortex viscosity parameter. It has been determined that entropy generation and Bejan number intensifications for enlarged nanoparticle volume fraction.

Analysis of bio-nanofluid flow over a stretching sheet with slip boundaries

A viscous, incompressible, micropolar bio-nanofluid flowing across a stretching sheet in three dimensions while being driven to convect several slip boundaries in the presence of a magnetic field was studied. With the assistance of the relevant transformations, a mathematical model is presented. The finite difference method numerically solves the converted non-linear ordinary differential equations. A comprehensive assessment was conducted to examine the impact of governing parameters on dimensionless velocity, micro-rotation, temperature, nanoparticle volume fraction, microorganisms, and heat transfer rate. The findings of this investigation showed a strong correlation when compared to previous studies, indicating a high level of agreement and consistency between the results. The study's conclusions indicate that the velocity profile increases with higher values of λ and δ, while it decreases with higher values of A, δv, and M. The micro-rotation profile F(η) drops as the spin gradient viscosity parameter rises, but G(η) increases. The temperature profile decreases with higher Prandtl numbers but increases with higher thermophoresis parameters. The concentration profile decreases with higher Schmidt numbers and Brownian motion parameters. The microorganism profile increases with higher Peclet numbers and microorganism slip parameters but decreases with higher bio-convection Schmidt numbers. Lastly, the local Nusselt number grows with increasing values of the stretching parameter λ.

Double stratification impacts on MHD flow of micropolar nanofluid over a stretching surface inserted in porous medium

A comprehensive analysis of double stratification impacts on the MHD flow of a nanofluid produced by a porous stretching sheet has been conducted by using a numerical approach. The convective boundary conditions (CBCs) and Newtonian heating (NH) cases have been particularly considered in this problem. The governing equations defined in partial differential equations (PDEs) form are converted into ordinary differential equations (ODEs) by using appropriate transformations to meet the requirement of the used numerical method which is bvp4c in the MATLAB software package. Moreover, the numerical findings of the ODEs are displayed via graphical and tabular forms. The impacts of different flow parameters used in particular problem are discussed for the profiles of the velocity, temperature and concentration of micropolar nanofluid along the values of coefficient of skin-friction [Formula: see text], Nusselt number [Formula: see text], the Sherwood number [Formula: see text] and in relation with the variation parameters in general, CBC and NH are calculated to get a clear insight into the flow situation. Some of the findings show that the skin friction increases by increase in magnetic, permeability and material parameters in all cases but the skin friction is reduced by increasing the thermophoresis parameter for CBC and NH cases, respectively. Microrotation profile decreases when material parameter increases, whereas microrotation profiles enhance with increase of the magnetic field and porosity of porous medium.

Two Methods Used for Radiative Micropolar Nanofluid Passed Through a Porous Channel

In this study, radiative micropolar nanofluid passed through a porous channel was analyzed. Because of the considerable amount of difference, a Finite element technique with the approval of the AGM method was used. Different parameter and dimensionless numbers like Reynolds number Re, Hartman number M, the Thermophoretic number N_t with a variety of velocity, temperature, and concentration profile are shown graphically. There was no change in velocity or microrotation profile while there was a change in Reynolds number. Although the concentration profile decreased with increasing Reynolds number

Unsteady flow of micropolar fluid on a magnetized sheet: Effects of magnetic and microrotation parameters on wall couple stress and skin friction

AbstractIn this study, we investigate the unsteady flow of a micropolar fluid past a magnetized stretchable/shrinkable sheet. Our research aims to analyze the effects of magnetic field, moving slit, and various parameters on the velocity, magnetic, and microrotation profiles of the fluid. By applying the Blasius–Rayleigh–Stokes variable, we derive ordinary differential equations from the partial differential equations that define the problem. We solve the transformed set of equations using the shooting method and obtain dual solutions. Our findings indicate that skin friction decreases with increasing values of the microrotation parameter and magnetic interaction parameter. We also observe that the magnetic interaction parameter enhances the microrotation of molecules. Overall, our study provides valuable insights into the behavior of unsteady flows in micropolar fluids and sheds light on the impact of various parameters on dual solutions.

Flow Analysis of a Micropolar Nanofluid Between Two Parallel Disks in the Presence of a Magnetic Field

The present article addresses the steady and laminar magnetohydrodynamics (MHD) flow of a micropolar nanofluid between two porous disks. The fluid is flowing uniformly in the inward and upward directions from both disks. The microrotation of the nanoparticles acts an important role in the flow regime. To show its significance, a comparative study of the analytical results and numerical results is presented. Titanium dioxide is chosen as nanoparticles in the water-based fluid. An appropriate transformation is used for transforming PDEs into ODEs. These nonlinear ODEs are computed by the differential transform method (DTM). The consequences of the Reynolds number, material parameter, and magnetic parameter on the radial velocity, axial velocity, and microrotation profile are graphically presented and discussed. The results calculated by DTM and the results calculated numerically are compared and tabulated. This comparison shows the accuracy and validity of DTM. The coefficient of skin friction is also tabulated and compared with the numerical result. At the end of this study, it is concluded that the behavior of the radial and the axial velocities and the microrotation profile are almost the same in the case of the Reynolds number and the magnetic field parameters.

Numerical investigation of the magnetohydrodynamic hybrid nanofluid flow over a stretching surface with mixed convection: A case of strong suction

The present work explores the physical aspects of the alumina and silver nanoparticles on the magnetohydrodynamic (MHD) flow of mixed convection micropolar hybrid nanofluid with ethylene glycol + water [Formula: see text] base fluid via stretching surface embedded in a porous medium. A strong magnetic field is employed normally in the flow direction. The behavior of the suction on the presented flow analysis is discussed strongly. Heat transport phenomena are analyzed. The current model’s mathematical modeling is based on higher-order nonlinear partial differential equations, which are then translated into higher-order nonlinear ordinary differential equations using appropriate similarity transformations. The modeled higher-order nonlinear ordinary differential equations are solved using NDSolve technique. The physical significance of the different flow parameters on the velocity, microrotation, and temperature profiles of the hybrid nanofluid are described in a graphical form. In a tabular form, the skin friction coefficients for nanofluid and hybrid nanofluid against various flow parameters are calculated. Some important results from this investigation are demonstrated that the velocity of the hybrid nanofluid is higher for the stretching ratio parameter and it is detected that the suction parameter enhanced the microrotation profile of the hybrid nanofluid. From the comparison, it is noted that the velocity, microrotation, and temperature of the hybrid nanofluid are higher as compared to the velocity, microrotation, and temperature of the alumina nanofluid and silver-nanofluid.

Multiple slip impacts on unsteady MHD micropolar fluid past a stretching sheet with non‐Darcy porous medium and uneven heat source/sink

AbstractThe major scope of this research is to scrutinize the effects of multiple slips on unstable magnetohydrodynamic micropolar fluid past a stretched sheet with a non‐Darcy porous medium. In the momentum equation, the non‐Darcy porous medium effect is also taken into consideration. The effects of uneven heat source/sink and thermal radiation in the energy equation are also analyzed. By implementing the similarity transmission, the mathematical modeling of the set of managing partial differential equations is reframed into nonlinear ordinary differential equations. These equations are numerically solved by applying Matlab built‐in solver bvp5c. The implications of foremost parameters such as micropolar parameter, magnetic parameter, permeability parameter, Prandtl, Eckert, and Schmidt numbers, Chemical reaction, slip parameters on velocity, microrotation, temperature as well as concentration profiles are displayed pictorially and explained. It is worthwhile to mention that the improving values of micropolar parameter escalate the velocity as well as microrotation profiles. However, the upsurge in non‐Darcy porous medium will cause a declining nature in the velocity profile. Also, an enhancement in the unsteadiness parameter brings about a lessening in all the profiles. Increment in all the three usual slip parameters will bring a declining nature in the respective profiles. An increase in Schmidt number will give a deduction nature in velocity as well as concentration profile. Moreover, the physical quantities are defined and Nusselt numbers are formulated in the table, and it enlarges while boosting up and , whilst a reverse nature is noticed for others. This present study compared with the earlier studies in special cases holds a better agreement.

A microstructural slip analysis of radiative thermophoretic flow of ternary nanofluid flowing through porous medium

Slip flows play a vital role in the microsystems, such as micro-valves, micro-pumps, hard disc drives, and nozzles. As a result, this study aims to examine the micro-structural slip behavior of ternary nanoliquid flow past a stretchable surface. Linear radiation is included in the law of energy, whereas the law of mass treats thermophoretic particle decomposition. The nonlinear partial differential system is reduced to an ordinary differential system by executing the appropriate transformations. Using a shooting approach with the help of Maple software, the flow, heat mass transportation, and micro-rotation profiles are estimated numerically. The effect of varying parameters on the physical quantities distributions is discussed via graphical demonstrations. The presence of microstructural slip reduces the velocity and micro-rotation profiles, whereas the nanoparticle concentration and temperature increase. The incrementing thermal radiation values augmented the temperature distribution. The concentration field narrows due to thermophoretic constraints.

Significance of an incident solar energy toward the MHD micropolar fluid flow over a stretching sheet

This paper studies the mixed convective flow of a magnetohydrodynamic micropolar fluid over an extending sheet. The first-order velocity slip condition is taken to observe the slip flow of the fluid. The applications of solar radiation toward the micropolar fluid flow are analyzed in this paper. Furthermore, the Brownian motion, thermophoresis and Joule heating impacts are also studied. Also, the Cattaneo-Christov heat flux model, chemical reaction and activation energy are observed. The leading PDEs have been transformed to ODEs and then solved with the help of homotopy analysis technique. The impacts of different physical parameters have been evaluated theoretically. The outcomes exhibited that the material factors have augmented the microrotation and velocity profiles. Moreover, the velocity slip parameter has a reverse relation with velocity and microrotation profiles, while there is a direct relation of a velocity slip with the energy curve. The velocity profile has increased with higher thermal and mass Grashof numbers. With increasing Brownian motion parameter, the thermal profile is amplified while the concentration profile is declined. On the other hand, the thermal and mass profiles have been boosted with greater thermophoresis parameter. The velocity profile has decreased with higher magnetic parameter, whereas the temperature profile has augmented with higher magnetic parameter. The couple stress and skin friction have been augmented with material parameter, whereas the skin friction has been reduced with thermal and mass Grashof numbers.

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

AbstractIn 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.