Influence of thermophoresis and chemical reaction on MHD micropolar fluid flow with variable fluid properties

This work investigates the effect of thermophoresis and chemical reaction on heat and mass transfer in hydromagnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and non-uniform heat source/sink in the presence of thermal radiation. It is assumed that the transverse magnetic field is a function of the distance from the origin. The analysis accounts for both temperature dependent fluid viscosity and thermal conductivity. Using the similarity transformation, the governing system of equations are transformed into non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA. Numerical results for the velocity, microrotation, temperature and species concentration as well as for the skin friction, heat and mass transfer are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties

This paper studies the heat transfer process in a two-dimensional steady hydromagnetic natural convective flow of a micropolar fluid over an inclined permeable plate subjected to a constant heat flux condition. The analysis accounts for both temperature dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim–Swigert iteration procedure. Results for the dimensionless velocity and temperature profiles and the local rate of heat transfer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that in modeling the thermal boundary layer flow when both the viscosity and thermal conductivity are temperature dependent, the Prandtl number must be treated as a variable to obtain realistic results. As the thermal conductivity parameter increases, it promotes higher velocities and higher temperatures in the respective boundary layers. The wall shear stress increases with the increase of thermal conductivity parameter. This is true of electrically conducting as well as electrically non-conducting fluids. The presence of heat generation invigorates the flow and produces larger values of the local Nusselt number compared with the case of zero heat generation.     

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.     

Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature

This work studies the natural convection boundary layer flow of a micropolar fluid near a vertical permeable cone with variable wall temperature. The transformed boundary layer governing equations are solved by the cubic spline collocation method. The local Nusselt numbers are presented as functions of suction variables for different values of vortex viscosity parameter, surface temperature exponent, and Prandtl number. Results show that the heat transfer rates of the permeable cones with higher suction variables are higher than those with lower suction variables. Moreover, the heat transfer rate from a vertical permeable cone in Newtonian fluids is higher than that in micropolar fluids.     

Asymptotic analysis for the conjugate heat transfer problem in an electro-osmotic flow with temperature-dependent properties in a capillary

In this work, the conjugate heat transfer process in an electro-osmotic flow of a Newtonian liquid is studied asymptotically. The analysis includes Joule heating effects by taking into account the temperature dependent viscosity and electrical conductivity of the electrolyte solution and assuming finite thermal conductivity of the capillary wall. Due to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the capillary, altering the electric potential and flow fields. The dimensionless temperature profiles in the fluid and the capillary wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled continuity, momentum, thermal energy, and potential electric equations are examined in detail. Results show that the Joule heating induces a pressure gradient along the capillary, which in turn modifies the normal plug-like electroosmotic velocity profiles. In addition, it is pointed out that, depending on the values of the dimensionless parameters, the modified velocity profiles can induce positive or negative pressure gradients at the inlet or outlet of the capillary.     

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.     

Transient mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate

The flow of viscous incompressible micropolar fluid past a semi-infinite vertical porous plate is investigated with the presence of thermal radiation field, taking into account the progressive wave type of disturbance in the free stream. The effects of flow parameters and thermophysical properties on the flow and temperature fields across the boundary layer are investigated. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. Numerical results of velocity profile of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. It is observed that, when the radiation parameter increases the velocity and temperature decrease in the boundary layer, whereas when Grashof number increases the velocity increases.     

Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

The unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.     

Natural convection of a micropolar fluid from a vertical truncated cone with power-law variation in surface temperature

This work presents a boundary-layer analysis about the natural convection heat transfer near a vertical truncated cone with power-law variation in surface temperature in a micropolar fluid. The transformed boundary layer governing equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of vortex viscosity parameter, the surface temperature exponent, and the Prandtl number. The heat transfer rates of the truncated cones with higher surface temperature exponents are higher than those with lower surface temperature exponents. Moreover, the heat transfer rate from a vertical truncated cone in Newtonian fluids is higher than that in micropolar fluids.     

Boundary layer flow and heat transfer on a continuous accelerated sheet extruded in an ambient micropolar fluid

An analysis is presented for the boundary layer flow and heattransfer on a continuous accelerated sheet extruded in a stationary ambient micropolar fluid. The governing non-linear differential equations have been solved numerically using implicit finite difference method. Numerical results explaining the effects of various parameters associated with the problem are discussed. Comparison results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag and cool the boundary. Larger acceleration is accompanied by larger skin-friction and heat transfer coefficients. In addition, varying the prescribed power law constant for the surface temperature affects the mechanism of heat transfer. Melt-spinning, polymer and glass industries and cooling of extruded melting plates are practical applications of this problem.     

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.     

Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations

This work examines the effects of the vortex viscosity parameter and the buoyancy ratio on the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The closed-form analytic solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived. Increasing the vortex viscosity parameter tends to increase the magnitude of microrotation and thus decreases the fluid velocity in the vertical channel. Moreover, the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid for micropolar fluids are lower than those of Newtonian fluids.     

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.     

LAMINAR IMPINGING JET HEAT TRANSFER WITH A PURELY VISCOUS INELASTIC FLUID

Laminar impinging flow heat transfer is considered with a purely viscous inelastic fluid. The rheology of the fluid is modeled using a strain rate dependent viscosity coupled with asymptotic Newtonian behavior in the zero shear limit. The velocity and temperature fields are computed numerically for a confined laminar axisymmetric impinging flow. Important features of the non-Newtonian developing flow field are described and contrasted with the Newtonian situation. It is demonstrated that very small departures from Newtonian rheology lead to qualitative changes in the Nusselt number distribution along the impinging surface. In particular, a mildly shear thinning fluid displays a pronounced off-stagnation point heat transfer maxima, a feature that is not observed with a Newtonian fluid. Hence, Newtonian fluid approximations cannot adequately describe experimental heat transfer measurements in such situations even though they may be deemed acceptable in terms of describing the velocity field in the incoming nozzle. Numerical results are presented to analyze the effect of the dimensionless nozzle-to-plate distance, the rheological parameters, and the Reynolds and Prandtl numbers on the magnitude of the off-stagnation point peak heat transfer rate. The influence of the rheology of the fluid is particularly significant at low nozzle-to-plate distances since the mean strain rate in the flow field increases as the nozzle-to-plate distance is reduced. The numerical heat transfer results are interpreted in the context of the developing flow field.     

Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation

An analysis is presented for the effects of chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of heat generation. The plate moves with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Analytical expressions are computed numerically. Numerical calculations are carried out the purpose of the discussion of the results which are shown on graphs and the effects of the various dimensionless parameters entering into the problem on the velocity, angular velocity, temperature, concentration. Also, the results of the skin-friction coefficient, the couple stress coefficient and the rates of the heat and mass transfers at the wall are prepared with various values of fluid properties and the flow conditions are studied.     

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.     

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.     

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 Pr_n, the velocity exponent parameter m and the temperature exponent parameter λ on the flow and heat transfer characteristics are analyzed in detail.     

TRANSIENT ANALYSIS OF COMBINED FORCED AND FREE CONVECTION-CONDUCTION ALONG A VERTICAL CIRCULAR FIN IN MICROPOLAR FLUIDS

The conjugate, transient, laminar, combined convection and conduction problem of mi-cropolar fluids along a vertical circular fin has been investigated. The coupled governing equations in dimensionless form are solved numerically using cubic spline collocation formulation. The analyses of heat transfer are divided into constant root temperature and constant heat flux from the root. Numerical results show that the heat transfer rate increases with increasing buoyancy force. A comparison of the heat transfer characteristics between a Newtonian fluid and a micropolar fluid is also discussed.     

MHD dissipative fluid past a stretching sheet in the presence of Soret effect with Newtonian convective heat and mass conditions

This article deliberates a theoretical study on a two‐dimensional magnetohydrodynamic free convection flow of an electrically conducting, heat generation/absorption fluid flowing past a linearly stretching sheet, placed vertical in a non‐Darcian porous medium with Soret effect. As the magnetic Reynolds number of the flow field considered very small (due to noncomparability of the induced and applied magnetic fields), the influence of the induced magnetic field is thus neglected. Again due to weak applied voltage differences at the lateral ends, the influence of the electric current is also ignored. A homotopy analysis method is developed to solve the similarity transformed equations subject to a set of convective heat and mass boundary conditions. Numerical data simulations are made on various fluid variables by using some practical/selected values of the governed parameters and illustrated through graphs and tables. It is found that the Newtonian heating parameter enhanced the velocity, temperature, and concentrations, while the solutal Newtonian heating parameter accelerates the rate of flow of heat and masses but minimizes the temperature gradient. The local Forchheimer and dissipation parameters are found to raise the temperature and concentrations, while the flow rate accelerates due to dissipation parameter but decelerates in presence of Forchheimer parameter.