Combined influence of cross-diffusion and variable fluid properties on free convection flow past a vertical cone

The free convective flow of an incompressible viscous fluid over an isothermal vertical cone with variable viscosity and variable thermal conductivity is examined in the presence of the Soret and Dufour effects. As thermal and solutal boundary conditions at the cone's surface, the constant temperature and concentration (WTC) and constant heat and mass flux (HMF) cases are taken into account. The successive linearization method is applied to linearize a system of nonlinear differential equations that describes the flow under investigation. The numerical solution for the resulting linear equations is attained by means of the Chebyshev spectral method. The obtained numerical results are compared and found to be in good agreement with previously published results. The impact of significant parameters on the heat and mass transfer rates is evaluated and presented graphically for the WTC and HMF situations. In both cases, the Soret number increases the skin friction coefficient and rate of heat transfer while decreasing the Sherwood number. With an increase in the Dufour parameter, the coefficient of skin friction and Sherwood numbers increase while the heat transmission rate decreases.     

Diffusion of liquid hydrogen and oxygen in nonlinear mixed convection nanofluid flow over vertical cone

The phenomenon of triple diffusive nonlinear mixed convection over a vertical cone is completely a new concept of rheological study and behaviours of such flows are not reported in the open literature as yet. The study of such flows has relevance to various industrial applications. In the current study, nanoparticles are considered in the working fluid that comprises of water as base fluid with three diffusive components, namely, heat, liquid hydrogen and oxygen. This innovative physical problem has mathematical formulation in the form of nonlinear partial differential equations (PDE's). In order to simplify the mathematical analysis, these equations are non-dimensionalised and then linearized, by utilizing non-similar Mangler's transformations and technique of Quasilinearization, respectively. The implicit finite difference scheme is used to transform the linear PDE's into block tri-diagonal system, which is then solved by utilizing Varga's algorithm. In this work, interesting results have been obtained, for example, the presence of nonlinear convection parameter for temperature leads to increase in the velocity profile, local skin-friction coefficient as well as the local wall heat transfer rate, while it causes reduction in the temperature profile. The wall suction reduces the concentration profiles, while it increases the corresponding gradients. The local Nusselt number is low for the mixture of nanoparticles, liquid hydrogen and oxygen, and water as compared to that for the corresponding ordinary mixture (i.e. not containing the nanoparticles). The surface roughness effects on transport rates are observed in terms of their sinusoidal variations which are prominent away from the apex of the cone. Further, the impacts of nanoparticles remains same for the present flow regime as in case of regular water based nanofluid flow systems.     

Linear stability analysis of MHD flow of micropolar fluid with thermal radiation and convective boundary condition: Exact solution

Magnetohydrodynamic (MHD) flow of micropolar fluid by including the thermal radiation and convective condition on a shrinking surface in the presence of mass suction effects has been investigated. The momentum, angular momentum and energy equations, and the solutions of these equations are valid for whole Navier stokes, and microrotational and energy equations have been solved exactly. We obtain the solution in the form of an incomplete γ function for the energy equation. The results reveal that dual solutions exist for certain domains of different physical parameters. Furthermore, high suction produces the high effect of drag force, and as a result, coefficient of skin friction increases in the first solution. Stability analysis has been performed and determined that the first solution is more stable.     

Study of liquid oxygen and hydrogen diffusive flow past a sphere with rough surface

The impact of roughness on nonlinear mixed convective nanofluid flow past a sphere is analysed in the presence of nonlinear density variations. This study is found to be innovative as it investigates the effects of nanoparticles, nonlinearity and surface roughness on mixed convective flow past a sphere with three diffusive components. The problem is modelled in the form of nonlinear partial differential equations that are dimensional in nature. This set of equations is transformed to dimensionless form by applying non-similar transformations. The technique of Quasilinearization is employed to linearize the transformed set of equations and then the implicit finite difference scheme is used for further simulation to get the required numerical solutions. The graphical presentation of numerical results exhibit that the friction, heat, mass and nanoparticles mass transfer rates at the surface of sphere increase along with the fluid's velocity due to the roughness of the surface, while the fluid's temperature reduces, significantly. The steep jump in the fluid's velocity near the wall is observed due to the surface roughness. The present analysis reveals that separation of boundary layer can be delayed with the proper selection of roughness and mixed convection parameters. Also, the third diffusing component, namely, liquid oxygen influences the fluid flow significantly. That is, the introduction of liquid oxygen diffusion into the liquid hydrogen diffusion diminishes the species concentration boundary layer, while it increases the corresponding mass transfer rate.     

Influence of liquid hydrogen and nitrogen on MHD triple diffusive mixed convection nanoliquid flow in presence of surface roughness

An innovative study of influence of surface roughness and nanoparticles on mixed convection flow is considered in presence of liquid hydrogen and liquid nitrogen. In fact, in order to understand the effects of surface roughness and nanoparticles on the flow characteristics of MHD triple diffusive mixed convection nanoliquid flow along an exponentially stretching rough surface, the flow problem is modelled in terms of highly nonlinear partial differential equations subject to the appropriate boundary conditions. Then, those equations are made non-dimensional with the application of non-similar transformations. The resultant nonlinear dimensionless coupled partial differential equations with boundary constraints are solved by using the Quasilinearization technique in combination with the implicit finite difference scheme. The liquid hydrogen and liquid nitrogen are considered as species concentration components. The surface roughness is modelled by a sine wave representation and hence the sinusoidal variations have been observed in gradients such as skin-friction coefficient, heat and mass transfer rates. It is observed that the effects of surface roughness on the skin-friction coefficient are more prominent near the origin than that in downstream. The addition of nanoparticles into the ambient ordinary fluid enhances the skin-friction coefficient and reduces the magnitude of wall heat transfer rate for both cases of smooth and rough surfaces. The rapid variations have been observed in the wall mass transfer rate due to the surface roughness in comparison to that of skin-friction coefficient and wall heat transfer rate. Further, the magnitude of wall mass transfer rate of liquid nitrogen is higher than that of liquid hydrogen.     

Comprehensive analysis of radiation impact on the transfer of heat and mass micropolar MHD free convective fluid flow across a stretching permeability sheet with suction/injection

As part of our research, we investigate the analysis influence of radiation on heat and mass transfer free convection of micropolar MHD fluids over a stretched porosity sheet involving suction and injection. The governing energy, rotational momentum, and concentration and momentum partial differential equations are transformed into ordinary differential equation ones via a similarity transformation. This system of equations is then solved by using MATLAB's built-in solver. The Sherwood numbers, Nusselt, friction factor, wall couple shear stress, and dimensionless profiles are all influenced by the various physical parameters of the flow. When the material parameter is increased, velocity rises but decreases when the magnetic parameter and surface condition factor are increased.     

Irreversibility analysis for Casson thermo-fluidics inside a cone: Cattaneo–Christov heat flux

In this communication, thermodynamic irreversibility arising in dissipative Casson fluid flow inside a cone is investigated. The boundary–layer flow is considered wherein the motion is caused due to a point sink at the cone's vertex and the movement of the wall of the cone. The wall of the cone is subjected to mass transpiration that alters the flow and thermal regime. The cone having fluid-saturated porous medium experiences Cattaneo–Christov heat flux. The configuration admits a similarity transformation that yields a boundary value problem (BVP) comprising an ordinary differential equation. The BVP is treated by the fourth-order R-K method along with the shooting algorithm. The system yields a dual solution for momentum and energy, which gives rise to a dual regime for entropy distribution. Numerical computations provide quantities of interest viz. velocity and temperature distributions, skin friction coefficient, Nusselt number, and entropy distribution. Phenomena exhibited through profiles/tables for velocity, temperature, entropy, streamlines, and other quantities of interest reveal interesting results.     

On the effectiveness of viscous dissipation and Joule heating on steady MHD flow and heat transfer of a Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents

The combined effects of viscous dissipation and Joule heating on steady magnetohydrodynamics (MHD) flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents is studied. An external uniform magnetic field is applied in the z-direction and the fluid is subjected to uniform suction. Numerical solutions are obtained for the governing momentum and energy equations. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

Impact of thermal diffusion and chemical reaction on oscillatory MHD convective flow of a viscoelastic fluid through a porous medium in a slip flow regime

The purpose of the current investigation is to analyze the influence of thermal diffusion on magnetohydrodynamic viscoelastic fluid flow with concurrent heat and mass transfer near an oscillating porous plate in a slip flow Regime under the influence of a uniform transverse magnetic field. The uniqueness of the present study is to examine the effects of viscoelastic property (Walters B' model) on the flow and heat transfer phenomena when a transverse magnetic field and time-dependent fluctuating suction at the boundary surface are present in a porous medium with a uniform porous matrix. A regular perturbation technique is used to solve the governing equations for small elastic parameters. Graphical representations are used to show how different parameters affect skin friction, temperature, concentration, and velocity. It is observed that concentration distribution as well as the coefficient of friction is enhanced due to the thermal diffusion effect. It is noticed that the visco-elastic parameters reduce the velocity of the fluid. In addition, chemical reactions and suction factors cause the flow field's temperature to drop. Furthermore, the fluid concentration drops under the chemical reaction effect.     

Heat and mass transfer effect on an unsteady MHD radiative chemically reactive Casson fluid over a stretching sheet in porous medium

The objective of the present study is to investigate the effects of the variable magnetic field, chemical reaction, thermal radiation, Soret effect, and variable heat absorption on the fluid flow and heat and mass transfer of an unsteady Casson fluid past a stretching surface in a saturated porous medium. Velocity slip near the plate and conjugate heating boundary conditions in heat and mass transfer have been considered in this study. Due to the complexities in boundary conditions, the analytic solution of the governing equations of the present model is not possible. Thus, to overcome these issues, the coupled partial differential equations of the model are converted into a set of ordinary differential equations using similarity transformation. These equations have then been solved numerically using the fourth-order Runge-Kutta technique via the shooting method. The effects of various pertinent flow parameters on the velocity, concentration, and temperature field have been studied graphically. For the field of engineering, to get an insight into the physical quantities, especially Nusselt number, Sherwood number, and skin friction, their numerical values have been estimated against various parameters and presented in tables. From the tabulated values, it has been perceived that the shear stress increases with an increase in magnetic parameter, unsteadiness parameter, Casson parameter, and heat source parameter, whereas the Biot number shows the reverse trend. The mixture of porous media has justified that the heat transport process over a stretching sheet results in averting heat loss and accelerating the process of cooling, which is a significant outcome of the study. Furthermore, it has also been revealed that with the increase in the Soret effect and magnetic field, there is a reduction in the fluid velocity and temperature near the plate, whereas there is an increase in the species concentration. It has also been mentioned that the effects of the variable magnetic field have been widely applied in various engineering applications like magnetohydrodynamic (MHD) propulsion forces, rate of cooling, MHD power generation, and so on.     

Steady magnetohydrodynamic Poiseuille flow of two immiscible non-Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

In this paper, an analytical study has been carried out on a steady magnetohydrodynamics (MHD) Poiseuille flow of two immiscible fluids in a horizontal channel with ohmic heating in the presence of an applied magnetic field. The channel is divided into two sections, Region I and Region II, respectively. Region I contains an electrically conducting, third grade, non-Newtonian fluid while Region II is a Newtonian fluid. The regular Perturbation series method is used to transform the coupled nonlinear differential equations governing the flow into a system of linear ordinary differential equations in both fluid regions. Suitable interface matching conditions were chosen to obtain separate solutions for each fluid in both regions and the results were displayed graphically for various values of physical parameters, such as pressure gradient, suction parameter, Hartmann number, Prandtl number, viscosity, and conductivity ratios to show their effects on the flow. The effect of skin friction and Nusselt number was shown with the aid of tables. The results obtained among other findings clearly shows that as the value of the magnetic parameter increases, the velocity and temperature of the fluid decrease.     

Mixed convection boundary layer flow over a thin vertical cylinder with localized injection/suction and cooling/heating

The effects of localized cooling/heating and injection/suction on the mixed convection flow on a thin vertical cylinder have been studied. The localized cooling/heating and (or) injection/suction introduce a finite discontinuity in the mathematical formulation of the problem which increases its complexity. In order to overcome this difficulty, a nonuniform distribution of wall temperature (heat flux) and surface mass transfer is considered at certain sections of the cylinder. The nonlinear coupled parabolic partial differential equations governing the mixed convection flow under boundary layer approximations have been solved numerically by using an implicit finite-difference scheme. The effects of the localized cooling/heating and (or) injection/suction on the heat transfer are found to be significant, but the effects of cooling/heating on the skin friction are comparatively small. The positive buoyancy force which assists the flow and the curvature parameter increase the skin friction and heat transfer.     

Laminar,transitional and turbulent friction factors for gas flows in smooth and rough microtubes

Theoretical and experimental works on microscale transport phenomena have been carried out in the past decade in the attempt to analyze possible new effects and to assess the influence of downscaling on the classical correlations which are used in macro-scale heat and fluid flow, following the need to supply engineers with reliable tools to be used in the design of micro-scale devices. These results were sometimes in mutual contrast, as is the case for the determination of the friction factor, which has been found to be lower, higher or comparable to that for macroscopic channels, depending on the researchers. In this work the compressible flow of nitrogen inside circular microchannels from 26 μm to 508 μm in diameter and with different surface roughness is investigated for the whole range of flow conditions: laminar, transitional and turbulent. Over 5000 experimental data have been collected and analysed. The data confirmed that in the laminar regime the agreement with the conventional theory is very good in terms of friction factors both for rough and smooth microtubes. For the smaller microchannels (<100 μm) when Re is greater than 1300 the friction factor tends to deviate from the Poiseuille law because the flow acceleration due to compressibility effects gains in importance. The transitional regime was found to start no earlier than at values of the Reynolds number around 1800. Both smooth and sudden changes in the flow regime have been found, as reported for conventional tubes. Fully developed turbulent flow was attained with both smooth and rough tubes, and the results for smooth tubes seem to confirm Blasius' relation, while for rough tubes the Colebrook–White correlation is found to be only partially in agreement with the experimental friction factors. In the turbulent regime the dependence of the friction factor on the Reynolds number is less pronounced for microtubes than the prediction of the Colebrook–White correlation and the friction factor depends only on the microtube “relative roughness”.     

动载径向粗糙轴承分析

摘要本文采用H. Christensen提出的随机粗糙模型,推导了径向轴承的纵向粗糙和横向粗糙型的雷诺方程和相应的承载力、流量系数、摩擦系数公式.对有限长径向轴承的两种粗糙型雷诺方程用差分方法进行数值求解,得到了粗糙度对轴承的承栽力、流量系数和摩擦系数影响的图表,并对实例进行了粗糙轴承的轴心轨迹的计算和分析.     

Effects of surface roughness on mixed convection nanoliquid flow over slender cylinder with liquid hydrogen diffusion

The influence of surface roughness on boundary layer flow characteristics over moving surfaces is of considerable research interest in recent times. In the present study, the effects of surface roughness on flow over moving slender cylinder are analyzed in presence of mixed convection nanoliquid boundary layer flow. The problem is modelled in terms of highly nonlinear dimensional partial differential equations, which are written in non-dimensional form with the help of non-similar transformations. The resulting equations are reduced to linear partial differential equations by utilizing Quasilinearization technique, which are discretized using implicit finite difference scheme. The results obtained during the numerical simulation are then depicted through graphs in terms of various profiles and gradients and are analyzed with proper physical explanations. The roughness of slender cylinder surface is represented in a deterministic model as a sine wave form and yields sinusoidal variations in the values of skin-friction coefficient, wall heat and mass transfer rates. It is observed that the surface roughness effects are more prominent away from the orifice. The local frequency of gradients increases (i.e. wavelength decreases) with the increase in the frequency of surface roughness (n). The addition of nanoparticles into the ordinary fluid enhances the skin-friction coefficient and wall mass transfer rate. However, due to its effects, significant reduction is observed in the wall heat transfer rate. The phase difference of gradient oscillations arising in presence of nanoparticles is suppressed further away from the origin due to surface roughness. Interestingly, the amplitude of gradient oscillations remain higher in case of nanoliquid in comparison with that in case of ordinary fluid. Furthermore, the magnitude of wall mass transfer rate of liquid hydrogen is higher than that of nanoparticle wall mass transfer rate, which signifies the higher diffusivity of nanoparticles. The results of present study are of practical relevance to industrial applications such as polymer fibre coating and coating of wires.     

MHD viscoelastic fluid non-Darcy flow over a vertical cone and a flat plate

A study has been carried out to analyze the double dispersion effects on unsteady, free convective, chemically reacting, MHD viscoelastic fluid (Walters liquid-B model) flow over a vertical cone and a flat plate saturated with non-Darcy porous medium in the presence of Soret and Dufour effects. The constitutive equations for the boundary layer regime are solved by an efficient finite difference scheme of the Crank-Nicolson type. The features of the fluid heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail to interpret the effect of significant parameters of the problem. The overall heat and mass transfer profiles are enhanced for increasing the thermal and solutal dispersion effects, respectively. The results indicate that the Soret and Dufour effects have considerable effect on the viscoelastic fluid flow through non-Darcy porous medium.     

MHD mixed convection flow adjacent to a vertical plate with prescribed surface temperature

The steady MHD mixed convection flow adjacent to a bounding surface immersed in an incompressible viscous fluid is considered. The governing system of partial differential equations is first transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference scheme. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles. It is found that dual solutions exist for both assisting and opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of a magnetic field.     

Numerical investigation of the influence of roughness on the laminar incompressible fluid flow through annular microchannels

The main objective of this work is to investigate, by means of numerical simulation, the effects of the surface roughness on the laminar fluid flow through annular microchannels, and to propose a method to take into account the surface roughness effects in the calculation or simulation of the fluid flow through these microchannels. This method is based on the classical viscous flow equations, and consists in building an equivalent smooth channel with the same flow resistance as the “rough” one.     

Numerical solution of MHD,Soret, Dufour,and thermal radiation contributions on unsteady free convection motion of Casson liquid past a semi-infinite vertical porous plate

In this paper, the unsteady motion of Casson liquid over a half-infinite penetrable vertical plate with MHD, thermal radiation, Soret, and Dufour contributions have been explored numerically. In the physical geometry, the Casson liquid flows to the layer from the penetrable vertical plate. At the layer, Casson liquid is set into motion and the flow equations are illustrated using coupled partial differential equations (PDEs). This set of PDEs is simplified to form dimensionless PDEs with the use of normal nondimensional transformation. The controlling parameters' effects on the working fluid are extensively discussed on velocity, concentration, and temperature and presented graphically. Computational values of Nusselt plus Sherwood number and skin friction for controlling parameters are depicted in a tabular form. Our outcomes show that a raise in the Casson term depreciates the velocity because of the magnetic parameter influence on the fluid flow. The Soret parameter was found to accelerate the skin friction along with the Sherwood number coefficients. An incremental value of the Dufour parameter was detected to hike the skin friction alongside the Nusselt number. Results of this study were found to be in conformity with previously published work.