Effects of surface roughness on mixed convective nanofluid flow past an exponentially stretching permeable surface

A numerical study is carried out to display the effects of surface roughness on mixed convective nanofluid flow along an exponentially stretching surface in presence of suction/injection. The dimensional coupled nonlinear partial differential equations are transformed into dimensionless form by using suitable non-similar transformations. The resulting equations are solved by utilizing the Quasilinearization technique as well as the implicit finite difference scheme. The influence of several non-dimensional parameters on various profiles and gradients is examined. The results are presented graphically, which are analyzed to depict the effects of various physical parameters, for example, Brownian diffusion parameter Nb, thermophoresis parameter Nt, suction/blowing parameter A and Lewis number Le. In order to analyse the influence of surface roughness on mixed convective nanofluid flow, the major part of this research paper is devoted to investigate the effects of the small parameter α and frequency parameter n over the gradients defined at the wall. The results reveal that an increase in the values of Nb and Nt, enhances the velocity and temperature of the fluid. The increasing value of suction parameter (A > 0) reduces the velocity of the fluid. Further, the increasing values of Nb and Le decrease the nanoparticle volume fraction profile. The sinusoidal variations are observed in the skin-friction coefficient, Nusselt number as well as the nanoparticle Sherwood number. Moreover, with the addition of nanoparticles, the magnitude of the skin-friction coefficient increases, while the magnitude of heat transfer rate decreases, significantly.     

Variable Fluid Property Effect on Heat Transfer and Frictional Flow Characteristics of Water Flowing through Microchannel

The effects of temperature-dependent viscosity and thermal conductivity on heat transfer and frictional flow characteristics of water flowing through a microchannel are numerically investigated in this work. The hydrodynamically and thermally developing flow with no-slip, notemperature jump, and constant wall heat flux boundary condition is numerically studied using 2D continuum-based conservation equations. A significant deviation in Nusselt number from conventional theory is observed due to flattening of axial velocity profile due to temperaturedependent viscosity variation. The Nusselt number shows a significant deviation from conventional theory due to flattening of the radial temperature profile due to temperature-dependent thermal conductivity variation. It is noted that the deviation in Nusselt number from conventional theory is maximum for combined temperature-dependent viscosity and thermal conductivity variations. The effects of temperature-dependent viscosity and thermal conductivity on the Fanning friction factor are also investigated. Additionally, the effects of variable fluid properties on Poiseuille number, Prandtl number, and Peclet number are also investigated.     

MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation

This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.     

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell （UCM） fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.     

Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing

The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated.The transformed equations are solved numerically by using the shooting method.The exact solution corresponding to the momentum equation for the steady case is obtained.Fluid velocity initially decreases with the increase of unsteadiness parameter.Due to an increasing Casson parameter the velocity field is suppressed.Thermal radiation enhances the effective thermal diffusivity and the temperature rises.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.     

Simultaneous investigation of MHD and convective phenomena on time-dependent flow of Carreau nanofluid with variable properties: Dual solutions

In countless applications, there is a thoughtful necessity for augmenting the poor thermal conductivity of conventional liquids to improve effectual heat transfer liquids. Nanofluids are fluids interruptions of nanoparticles and broad scrutiny have been presented on nanoliquid solicitations in heat transfer progressions. The intention of this exertion is to scrutinize the dual nature solutions of unsteady magnetite Carreau nanofluid influenced by porous stretching/shrinking surface. The phenomena of heat and mass transfer have been established in the manifestation of combined convective conditions with heat sink/source and variable thermal conductivity. By utilizing compatible conversions to rehabilitate the structure of nonlinear partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs) which were then elucidated numerically via bvp4c. Under the impact of diverse somatic parameters the graphical depiction of all the probable dual solutions of velocity, temperature, concentration, skin-friction coefficient, local Nusselt and Sherwood numbers are scrutinized. These outcomes specify that the liquid velocity display similar tendency for both upper and lower solutions and decline for unsteadiness parameter, while it enhance for Weissenberg number.     

MHD Maxwell flow modeled by fractional derivatives with chemical reaction and thermal radiation

Heat transfer in a time-dependent flow of incompressible viscoelastic Maxwell fluid induced by a stretching surface has been investigated under the effects of heat radiation and chemical reaction. The magnetic field is applied perpendicular to the direction of flow. Velocity, temperature, and concentration are functions of z and t for the modeled boundary-layer flow problem. To have a hereditary effect, the time-fractional Caputo derivative is incorporated. The pressure gradient is assumed to be zero. The governing equations are non-linear, coupled and Boussinesq approximation is assumed for the formulation of the momentum equation. To solve the derived model numerically, the spatial variables are discretized by employing the finite element method and the Caputo-time derivatives are approximated using finite difference approximations. It reveals that the fractional derivative strengthens the flow field. We also observe that the magnetic field and relaxation time suppress the velocity. The lower Reynolds number enhances the viscosity and thus motion weakens slowly. The velocity initially decreases with increasing unsteadiness parameter δ. Temperature is an increasing function of heat radiation parameter but a decreasing one for the volumetric heat absorption parameter. The increasing value of the chemical reaction parameter decreases concentration. The Prandtl and Schmidt numbers adversely affect the temperature and concentration profiles respectively. The fractional parameter changes completely the velocity profiles. The Maxwell fluids modeled by the fractional differential equations flow faster than the ordinary fluid at small values of the time t but become slower for large values of the time t.     

Visualization of molten pools and invisible laser beam profiles using an ultraviolet CCD camera

Experiments were conducted on the effects of a wall distance and velocity ratio of suction flow to injection flow on the flow and heat transfer characteristics of a circular impinging jet accompanying an annular suction flow. As a result, it is found that in the case of accompanying suction flow, a higher Nusselt number can be obtained compared with in the case without suction flow, under a condition of the wall distance within eight times of injection pipe diameter from the near pipe exit edge. In addition, when the effect of velocity ratio is examined at a fixed arbitrary wall distance, it is found that there exists an optimum velocity ratio where the Nusselt number becomes the maximum. It is shown that these heat transfer characteristics are closely associated with the fluctuating velocity and the mean velocity in the two-dimensional velocity field observed by Particle Image Velocimetry (PIV).     

Analysis of Melting Heat Transport in a Cross Flow Direction: A Comparative Study

An incompressible three-dimensional laminar flow in a cross flow direction is described in this work. The term of melting and viscous dissipation is incorporated in the mathematical modeling of present flow problem. The flow expressions are converted into dimensionless equations, which are solved with help of Runge-Kutta scheme. Impact of the emerging parameters on the non-dimensional velocities and temperature and friction-factors and local Nusselt number are examined. The convergence analysis is found for ∈ < 0 and 0 < ∈ ≤ 2. Comparative analysis is made between the obtained results and published data for limiting case. It is explored at the surface that the melting parameter retards the liquid temperature while it enhances the fluid velocity.     

Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties

The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field as well as uniform suction and injection applied perpendicular to the parallel plates. A numerical solution for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature-dependent viscosity and thermal conductivity on both velocity and temperature distributions is examined.     

Influence of radiative heat flux in nonlinear convection of quartic order in Casson fluid past a vertical permeable plate with variable suction and Hall current

The current study centralizes on unsteady free convection slip flow of Casson fluid past a vertical permeable plate with Hall current, radiative heat flux, and variable suction. The nonlinear convection is subjected to quartic order. Perturbation method is used to convert the non-linear coupled partial differential equation of the momentum and energy to a system of ordinary differential equations. The dimensionless governing equations are solved analytically for velocity and temperature profiles. The graphs are plotted for sundry parameters for variations in the distinct flow fields w.r.t distance from the plate. Variation in the skin friction for the axial and transverse cases are presented in the form of graphs for various parameters. It is observed that with the increase in the order of non-linear convection and value of radiation parameter, the velocity field increases in Casson fluid. The increase in heat absorption parameter and Prandtl number decreases the temperature profile and increase in radiative heat flux parameter increases the temperature profile.     

Numerical analysis for peristalsis of Carreau–Yasuda nanofluid in an asymmetric channel with slip and Joule heating effects

This study investigates the peristaltic transport of magnetohydrodynamic (MHD) Carreau–Yasuda nanofluid through an asymmetric channel. Viscous dissipation, Joule heating and Hall effects are also included in the analysis. Velocity, thermal and concentration slip conditions are considered. The problem is modeled subject to long wavelength and low Reynolds number assumptions. Resulting nonlinear equations are numerically solved. Impact of embedded parameters on the fluid velocity, temperature, concentration of nanoparticles and heat and mass transfer rates at the wall are examined. Graphical results show that an escalation in the strength of appliedmagnetic field and increase in the value of Hall parameter reduce the velocity of nanofluid. Brownian motion and thermophoresis effects increase the temperature of the nanofluid. The present study shows an excellent agreement with the previously available studies in the limiting case.     

The influence of heat radiation on mixed convection boundary layer flow of a viscoelastic fluid over a circular cylinder with constant surface temperature

The influence of mixed convection boundary layer flow of a viscoelastic fluid over an isothermal horizontal circular cylinder has been analyzed. The boundary layer equations governing the problem are reduced to dimensionless nonlinear partial differential equations and then solved numerically using Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against curvature parameter. Effects of mixed convection parameter and radiation-conduction parameter on skin friction coefficient and Nusselt number are illustrated through graphs and table. The boundary layer separation points along the surface of cylinder are also calculated with/without radiation, and a comparison is shown. The presence of radiation helps to reduce the skin friction coefficient in opposing flow case and enhances it for assisting flow case. The increase in value of radiation-conduction parameter helps increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids. The boundary layer separation delays due to thermal radiation.     

Mass transpiration on Newtonian flow over a porous stretching/shrinking sheet with slip

The motivation behind this article is to research the Newtonian liquid flow porous stretching/shrinking sheet utilizing a Brinkman model. The leading system of non-linear partial differential equations relating the article is mapped to standard ordinary differential equations via similarity transformations. Exact result is obtained for velocity. The effects of the Brinkman number or viscosity ratio, slip parameter, Darcy number, suction/injection (mass transpiration) parameter and the mass suction parameter on the velocity dispersion are introduced graphically and talked about. The outcomes have conceivable innovative applications in extrusion process and such other unified zones and in the fluid based frameworks including stretchable materials. Examination of fluid flow past a permeable stretching/shrinking sheet embedded in a non-Darcy permeable medium has been performed for a wide scope of various parameters. Exact solution has been obtained.