Unsteadiness Parameter Research Articles

Investigation on Thermally Radiative Mixed Convective Flow of Carbon Nanotubes/Al2O3 Nanofluid in Water Past a Stretching Plate with Joule Heating and Viscous Dissipation

The nature of this prevailing inquisition is to scrutinize the repercussion of MHD mixed convective flow of CNTs/ nanofluid in water past a heated stretchy plate with injection/suction, heat consumption and radiation. The Joule heating and viscous dissipation are included in our investigation. The Navier–Stokes equations are implemented to frame the governing flow expressions. These flow expressions are non-dimensioned by employing suitable transformations. The converted flow expressions are computed numerically by applying the MATLAB bvp4c procedure and analytically by the HAM scheme. The impacts of relevant flow factors on fluid velocity, fluid temperature, skin friction coefficient, and local Nusselt number are illustrated via graphs, tables and charts. It is unequivocally shown that the fluid speed declines when escalating the size of the magnetic field parameter; however, it is enhanced by strengthening the Richardson number. The fluid warmness shows a rising pattern when enriching the Biot number and heat consumption/generation parameter. The findings conclusively demonstrate that the surface drag force improves for a larger scale of Richardson number and is suppressed when heightening the unsteady parameter. In addition, it is evident from the outcomes that the heat transfer gradient decreases to increase the quantity of the Eckert number in the convective heating case; however, the opposite nature is obtained in the convective cooling case. Our numerical results are novel, unique and applied in microfluid devices such as micro-instruments, sleeve electrodes, nerve growth electrodes, etc.

Mixed convective Williamson nanofluid flow over a rotating disk with zero mass flux

AbstractThis analysis concentrates on mixed convective unsteady two‐dimensional, viscous hydro‐magnetic Williamson nanofluid flow with heat, and mass transport toward a stretchable rotating disk with suction/injection and joule heating. In addition, convective and zero mass flux conditions are implemented at the boundary to study the flow characteristics. The converted coupled nonlinear ordinary differential equations (ODEs) are tackled utilizing a semi‐analytical technique known as Optimal Homotopy Analysis Method (OHAM). The obtained outcomes are illustrated graphically to anticipate the features of the governing terms affecting the flow model. The surface skin friction, heat, and mass transport rates are deduced and discussed in detail. The validation of the present article is verified and converges to earlier published statistics. Interestingly, analysis reveals that suction/injection parameter on axial and radial velocity profiles are quite the opposite and is identical in the case of thermal and concentration buoyancy parameter. Furthermore, the Weissenberg number dominates the flow movement; the unsteady parameter lessens the momentum and thermal boundary layer (BL) thickness.

Numerical Study of Heat and Mass Transfer for Williamson Nanofluid over Stretching/Shrinking Sheet along with Brownian and Thermophoresis Effects

The purpose of the current study is to investigate the non-Newtonian unsteady Williamson fluid on a stretching/shrinking surface along with thermophoresis and Brownian effects. Basically, the model consists of a time-dependent magnetic field. The fluid is considered to be electrically conducting due to the effect of the external magnetic field. The values of magnetic Reynolds number are so small that the induced magnetic field is assumed to be negligible. In the concentration equation, the effects of Brownian motion and thermophoresis are discussed. Employing the similarity transformations, the governing nonlinear Partial Differential Equations (PDEs) are converted into the Ordinary Differential Equations (ODEs). The resulting ODEs are solved with the combined effects of the Successive Over Relaxation (SOR) method and Finite Difference Method (FDM). The impact of all the including parameters such as suction parameter, injection parameter, stretching/shrinking parameter, the ratio of viscosity, local Weissenberg number, unsteadiness parameter, Eckert number, Prandtl number, Lewis number, Nusselt number, Brownian motion parameter, shear stress, heat transfer rate, and mass transfer rate are analyzed using graphs and tables. Results show that the values of fluid velocity are better for S=8, −S=0, λ=0.3, β*=0.9, Wi=0.3, and Aa=2.0. It is also depicted from the results that the values of boundary layer thickness are better for S=0, −S=−8, λ=0.3, β*=0.1, Wi=1.5, and Aa=0.25. From the above numeric results, it is concluded that the fluid velocity is reduced and the thermal boundary layer thickness is enhanced by the enhancement of the stretching parameter.

Theoretical Survey of Time-Dependent Micropolar Nanofluid Flow over a Linear Curved Stretching Surface

The heat and mass transfer of the unsteady flow of a micropolar fluid over a curved stretching surface was considered in this study. The Brownian motion and thermophoresis effects were explored in this analysis. The effects of suction/injection cases on the curved surface were discussed. Under flow assumptions, a mathematical model was designed employing boundary layer approximations using partial differential equations. A suitable transformation was developed using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique, namely bvp4c. The involved physical parameters’ influences are described in the form of graphs as well as numerical results in the form of tables. Our current work is helpful in the engineering and industrial fields. The unsteadiness parameter increases which Nusselt number at increased but concentrations declined. The thermophoresis parameter increases when increasing the Nusselt number because the small number of nanoparticles enhances the heat transfer rate. The temperature profile declined due to increasing values of unsteadiness parameter for both cases of suction and injection cases.

Koo and Kleinstreuer–Li correlation and modified Buongiorno model on unsteady radiative non-Newtonian fluid flow

This research paper investigates the heat and mass transport characteristics in an unsteady flow of Maxwell nanofluid (NF). While examining heat transfer properties, thermal radiation is taken into account. Further, copper oxide with water-based NF is considered. The mass transfer and effective thermal conductivity of nanofluid flow are scrutinized by Koo and Kleinstreuer–Li (KKL) NF model. Through apt transformations, relevant flow expressions are converted to ordinary differential equations (ODEs). The numerical approach Runge–Kutta–fourth–fifth Fehlberg’s order process (RKF-45) algorithm with shooting technique is utilized to solve the generated ODEs. Results reveal that, the rise in values of unsteadiness parameter has a positive impact on both concentration and thermal profiles. The Deborah number has constructive impact on heat transport and reverse influence on velocity field. The improved heat transport is seen for augmented values of radiation and heat source/sink parameters. The Brownian motion parameter has positive influence on heat transport and reverse effect on mass transport.

Unsteady flow of magnetohydrodynamic hybrid nanofluid over a stretching/shrinking sheet: Multiple solutions

The main goal of this article is to perform a heat transfer analysis of unsteady magnetohydrodynamic hybrid nanofluid flow over a stretching/shrinking sheet. The hybrid nanofluid is synthesized by adding two kinds of nano-sized particles. In this examination, TiO2 and Cu nano-sized particles are taken with water as a base fluid. Using an appropriate similarity transformation approach, a set of nonlinear equations is obtained from the governing equations of the current study. To solve the changed system, the Runge–Kutta–Fehlberg approach is applied combined with the shooting method. The obtained data is presented in graphs and tables. Here, dual solutions can be seen utilizing upper and lower division solutions particularly aimed at a specific domain of unsteadiness parameter. The skin friction coefficient parameter shows a considerable improvement. Whereas in the case of the shrinking sheet, larger values of the magnetic parameter and solid volume fraction results in a significant drop in the local heat transfer rate for the upper branch case, while the lower branch case shows a different pattern.

Williamson magneto nanofluid flow over partially slip and convective cylinder with thermal radiation and variable conductivity

This article is concerned with the study of MHD non-Newtonian nanofluid flow over a stretching/shrinking cylinder along with thermal radiation effects. Two-component slip mechanism models, namely Brownian motion and thermophoresis of nanofluid for the mass and energy transportation, developed by Buongiorno, are used. Convective heat transfer and nonuniform magnetic field are retained for the expanding/contracting cylinder. Variable thermal conductivity and heat generation effects along with slip boundary conditions are utilized over the cylinder surface. By utilizing the similarity transformation, these governing partial differential equations are converted into nonlinear ordinary differential equations (ODEs). To obtain numerical results, these ODE’S are solved by the shooting method using MATLAB software. The impact of different parameters like variable thermal conductivity, radiation parameter, magnetic parameter, Prandtl number, Brownian motion parameter, the magnetic parameter, Weissenberg number, the viscosity ratio parameter and mass transfer parameter, on the velocity, temperature and concentration is discussed graphically. Further, the Sherwood number, Nusselt number, the skin friction coefficient are also discussed through figures. It is noted through analysis that the speed of the nanofluid reduces for the higher Weissenberg number and expanding cylinder. For the contracting cylinder, i.e., for the negative unsteadiness parameter, the velocity increases.

A Numerical Analysis on the Unsteady Flow of a Thermomagnetic Reactive Maxwell Nanofluid over a Stretching/Shrinking Sheet with Ohmic Dissipation and Brownian Motion

The major objective of this current investigation is to examine the unsteady flow of a thermomagnetic reactive Maxwell nanofluid flow over a stretching/shrinking sheet with Ohmic dissipation and Brownian motion. Suitable similarity transformations were used to reduce the governing non-linear partial differential equations of momentum, energy and species conservation into a set of coupled ordinary differential equations. The reduced similarity ordinary differential equations were solved numerically using the Spectral Quasi-Linearization Method. The influence of some pertinent physical parameters on the velocity, temperature and concentration distributions was studied and analysed graphically. Further investigations were made on the impact of the Eckert number, Prandtl number, Schmidt number, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter and chemical reaction parameter on the skin friction coefficient, surface heat and mass transfer rates. The results were displayed in a tabular form. Obtained results reveal that the Maxwell parameter and the unsteadiness parameter reduce the Maxwell nanofluid velocity and the fluid temperature is increased with an increase in the Eckert number and thermal radiation parameter.

Flow and Heat Transfer Analysis of a Thin Film Ferromagnetic Liquid over an Unsteady Stretching Sheet

A two-dimensional, unsteady flow of a thin layer of ferromagnetic liquid over a stretching sheet is considered. The flow is exposed to an external magnetic field in the direction of the stretching sheet. The boundary layer equations with the associated boundary conditions are transformed into ODEs using suitable similarity transformations. The resultant system of ODEs is numerically solved using the shooting technique by appropriately guessing the initial values and then correcting them by the Newton-Raphson scheme. The effects of the dimensionless parameters on the flow and heat exchange characteristics are graphically analyzed. It is found that the thickness of the film reduces with magnetization and unsteadiness parameters.

Unsteady hybrid nanofluid flow over a convectively heated cylinder with inclined magnetic field and viscous dissipation: A multiple regression analysis

The current study explores the aspects of unsteady stagnation point flow of hybrid nanofluid (Cu-Al2O3/H2O) over a continuously moving and convectively heated stretching cylinder under the influence of oblique Lorentz force. The impacts of velocity slip, Joule dissipation, thermal radiation, viscous dissipation and internal heat generation are also incorporated into this study. Appropriate thermo-physical relations for the hybrid nanofluid are accomplished by following the Xue model. With the use of suitable similarity transformations, the governing dimensional mathematical equations are converted into dimensionless forms. Numerical solutions are obtained for the velocity and energy fields with the help of a shooting technique based on the Runge–Kutta–Fehlberg method of 5-th order and secant iteration. Graphical and tabular representations of numerical data are used to explore the physical impacts of various pertinent parameters on the hybrid nanofluid velocity and temperature. The stability of this approach and the validity of the obtained results are illustrated by comparing the current findings to previously reported data for a specific case. Further, the multiple (quadratic) regression analysis is performed to show the dominance of physical parameters on local skin-friction coefficient and Nusselt number. The thermal buoyancy force boosts the fluid flow while a reverse trend is observed for the magnetic and the velocity slip parameters. Heat transfer rate at the surface is improved with the enhancement in Biot number, thermal radiation and unsteadiness parameters.

Magnetic Impact on the Unsteady Separated Stagnation-Point Flow of Hybrid Nanofluid with Viscous Dissipation and Joule Heating

The behaviour of magnetic impact on the unsteady separated stagnation-point flow of hybrid nanofluid with the influence of viscous dissipation and Joule heating is investigated numerically in this study. A new mathematical hybrid nanofluid model is developed, and similarity solutions are obtained in the form of ordinary differential equations (ODEs). The bvp4c approach in MATLAB is used to determine the reduced ODEs’ estimated solutions. The influence of various physical parameters is scrutinised. The findings revealed that the skin friction coefficient increases with the increment of the nanoparticle volume fraction and the unsteadiness parameter. This observation is also applied to the heat transfer rate of the fluid. Additionally, the presence of the magnetic and acceleration parameter provides a significant result in the heat transfer performance. The addition of the Eckert number increased the temperature profile distribution, thereby spontaneously decreasing the heat transfer rate. The first solution is declared stable by the analysis of solution stability.

Mathematical modelling of boundary layer flow over a permeable and time-dependent shrinking sheet – A stability analysis

Micropolar fluid is one type of non-Newtonian fluid which consists of non-deformable spherical particles that suspended in viscous medium. In this paper, the problem of two-dimensional boundary layer flow over a permeable shrinking sheet with time dependent velocity in strong concentration micropolar fluid is studied theoretically. The mathematical model is governed by continuity, momentum and microrotation equations. Similarity variables are introduced so that, after performing the similarity transformation on the governing equations, the resulting system of nonlinear ordinary differential equations is then numerically solved using the program bvp4c in Matlab software. The effects of the micropolar material parameter, the unsteadiness parameter, the shrinking parameter and the mass suction parameter to the skin friction coefficient, velocity profiles and microrotation profiles are investigated. It is found that triple solutions exist for some values of the parameters that were considered. Based on the stability analysis that was performed, it showed that only two branches of solutions are categorized as stable, whereas one solution branch is unstable.

Unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on a stretched/contracted plate with modified pressure field

Purpose The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model. Design/methodology/approach Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge. Findings Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks. Originality/value First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Unsteady thermally radiative Prandtl fluid flow past a magnetized inclined porous stretching device with double-diffusion, viscous dissipation, and Joule heating

The extensive applications and complex nature of non-Newtonian fluids inspire researchers to explore them so it serves more precisely humankind. In this scenario, the Prandtl fluid over the inclined porous surface has been explored and formulated the mathematical model considering the magnetic, thermal radiation, and double diffusion effect. Also, the viscous dissipation and joule heating effect are taken into account to explore more features of the flow situation. The mathematical model of flow is renovated with the effective implementation of similarity invariants. The numerical investigation is carried out using the Runge–Kutta method and the results obtained are interpreted graphically. The effects of physical parameters such as Dufour and Soret number, radiation parameter, magnetic parameter, etc., on non-dimensional quantities, are graphically illustrated with MATLAB. The thermal boundary layer gets elevation for rising values of Eckert number, magnetic parameter, unsteadiness parameter, Dufour number, and thermal radiation.

Dynamics of Unsteady Flow of Chemically Reactive Upper-Convected Maxwell Fluid with Temperature-Dependent Viscosity: Keller Box Analysis

The heat and mass transfer characteristics of unsteady flow of incompressible chemically reactive upper-convected Maxwell fluid along a stretching surface in the presence of temperature-dependent viscosity has been studied. The theoretical analysis on heat and mass transfer over a stretching sheet is investigated for numerical analysis. With the use of stream function formulation, the governing boundary layer equations of momentum, energy, and concentration are reduced to a set of linked ordinary differential equations. The nonlinear ordinary differential equations are then solved numerically by using the Keller Box method. The physical behavior of governing parameters on velocity, temperature, and concentration profiles and the local skin friction coefficient and heat and mass transfer rates are graphed and tabulated. The physical impact of Maxwell parameter β, unsteadiness parameter M, Schmidt number Sc, Prandtl number Pr, reaction rate parameter γ, and variable viscosity parameter ε on the heat and mass transfer has been examined along the stretching surface numerically. The novelty of the present work is to examine the importance of destructive reaction and contractive reaction on the dynamics of upper-convected Maxwell fluid flow in the presence of temperature-dependent viscosity effects. It is observed an interesting behavior of temperature distribution and concentration profile is noted for lower value of viscosity parameter ε in the presence of chemical reaction. It is also found that skin friction and the rate of heat transfer are decreased by increasing the variable viscosity parameter ε .

Lie symmetry analysis of heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation and external magnetic field

Fluid flow and heat transfer in thin films over unsteady stretching sheets are studied and analyzed by employing similarity transformations and analytical or numerical solution schemes. We derive Lie point symmetries for system of partial differential equations describing the flow and heat transfer in a thin liquid film on an unsteady stretching surface with viscous dissipation in the presence of external magnetic field. We deduce a 5-dimensional Lie point symmetry algebra. We use a couple of the admitted Lie point symmetry generators to construct new similarity transformations for the considered model, through associated invariants. These transformations enable reductions of the model to nonlinear ordinary differential equations. We construct analytic solutions for this system using the Homotopy analysis method to study the considered MHD flow and heat transfer. These results are presented in the form of tables and figures to reflect variations in fluid velocity, film thickness and heat transfer with the magnetic parameter, Prandtl number, Eckert number and unsteadiness parameter. We show that these variations in the velocity and temperature profiles are different from those reported earlier for the flow and heat transfer within a thin film under the effects of viscous dissipation and external magnetic field.

Unsteady Separated Stagnation-Point Flow Past a Moving Plate with Suction Effect in Hybrid Nanofluid

Previous research has shown that incorporating stagnation-point flow in diverse manufacturing industries is beneficial due to its importance in thermal potency. Consequently, this research investigates the thermophysical properties of the unsteady separated stagnation-point flow past a moving plate by utilising a dual-type nanoparticle, namely a hybrid nanofluid. The impact of suction imposition on the entire hydrodynamic flow and heat transfer as well as the growth of boundary layers was also taken into account. A new mathematical hybrid nanofluid model is developed, and similarity solutions are obtained in the form of ordinary differential equations (ODEs). The bvp4c approach in MATLAB determines the reduced ODEs estimated solutions. The results show that increasing the stagnation strength parameters expands the skin friction coefficient and heat transfer rate. The addition of the suction parameter also resulted in an augmentation of thermal conductivity. Interestingly, reducing the unsteadiness parameter proportionately promotes heat-transfer performance. This significant involvement is noticeable in advancing industrial development, specifically in the manufacturing industries and operations systems.

Stability Analysis of Unsteady Hybrid Nanofluid Flow over the Falkner-Skan Wedge.

Numerous manufacturing processes, including the drawing of plastic films, have a major impact on mass transport. These functionalities necessitate the solution of the Falkner–Skan equation and some of its configurations when applied to various geometries and boundary conditions. Hence, the current paper discusses the impact of unsteady hybrid nanofluid flow on a moving Falkner–Skan wedge with a convective boundary condition. This problem is modeled by partial differential equations, which are then converted into ordinary (similar) differential equations using appropriate similarity transformations. The bvp4c technique in MATLAB solves these ordinary differential equations numerically. Since more than one solution is possible in this paper, stability analysis is conducted. Thus, it is found that only one stable solution is identified as reliable (physically realizable in practice). The skin friction coefficient and heat transfer rate, along with the velocity and temperature profile distributions, are examined to determine the values of several parameters. The findings reveal that dual-type nanoparticles and wedge angle parameters improve thermal efficiency. A lower value of the unsteadiness parameter reduces the efficiency of hybrid nanofluids in terms of heat transfer and skin friction coefficient, whereas increasing the Biot number of the working fluid does not affect the critical point in the current analysis.

On numerical analysis of hydromagnetic radiative Jeffery nanofluid flow by variable thickness surface with activation energy and unsteadiness aspects

The mass and thermal flow of an unsteady Jeffery fluid over a surface having variable thickness with the presence of magneto-hydrodynamics is considered here. For this physical problem, we develop a mathematical formulation using Buongiorno’s model for the Jeffery fluid. Characteristics of pedesis motion and thermo-migration of nanoparticles with the thermal link of heat source/sink are also examined. An arrangement of similarity variables is introduced to transform the transport equations into solvable forms in Cartesian configuration. A numerical solution of the differential system is obtained by using the algorithm of Runge–Kutta-Fehlberg fourth-fifth (RKF-45) method. Physical interpretations of obtained outcomes are established with the help of various plots, isotherms, and streamlines. Flow velocity reduces wall-thickness and unsteadiness parameters. Temperature enhances with the advances of radiation parameters, whereas regresses for the progression of Deborah number. Concentration improves with the progression of the activation energy parameter. Nusselt number condenses for velocity index and Eckert number. A comparison benchmark is also presented for solution validation.

Unsteady magnetohydrodynamic nanofluid flow over a permeable exponentially surface manifested with non-uniform heat source/sink effects

Current research inspects the influences of two-dimensional unsteady nanofluid flow over a permeable exponential stretching sheet with the impact of magnetic field parameter, thermal radiation together with a non-uniform heat source or sink. The dimensional equations namely Partial differential equations (PDE’s) are transformed into dimensionless form as ordinary differential equations (ODE’s) by using the suitable transformations. The reframed ODE’s are solved numerically through the computer-based tool MATLAB with the bvp4c package. The derived results of velocity, temperature and species distributions are depicted graphically. Also, the numerical results of skin friction coefficients, heat transfer rate and mass transfer rate in terms of Nusselt number and Sherwood number are deployed via tables. The comparison of the present work with published work shows complete agreement for skin friction factor and Nusselt number. In absolute sense skin friction enhances as magnetic field parameter enhances. The Brownian motion and thermophoresis parameters play an essential role towards thermophysical flow field of nanofluids. Further, we noticed that both Brownian motion parameter and thermophoresis parameter cause an enhancement in the fluid temperature. Furthermore, the unsteady parameter causes increase in wall friction and heat transfer rate. However, the opposite trend is observed for the heat source/sink parameters.