Stretching Sheet Research Articles

Mhd Stagnation Point Flow and Heat Transfer of Cu –Water Nanofluid over A Stretching Sheet

A comprehensive study of Magnetohydrodynamics flow (stagnation Point) with heat transferal properties of Cu–Water nanofluid along a stretched sheet in the existence of a transverse magnetic field is analyzed. The governing equalities along with their conditions on boundary points are firstly converted to ordinary differential equations of non-linear category by similarity transformations. Lastly finite difference discretization is utilized. The flow and heat transfer parameters, namely: stretching parameter, magnetic parameter, the Prandtl number and solid volume fraction are investigated by tablular and graphical representation.

Numerical Solution of Two-Phase Radiated Unsteady Flow Over a Horizontal Stretching Sheet with Simultaneous Effect of Electrification, Radiation and Non-Uniform Internal Heat Source/Sink

A parametric study to investigate the impact of electrification and radiation inside a thermal particulate boundary layer, where the flow is due to an unsteady stretching sheet in presence of non-uniform heat source/sink. Both the fluid as well as the particles are assumed to be gray, emitting and absorbing radiation. Again, neither the fluid is considered in electric medium nor supplied by an external electric force. But, due to the random motion of the particles i.e., the interaction between particle-particle, particle-fluid and particle-wall, a tribo-electrification occurred. As on impact, both the fluid and particles are electrified though the flow has been considered in a neutral medium. Hence, a balanced mathematical model of highly non-linear partial differential equations has been formulated for two-phase unsteady boundary layer considering the above parameters/impacts on both the phases. An appropriate similarity transformation has been employed to transfer the governing equations into ordinary differential equations and solved numerically by built in solver Bvp4c of MATLAB. An excellent agreement between the present and previous literature has been made to validate the result. Moreover, the influence of Electrification parameter, Radiation parameter, Internal heat source/sink parameter on the rate of heat transfer and other flow characteristics has been analyzed.

Chemical Reaction Effects on of Nanofluid Past a Permeable Stretching Sheet with Slip Boundary Conditions and MHD Boundary Layer Flow

The overall exploration is excited to investigate the MHD limit layer float of a nanofluid with the results of attractive field, slip limit situation, warm radiation and synthetic reaction has been researched. Closeness change is utilized to change over the administering non-straight limit layer conditions into coupled better request non-direct normal differential conditions. those conditions are mathematically addressed utilizing fourth request R-k technique alongside shooting strategy. An assessment has been accomplished to explain the outcomes of overseeing boundaries like assorted materially conditions. Mathematical results are gotten for the speed, temperature and mindfulness, as well as, for the pores and skin rubbing, close by Nusselt reach and neighborhood Sherwood range for a few benefits of overseeing boundaries. The mathematical results are talked about through graphically and referenced subjectively.

Note on the Numerical Solutions of Unsteady Flow and Heat Transfer of Jeffrey Fluid Past Stretching Sheet with Soret and Dufour Effects

A numerical investigation of unsteady boundary layer flow with heat and mass transfer of non-Newtonian fluid model, namely, Jeffrey fluid subject, to the significance of Soret and Dufour effects is carried out by using the local nonsimilarity method and homotopy analysis method. An excellent agreement in the numerical results obtained by both methods is observed and we establish a new mathematical approach to obtain the solutions of unsteady-state flow with heat and mass transfer phenomenons. Similarity transformation is applied to governing boundary layer partial differential equations to obtain the set of self-similar, nondimensional partial differential equations. Graphical results for different emerging parameters are discussed. The dimensionless quantities of interest skin friction coefficient, Sherwood number, and Nusselt number are discussed through tabulated results. The main novelty of the current work is that the average residual error of the mth-order approximation of the OHAM scheme for steady-state solution is decreased for higher-order approximation. Further, a rapid development of the boundary layer thickness with the increasing values of dimensionless time τ is observed. It is noted that for large values of τ, the steady state in the flow pattern is gained. It is worth mentioning that the magnitude of Sherwood number is increased with the increasing values of Schmidt number Sc and Dufour number Df. The magnitude of local Nisselt number is increased for the increasing values of Soret number, Sr.

Magnetohydrodynamics Micropolar Boundary Layer Flow Past a Stretching Sheet with Microstructural Slip Heat Generation with Convective Boundary Condition

The formulation depicting the magnetohydrodynamics MHD boundary layer of a micropolar fluid on a moving sheet with heat generation and convective boundary conditions in its rectangular form is presented. The PDEs formulated are transformed into nonlinear ODEs via the stream functions and appropriate similarity variables. The solution to the nonlinear coupled equations were presented in decomposed form. The comparison of skin friction values with literatures for validation were carried out and an agreement depicted. The implications of dimensionless physical parameters that appear in this work are graphically studied in the presence of microstructural slip. Physical parameters such as Biot number and heat generation parameters are found to enhance the fluid temperature profile.

Joint Effects of Thermophoresis and Brownian Motion on Williamson-Nano Fluid Flow Near a Non-Linearly Stretching Sheet Filled by Porous Medium

With the help of influences of Thermophoresis and Brownian motion, as well as magneto hydrodynamic boundary layers, we study an electrically conducting, incompressible, viscous Williamson-Nanofluid flow towards a stretched sheet surrounded by the porous material. Because of its form, the stretched sheet is regarded as nonlinear. The basic flow-regulating non-rectilinear fractional differential conditions are declined to non-rectilinear coupled differential equations in their most simplest form for this flow thru applying the necessary resemblance conversions arranged as fractional derivatives. Toward solve these non-rectilinear coupled conventional fractional derivatives, the Runge-Kutta technique of fourth order with shooting technique is used, depending on the boundary conditions. It is given in this research report, as well as a graph and a comprehensive analysis of the consequences of physical limitations towards flow variables including velocity besides hotness, over and above nanoparticle concentration, among other things. Numerous factors were used to compute and analyse values in numbers of the Cf, as well as Nux and Shx in addition other related variables. These plots are used to make conclusions, and the conclusions that are drawn are verified to ensure that they are accurate. From this problem, the velocity profiles are decreasing with boosting the importance of Maxwell fluid stricture in addition Element of such magnetization. With increasing effects of Thermophoresis and Brownian motion, the patterns of temperatures too increases. By means of the importance of Dufour number increases, temperature sketches are also increases. An expansion of the Thermophoresis parameter leads to increased nanoparticle volume concentration distribution and the in the instance of, the opposite effect is observed. Brownian motion effect. concentration profiles are increasing with rising values of Soret number parameter.

Entropy Optimization and Heat Transfer Analysis of Magneto-Bioconvective Powell Eyring Nanofluid with Nonlinear Thermal Radiation and Chemical Reaction Over a Stretching Sheet

This paper investigates the entropy generation in the bioconvection of Powell Eyring nanofluid containing motile gyrotactic microorganisms over a convectively stretching sheet. The influences of magnetohydrodynamic forces, nonlinear thermal radiation effects, chemical reactions of species in a Powell Eyring nanofluid flow are analyzed. Motile microorganisms are added along with nanoparticles in the Powell Eyring base fluid for the prevention of nanoparticles agglomeration and to stabilize the nanoparticles in the suspension. The governing nonlinear partial differential equations along with boundary conditions are solved numerically after these equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformation. The results are compared with previously published research papers. The impact of significant physical and bioconvection parameters on the profile of nanofluid velocity, temperature, nanoparticles concentration, the density of motile microorganisms, and entropy generation are analyzed graphically. It is noticed that the velocity profile increases by increasing the values of the Powell Eyring fluid parameter. The incidence of nanoparticles in Powell Eyring nanofluid decreases the nanoparticle concentration due to an increase in the value of the chemical reaction parameter and Lewis number. Also, the profile of entropy generation increases as the values of Br, γ1, and γ2 are increased.

Impact of Melting Heat Transfer Analysis in MoS2 and MgO Nanoparticles

In this extraordinary work, heat transfer examined around boundary layer of nanofluids MoS2–H2O and MgO–H2O. Micropolar ferrofluid is addressed in this investigation. Energy equation can be elaborated by employing Cattaneo-Christov heat flux analysis with relevant thermal conductivity. This article manages Darcy-Forchheimer. Disturbance in stretchable sheet has been represented by Darcy Forchheimer expression. Mixed convection heat flow at the incidence of melting effect from a stretching surface embedded in a porous medium is described. Governing PDE’s of current analysis are lessen into a set of ODE’s using requisite congruity transformations. Set of similarity equations can be fixed out with RKF-45. Achievements of distinct parameters on f′, θ distributions are represented by the aid of graphs.

Flow and Heat Transfer Analysis MHD Nanofluid due to Convective Stretching Sheet

Objectives: The study of flow and heat transfer on a permeable stretching sheet of Magnetohydrodynamic nanofluid under the influence of convective boundary condition is presented in this article. Mathematical modeling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed. Methods: Governing nonlinear partial differential equations are reduced into nonlinear ordinary differential equations and then shooting method with fourth order Adams-Moulton Method is employed for its solution. Findings: The effects of magnetic parameter (0  M  2), Thermophoresis parameter (0:1  Nt  0:7) Lewis number (1  Le  4), Suction parameter (0  fw  3), Biot number(0:1  Bi  0:7) and Viscous dissipation(0  Ec  4) on axial velocity, temperature and concentration profiles are shown graphically. Numerical results were compared with another numerical approach and an excellent agreement was observed. The solutions under the impacts of different physical governing parameters are illustrated by means of graphs and tables. Effects of viscous dissipation is also discussed. Novelty: Despite the enormous importance and repeated application of nanofluids in industry and science, no attempt has been made to investigate the viscous dissipation effect on heat transfer with a permeable linear stretch sheet. Keywords: MHD; Nanofluid; Stretching Sheet; Viscous dissipation; Shooting technique; Adams-Moulton Method

Thermal radiative flux and energy of Arrhenius evaluation on stagnating point flowing of Carreau nanofluid: A thermal case study

This research extends to investigate the effects of activation energy and thermal radiation on mixed convection striation point flow of Carreau liquid toward the stretchable sheet. Heat transport assessment is utilized in the existence of activation energy. For flowing formulations, Carreau substance rheological relationships are used. For modelling and simulation, the Buongiorno nanoliquid model with thermophoretic and Brownian diffusion features is used. The obtained partial differential equation is converted to an ordinary differential equation by utilizing appropriate transmission. The mathematical formulation of the outcoming equation is achieved by utilizing the RK-Fehlberg approach with the bvp4c technique. This assessment illustrates several significant empirical features of flow and heat transport. Numerical simulations are taken for various scales of Hartmann number, temperature ratio parameter, and Schmidt number. The assumption is that the velocity estimation reduces the Hartmann number. The opposite result of the thermal ratio parameter remains valid for the Nusselt effect and temperature curve. Furthermore, the influence of Schmidt quantity on the Sherwood amount and solutal contour are extremely opposite.

Hybrid Nanofluid on Mixed Convection Flow Past a Stretching Sheet with Irregular Heat Source/Sink

This research studies the behaviour of hybrid nanofluid on mixed convection flow over a stretching sheet by considering the effect of non-uniform heat source/sink. The chosen base fluid is water with two different nanoparticles which are copper and aluminium oxide. The governing partial differential equations are reduced into ordinary differential equations using a similarity transformation technique. The resulting governing system then solved numerically using Keller-box method. The influence of space- and temperature-dependents of non-uniform heat source and sink parameters as well as the unsteadiness parameter is presented graphically. The current study shows that, the space- and temperature dependents of non-uniform heat source and sink significantly raises the fluid’s temperature. Comparative study also shows that hybrid nanofluid has higher temperature and heat transfer coefficient than single nanofluid and conventional fluid. It can also be concluded that, the enhancement of heat transfer rate can be achieved by reducing the parameter of space- and temperature dependents of non-uniform heat source and sink.

Numerical Study of the Electromagnetohydrodynamic Bioconvection Flow of Micropolar Nanofluid through a Stretching Sheet with Thermal Radiation and Stratification.

The current work explores the bioconvection micropolar nanofluid through a stretching surface subjected to thermal radiation, stratification, and heat and mass transmission. Bioconvection contains the gyrotactic (random movement of microorganism in the direction of gravity with weak horizontal verticity) unicellular microorganism in aqueous environments. Heat and mass transfer assists the bioconvection to occur. The aim of this research is to evaluate the heat transfer rate of nanofluid in the presence of a unicellular microorganism. Self-similar variables are induced to reduce the governing equations into a non-linear differential system which is further solved via the bvp4c algorithm to tackle the fluid problem. Using visual representations, the effects of a number of dimensional less factors arising from the dimensional less differential system are determined. For a range of limiting conditions, the obtained results of this model correspond precisely to those in the literature. This study's findings are highly regarded in the evaluation of the impact of key design factors on heat transfer and, therefore, in the optimization of industrial processes. Skin friction, local Nusselt number, Sherwood number, and density of microorganism concentrations are also studied for various parameters. Buoyancy ratio factor supports skin friction and density of microorganism profile to increase. Local Nusselt number drops due to the thermal radiation factor. Brownian motion speeds up the Sherwood number.

Three-dimensional rotating flow of Cu–Al2O3/kerosene oil hybrid nanofluid in presence of activation energy and thermal radiation

The present exploration talks to a steady and incompressible chemically reacting hybrid-nanofluid rotating flow toward a stretchable sheet in presence of activation energy and magnetic field. We have chosen kerosene oil as base fluid and two nanoparticles specifically Al2O3 and Cu for hybrid-nanofluid and Al2O3 for regular nanofluid. Relative studies of imprint factors between hybrid nanofluid and customary nanofluid have been implemented for our present article. The leading system of PDEs subject to their compatible boundary conditions are renovated into a system of ODEs and then resolved by the Runge–Kutta–Fehlberg quadrature method with shooting practice. The stimulus of ignite flow parameters on the flow precise is carried off accurately through figures, bar diagrams and tables. Our analysis conveys that the primary velocity profiles for both hybrid and regular nanofluid diminish with intensifying values of Hartmann number and rotational parameter, however secondary velocity profile enhances with augmentation of the rotational parameter. Temperature profiles of both category fluids lead to increase with growing values of radiation parameter and Hartmann number, whereas opposite phenomena observe for concentration profiles with improving values of chemical reaction parameter. Again, rate of heat transfer diminishes sharply for leading Hartmann number.

Entropy Analysis of EMHD Hybrid Nanofluid Stagnation Point Flow over a Porous Stretching Sheet with Melting Heat Transfer in the Presence of Thermal Radiation

In this study, the entropy formation of an electromagnetohydrodynamic hybrid nanofluid at a stagnation point flow towards a stretched surface in the presence of melting heat transfer, second-order slip, porous medium, viscous dissipation and thermal radiation are investigated. Hybrid nanoparticles alumina (Al2O3) and copper (Cu) are considered, with the base fluid water (H2O). Similarity transformations are used to address the governing partial differential equations (PDEs) that lead to the corresponding ordinary differential equations. The resulting ODEs are solved by employing bvp4c solver numerically in the MATLAB package. The effects of temperature, transport, production of entropy and Bejan number Be are graphically exhibited. Higher radiation parameters R and an electric field E lead to an increase in fluid temperature. The velocity boundary layer is lowered by the magnetic field and porous media parameters. The opposite behaviour is observed in the electric field E. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, electronics, heat exchangers, water purification, lubricants and soaps as well.

Exploration of Multiple Transfer Phenomena within Viscous Fluid Flows over a Curved Stretching Sheet in the Co-Existence of Gyrotactic Micro-Organisms and Tiny Particles

In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion behaviors are also investigated by assuming slip conditions at the boundary. A non-linear system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). For convergent solutions, the obtained ODE system is solved by the use of the BVP4C routine integrated MATLAB package. In addition, the impacts of different influential parameters on motile micro-organisms, temperature, velocity, and concentration profiles are deliberated. The velocity field is observed to be reduced when the slip parameter increases. As the main results, it is demonstrated that the distribution of motile microorganisms against the curvature parameter decreases significantly. Similarly, it is found that the nanofluid parameters (i.e., Brownian motion and thermophoresis parameters) and the Peclet number reduce the motile micro-organisms’ number. On the other hand, it is evidenced that the motile micro-organisms’ distribution can be improved with an increase in bio-convective Schmidt number.

Transportation of thermal and velocity slip factors on three-dimensional dual phase nanomaterials liquid flow towards an exponentially stretchable surface

The fundamental purpose of this research is to elaborate on slip boundary conditions and the flow of three-dimensional, stable, incompressible, rotating movements of nanoparticles lying across a stretchable sheet. The mathematical model for fluid flow is created using the assumptions stated above. The partial differentials are produced after utilizing boundary layer estimates. The partial differential governing equations are reduced into three coupled ordinary differential equations by using similarity transformations. After, applying transformations the system is solved numerically. Numerical results are approved with the help of the MATLAB bvp4c algorithm. The analysis shows that velocity and temperature are strongly dependent on essential parameters like stretching ratio, velocity slip, rotation, thermal slip parameter, and Prandtl number. Numerical values of distinct parameters on heat flux and skin friction factors are shown in a tabulated form. Partial velocity and thermal slip are applied to the temperature surface. The comparison among the nano-sized particles copper oxide and silver with water base nanofluid affecting velocity and temperature fields are used for analysis. Moreover, the Graphical depiction designates that the velocity and temperature spreading of the thermal slip parameter is increasing. It is observed that Ag-water is the best heat carrier as compared to CuO-water nanofluid.

EMHD Nanofluid Flow with Radiation and Variable Heat Flux Effects along a Slandering Stretching Sheet.

Nanofluids have gained prominence due to their superior thermo-physical properties. The current paper deals with MHD nanofluid flow over a non-linear stretchable surface of varying thickness in the presence of an electric field. We investigated the effects of nanometer-sized copper (Cu) particles in water (base fluid) as a nanofluid, as well as non-linear thermal radiation, variable fluid viscosity, Joule heating, viscous dissipation, and non-uniform heat flux. The current study's aim is influenced by the immense applications in industry and machine building. It has been observed that linear stretching sheets have been extensively used in heat transfer research. Moreover, no effort has been made yet to model a non-linear stretching sheet with variable thickness. Furthermore, the effects of electromagnetohydrodynamics (EMHD) boundary-layer flow of a nanofluid with the cumulative impact of thermal radiation, variable viscosity, viscous dissipation, Joule heating, and variable heat flux have been investigated. Sheets with variable thicknesses are practically significant in real-life applications and are being used in metallurgical engineering, appliance structures and patterns, atomic reactor mechanization and paper production. To investigate the physical features of the problem, we first examined the model and identified all the physical properties of the problem. This problem has been formulated using basic laws and governing equations. The partial differential equations (PDEs) that govern the flow are converted into a system of non-dimensional ordinary differential equations (ODE's), using appropriate transformations. The Adam-Bashforth predictor-corrector technique and Mathematica software are utilized to numerically solve the resulting non-dimensionalized system. The interaction of various developing parameters with the flow is described graphically for temperature and velocity profiles. It is concluded that the velocity of nanoparticles declines as the intensity of the magnetic field increases. However, the temperature of the nanomaterials rises, as increasing the values of the electric field also increases the velocity distribution. The radiation parameter enhances the temperature field. The temperature of the fluid increases the occurrence of space- and time-dependent parameters for heat generation and absorption and radiation parameters.

Numerical Analysis of Hybrid Nanofluid Flow Over a Nonlinear Stretching Sheet with Viscous Dissipation, Joule Heating Effects

The main objective of this article is to explore magnetohydrodynamic hybrid nanofluid flow past a stretching sheet. Mathematical model is developed by revisiting the work done by previous study and extended the same model for hybrid nanofluid flow scenario with viscous dissipation, joule heating and thermal radiation effects. Choosing appropriate similarity variables governing equations are transformed into system of ordinary differential equation and thereby solved by using shooting mechanism. Impact of various physical parameters on momentum, temperature and concentration profiles are shown through graphs. Important engineering quantities like skin friction coefficient, Nusselt number etc. are computed and discussed. In order to verify the code, the computed results are compared with existing literature and acceptable convergence notified in obtained results. Comparative analysis for mono particle nanofluid and hybrid nanofluid is explained for all flow parameters.

Entropy Optimization in MHD Nanofluid Flow over an Exponential Stretching Sheet

We numerically investigate mixed convective heat and mass transport in incompressible nanofluid flow through an exponentially stretching sheet with temperature-dependent viscosity. The fluid flow equations are transformed to a system of non-linear ordinary differential equations using appropriate similarity transformations and solved numerically by using the multi-domain bivariate spectral quasi-linearization technique. The fast convergence of the method is shown by demonstrating that the error is exponentially small for a finite number of iterations. The significance and impact of different fluid parameters are presented and explained. For engineering relevance, the entropy generation number has been calculated for different fluid parameter values.

Unsteady Two Dimensional Mixed Convection MHD Couple Stress Fluid Flow through an Inclined Stretching Sheet with Chemical Reaction

In this work, the investigation has focused on the unsteady hydromagnetic mixed convection couple stress fluid through an inclined linearly stretching sheet. The model equations governing the flow are converted to ordinary differential equations employing appropriate similarity transformation variables. An efficient technique, Runge-Kutta 4th order (RK4) technique together with shooting method is deployed to tackle the dimensionless equations with relevant boundary conditions. The impacts of various parameters such as unsteadiness parameter , Hartman number , mixed convection parameter , concentration buoyancy parameter , angle of inclination , chemical reaction parameter and Schmidt number are analysed and discussed with plots. Fluid velocity decreases as the unsteadiness, Hartman number, Schmidt number, and chemical reaction parameters rise; while the angle of inclination, mixed convection, and concentration buoyancy parameters speed up the flow. Furthermore, the unsteadiness, angle of inclination and mixed convection parameters reduce fluid temperature, while all the parameters reduce flow concentration.