Reduced Skin Friction Coefficient Research Articles

Magnetized Flow of Maxwell Fluid over a Slippery Stretching Reactive Surface with Thermophoretic Deposition

This manuscript investigated mathematically magnetized Maxwell fluid over slippery stretching reactive surface with thermophoretic deposition. Similarity transformation was used to recast partial differential equations modeling flow problem to nonlinear coupled ordinary differential equations which were solved using fourth order Range-Kutta method and Newton-Raphson shooting technique. Numerical results were compared with literature-based results and found to be in good accord. Skin friction coefficient, Nusselt number, Sherwood number, velocity profiles, temperature profiles and concentration profiles which are of importance to engineers, were found to be influenced by thermo-physical parameters governing the dynamics of flow. Their effects were illustrated in tabular form and graphically. The study found that increasing Thermophoretic deposition parameter, Momentum slip parameter and Biot number amplified rate of heat transfer but decreased rate of mass transfer and Skin friction coefficients. Thermal Grashof, Solutal Grashof, and Damkohler numbers reduced skin friction coefficients but increased heat and mass transfer rates.

Velocity slip effect on magnetized casson nanofluid over shrinking/stretching cylinder: duality and stability analysis

The aim of current research is to assess heat transfer characteristics over a cylinder undergoing stretching or shrinking using Cason Nanofluid. Additionally, dual solutions stability has been analyzed. The governing equations for the two-phase model consist of partial differential equations (PDEs), which are subsequently transformed into ordinary differential equations (ODEs) using the similarity transformation. The MATLAB software’s bvp4c solver is then used to numerically solve the transformed ODEs. The graph also shows the results of skin friction coefficient, heat transfer coefficient, and the Sherwood number. Furthermore, the validity of the current data is confirmed and shown to be in good agreement by comparing them to the existing literature. The variation of Casson nano fluid velocity, which is the variation of reduced skin friction coefficient increases as the Casson fluid parameter values increase. The critical values against and are respectively. The temperature variation indicates that the local Nusselt number variation decreases as the curvature parameter values increase. The first solution is characterized by positive values of the smallest eigenvalues suggesting stability. Conversely, the second solution is associated with negative values of the smallest eigenvalues indicating instability. To identify the stable and physically feasible solution, a stability analysis is performed. Graphical analysis is used to examine the influence of relevant physical parameters on the profiles of temperature, concentration, velocity and momentum.

Stratification and Radiation of Heat in Hybrid Gold-Graphene/Ethylene Glycol Nanofluid Flows Past a Leaning Cylinder

Hybrid gold-graphene/ethylene-glycol (EG) nanofluid past a permeable leaning cylinder is devoted in the current investigation under the effect of thermal radiation and stratification. The governing partial differential equations are reformulated into nonlinear ordinary differential equations by implementing similarity terms. A shooting approach is elected to reformulate the equations into a boundary value problem which is determined by applying a bvp4c code in MATLAB. The effects of selected parameters regarding the recent model on dimensionless velocity and temperature disseminations, reduced skin friction coefficient and reduced Nusselt number are analyzed and presented in graphs and tables. It is perceived that by rising the value of the thermal stratification and radiation parameter, the reduced Nusselt number for the preferred mono and hybrid nanofluids will be declined. The reduced Nusselt number is reported to be the highest value when considering hybrid gold (ϕ s1=0.02)-graphene (ϕ s2 = 0.04)/EG nanofluid.

Active and Passive Control of Nanoparticles Under the Influence of Magnetized Nanofluid Flow Over a Convectively Heated Slippery Wedge

This research investigate the upshots of actively and passively controlled nanofluid flow over a wedge. Comparison is done for various wedge angle parameter. Magnetic field is employed in normal to the flow direction. Velocity slip effect and external heat source is incorporate to the system. Leading partial differential equations are converted nonlinear ordinary differential equations with the help of suitable similarity transformation. Runge Kutta-4 method with shooting technique is used to solve the system. MAPLE-2019 software is applied to simulate the whole system. The results are described by graphs and corresponding values of engineering interest are tabulated properly. For magnetic parameter reduced skin friction coefficient value is increased by 7.31% but for injection situation and 9.32% or suction effect. Biot number also gives us escalated velocity profile. We get 10.56% increment in skin friction for suction effect and 7.25% for injection effect. Heat lines and mass lines also show excellent result for different parameter under the comparison of active and passive controlled of nanofluid flow.

Free Convection of Viscoelastic Nanofluid Flow on a Horizontal Circular Cylinder with Constant Heat Flux

The current research study is focusing on a mathematical model for free convection boundary flow on a horizontal circular cylinder in a viscoelastic nanofluid has been constructed in this paper with boundary conditions constant heat flux. The Tiwari and Das Nanofluid model have been chosen in this analysis to investigate more nanofluid effects. A dimensionless set of partial differential equations is formed by using suitable non-dimensional variables. The transformed boundary layer equations are solved numerically using a finite difference scheme namely the Keller-box method. The effects of a few chosen factors on flow and heat transmission are investigated. Numerical solutions were obtained for the reduced skin friction coefficient, Nusselt number and Sherwood number as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the viscoelastic parameter and nanoparticles volume fraction were analysed and discussed.

Engine oil enhanced performance with hybrid graphene-SWCNT nanomaterials over a Riga curvy surface

Hybrid graphene nanomaterials and single-wall carbon nanotubes (SWCNTs) saturated in a steady laminar viscous incompressible engine oil over a permeable and stretchable curvy Riga surface are focussed in the present study. The effects of nanoparticle shape factor, nanoparticle volume fraction and thermal radiation towards the non-Newtonian flow are considered. The proposed partial differential governing equations are initially transformed into non-linear ODEs aided with similarity expressions. Subsequently, the numerical MATLAB's bvp4c package is utilized to solve the equations. Then, the parameters' influences on dimensionless velocity and temperature distributions, reduced skin friction coefficient and reduced Nusselt number are presented tabularly and graphically. Hybrid graphene-SWCNTs/engine oil has the least velocity, yet the greatest temperature profile when φ1= 0.04 and φ2= 0.02 are considered. It is also observed that the heat transfer performance enhances as the values of nanoparticle shape factor and thermal radiation increase. The lamina-shape nanomaterials are highly recommended to elevate the heat transfer performance of hybrid graphene-SWCNTs/engine oil for realistic applications. The present hybrid nanofluid flow with consideration of thermal radiation and nanoparticle shape factor allows enhancement in the heat and mass transfer for various engineering, technological and industrial operations especially in the design of submarines, thermal reactors and micro-coolers.

Exact solutions for MHD and radiative wall jet hybrid nanofluid flow over a permeable surface with velocity slip and convective boundary conditions

AbstractIn this research, we investigated the wall jet problem for a hybrid nanofluid with MHD, thermal radiation, velocity slip, and convective boundary conditions. After converting the governing partial differential equations into nonlinear ordinary ones, by using the proper similarity transformations, they were theoretically solved in view of the hypergeometric function. Comparing the present results with those in the literature, a very good agreement was obtained for fixed values of the included parameters. For some included parameters, regions of physical solutions were presented. By deducing the critical and terminated values of the suction/injection parameter, dual solutions for the reduced skin friction coefficient have been determined. It was found that the hybrid nanofluid temperature is efficiently heated by increasing values of the moving wall, absolute value of the Biot number, and thermal radiation parameters. However, it is cooled by enlarging values of the velocity slip and suction parameters.

Modified Buongiorno’s model for biomagnetic hybrid nanoliquid past a permeable moving thin needle

PurposeThe purpose of this paper is to study the steady biomagnetic hybrid nanofluid (HNF) of oxytactic microorganisms taking place over a thin needle with a magnetic field using the modified Buongiorno’s nanoliquid model.Design/methodology/approachOn applying the appropriate similarity transformations, the governing partial differential equations were transformed into a set of ordinary differential equations. These equations have been then solved numerically using Runge–Kutta–Fehlberg method of fourth–fifth order programming in MAPLE software. Features of the velocity profiles, temperature distribution, reduced skin friction coefficient, reduced Nusselt number and microorganisms’ flux, for different values of the governing parameters were analyzed and discussed.FindingsIt was observed that as the needle thickness and solid volume fraction increase, the temperature rises, but the velocity field decreases. For a higher Peclet number, the motile microorganism curve increases, and for a higher Schmidt number, the concentration curve rises.Originality/valueOn applying the modified Buongiorno’s model, the present results are original and new for the study of HNF flow and heat transfer past a permeable thin needle.

Unsteady MHD Stagnation Point Flow of Al2O3-Cu/H2O Hybrid Nanofluid Past a Convectively Heated Permeable Stretching/Shrinking Sheet with Suction/Injection

The numerical investigation of unsteady magnetohydrodynamic (MHD) stagnation point flow of Al2O3-Cu/H2O hybrid nanofluid past a convectively heated permeable stretching/shrinking sheet with suction/injection effect is underlined. The characteristic of MHD and boundary condition with suction/injection has received a lot of consideration due to its across-the-board application in mechanical and chemical engineering. The governing continuity, momentum and energy equations are transformed into a system of nonlinear ordinary differential equations using similarity transformation, which is then solved using the bvp4c routine. Numerical results are obtained for the skin friction coefficient, local Nusselt number as well as the velocity and temperature profiles for certain values of the governing parameters, namely suction/injection parameter, copper nanoparticle volume fraction parameter and MHD parameter. Results showed that both velocity profile and temperature increase as the suction/injection parameter increases for the first solution and decreases for the second solution. Similarly, when increase the value of MHD parameter M, the velocity and temperature profiles are decreases for both solutions. The magnitude of the reduced skin friction coefficient and the local Nusselt number are notably increased for the first solution with increasing values of the suction/injection and MHD parameters. Finding also revealed that the skin friction coefficient is intensified in conjunction with the local Nussel number by adding up the copper nanoparticle volume fraction. In general, dual solutions are found to exist to a particular extent of the stretching/shrinking sheet.

Free Convection Boundary Layer Flow from a Vertical Truncated Cone in a Hybrid Nanofluid

The present study investigates the mathematical model of free convection boundary layer flow from a vertical truncated cone immersed in Cu/water nanofluid and Al2O3-Cu/water hybrid nanofluid. The governing non-linear equations are first transformed to a more convenient set of partial differential equations before being solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number and the reduced skin friction coefficient are obtained and illustrated graphically as well as temperature profiles and velocity profiles. Effects of the alumina Al2O3 and copper Cu nanoparticle volume fraction for hybrid nanofluid are analyzed and discussed. It is found that the high-density and highly thermal conductivity nanoparticles like copper contributed more in skin friction and convective heat transfer capabilities. The appropriate nanoparticles combination in hybrid nanofluid may reduce the friction between fluid and surface but yet still gave the heat transfer capabilities comparable to metal nanofluid.

Soret and heat generation effects on unsteady MHD Casson fluid flow in porous medium

This article studies motion with quadratic speed on the unsteady free convective MHD Casson fluid flow in a porous medium. The fluid in electrically conducting and bounding plate has ramped the surface concentration. The characteristics of heat and mass transfer are analyzed with thermal diffusion, heat generation, chemical reaction, and thermal radiation. The governing dimensionless equations are solved using the Laplace transform technique, and analytical expressions for velocity, temperature, and concentration are obtained. For both boundary conditions, the expression for Skin friction, Nusselt number, and Sherwood number are obtained and represented in tabular form. Effects of several pertinent parameters on velocity, temperature, and concentration distribution are presented graphically. It is seen that the mass buoyancy force increases with Soret number which leads to accelerated fluid flow. Chemical reaction and porosity of the fluid tend to reduced Skin friction coefficient, while Casson fluid and magnetic field tend to reverse effect on it.

Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

The flow of the hybrid nanofluid (copper–titanium dioxide/water) over a nonlinearly stretching surface was studied with suction and radiation effect. The governing partial differential equations were then converted into non-linear ordinary differential equations by using proper similarity transformations. Therefore, these equations were solved by applying a numerical technique, namely Chebyshev pseudo spectral differentiation matrix. The results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that the rising of the mass flux parameter slows down the velocity and, hence, decreases the temperature. Further, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases.

INFLUENCE OF VISCOUS DISSIPATION ON THE BOUNDARY LAYER FLOW OF HYBRID NANOFLUID

This study presents the mathematical modelling of two dimensional boundary layer flow of hybrid nanofluid where the impact of viscous dissipation has been accentuated in the energy equation. The copper and aluminium oxide nanoparticles are considered in this study. The surface of the model is stretched and shrunk at certain values of stretching/shrinking parameter. The partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the utilization of the suitable similarity transformations. Then Matlab software is utilized to produce the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are obtained with the correct guess values. The insertion of viscous dissipation in this model tremendously lessens the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter and concentration of copper enhance the magnitude of the reduced skin friction coefficient while the augmentation of the aluminium oxide nanoparticles shows a different trend.

Boundary layer flow on permeable flat surface in Ag-Al2O3/water hybrid nanofluid with viscous dissipation

Seeking the better performance nanofluid but with low cost of production, presence challenged. Metal nanomaterial is good in both thermal and electric conductivity but expensive while oxide nanomaterial does oppositely. The present study solved numerically the laminar boundary layer flow over a permeable flat surface in a blended metal-oxide hybrid nanofluid plate with viscous dissipation effects. The similarity equations in the form of the set of ordinary differential equations are reduced from the non-linear partial differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the reduced skin friction coefficient and reduced Nusselt number as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the Eckert number, permeability parameter and nanoparticle volume fraction are analyzed and discussed. The Ag-Al2O3 water-based hybrid nanofluid tested in this study shows competitive results with the Ag water-based nanofluid in certain cases.

Unsteady boundary layer flow of Williamson nanofluids over a heated permeable stretching sheet embedded in porous medium in the presence of viscous dissipation

The main objective of this paper is to focus on a numerical study of unsteady boundary layer flow of Williamson Nanofluids over a heated permeable stretching sheet embedded in porous medium in the presence of viscous dissipation. A mathematical modeled which resembles the physical flow problem has been developed. By using an appropriate transformation, we converted the system of dimensional nonlinear partial differential equations into system of coupled dimensionless ordinary differential equations. Numerical solutions of these equations are obtained by Runge-Kutta fourth order with shooting method. The velocity, temperature and concentration distributions are discussed numerically and presented through graphs. The numerical values of reduced skin-friction coefficient, Nusselt number and Sherwood number at the plate are derived and discussed numerically for various values of physical parameters which are presented through tables. The present results have been compared with existing one for some limiting case and found excellent validation. It is analyzed that the reduced skin friction coefficient enhances with increasing values of an unsteady parameter, magnetic parameter and porosity parameter. In addition, we observe that decrement in velocity profile of the fluid flow is observed for increasing values of the non-Newtonian Williamson parameter and a rise in Eckert number leads to the enhancement of the temperature of the fluid in the thermal boundary layer.

Hybrid Nanofluids Flows Determined by a Permeable Power-Law Stretching/Shrinking Sheet Modulated by Orthogonal Surface Shear.

The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications.

Exponential heat source effects on the stagnation‐point heat transport of Williamson nanoliquid with nonlinear Boussinesq approximation

AbstractThe nonlinear two‐point partial differential boundary value problem associated with the nano‐pseudoplastic material flow and heat transport subject to nonlinear Boussinesq approximation is computed and explored statistically. Heat transportation features are analyzed by the consideration of an exponential space‐related heat source and the Buongiorno model of nanofluids. The boundary‐driven expressions of the physical phenomenon are coupled and highly complicated due to the consideration of nonlinear convection terms. Reasonable variables are employed to reform the partial differential equations into a system of ordinary differential expressions and are solved numerically. Furthermore, correlation and regression techniques are employed for the statistical evaluation of the phenomenon. The probable error is implemented to calculate the reliability of the computed correlation factors. The exponential index and Schmidt number are positively correlated with the reduced skin friction coefficient whereas the other parameters are negatively correlated with it. The heat transfer rate is improved predominantly by the nonlinear thermal convection parameter. The temperature is enhanced by the intensification of the exponential‐based heat source factor. The temperature and concentration profiles are boosted by incrementing the Biot number values.

Time-Dependent Hydromagnetic Boundary Layer Flow across a Porous Vertical Surface with Internal Heat Generation

The time-dependent hydromagnetic boundary layer flow across a vertical surface with internal heat regeneration in porous media is investigated. The flow problem has been modelled mathematically in partial differential equations along with appropriate defined boundary conditions. These equations were expressed in dimensionless form using suitable similarity variables. The resulting dimensionless equations along with the conditions defined at the boundaries are solved by means of the Laplace transform methods. Results of the study are graphically illustrated for various quantities of practical importance. It was concluded that time positively influence the flow as a reduced skin friction coefficient was observed. Furthermore, the magnetic parameter, the radiation parameter, the heat absorption parameter and the permeability of the porous media can be used to influence the characteristics of a flow in porous media.

MHD Stagnation Point Flow and Heat Transfer Over a Stretching Sheet in a Blood-Based Casson Ferrofluid With Newtonian Heating

The present study investigated the magnetohydrodynamic (MHD) flow and heat transfer on a stagnation point past a stretching sheet in a blood-based Casson ferrofluid with Newtonian heating boundary conditions. The ferrite Fe3O4 and cobalt ferrite CoFe2O4 ferroparticles suspended into Casson fluid represent by human blood to form blood-based Casson ferrofluid are numerically examined. The mathematical model for Casson ferrofluid which is in non-linear partial differential equations are first transformed to a more convenient form by similarity transformation approach then solved numerically by using the Runge-Kutta-Fehlberg (RKF45) method. The characteristics and effects of the stretching parameter, the magnetic parameter, the Casson parameter and the ferroparticle volume fraction for Fe3O4 and CoFe2O4 on the variation of surface temperature and the reduced skin friction coefficient are analyzed and discussed. It is found that the blood-based Casson ferrofluid provided up to 46% higher in temperature surface compared to blood-based fluid with the presence of magnetic effects.