Skin Friction Parameter Research Articles

Effects of Arrhenius activation energy and melting heat transfer on Carreau fluid through a stretching sheet

ABSTRACT This article investigates the effect of activation energy on Carreau fluid flow in the presence of variable thermal conductivity, inclined magnetic field, melting heat transfer, and Soret and Dufour phenomena. A set of suitable similarity transformations is applied for transforming the governing partial differential equations (PDEs) considered for the physical phenomena into non-linear ordinary differential equations (ODEs). We obtained the results by solving the non-linear ODEs numerically which describe the behavior of the velocity, temperature, and concentration profiles of the fluid against the governing parameters and illustrated these graphically. The velocity distribution decreases for angle of inclination while it is increasing against higher melting parameter. The temperature distribution enhances with higher modified Dufour parameter and Prandtl number while it declines for thermal conductivity, activation energy, and melting parameters. The concentration distribution increases for melting parameter, Soret number, and activation energy parameter while decreasing for temperature difference parameter, Schmidt number, and reaction rate parameter. Skin friction, Nusselt and Sherwood numbers are evaluated numerically against the various governing parameters. Accuracy of the present work is illustrated and established through comparison carried out for skin friction versus magnetic parameter with existing results in the literature.

Insights of thermal characteristics with tri-hybrid nanofluid boundary layer flow past a thin needle

The innovative ternary nanofluid that we report herein is intended to improve the performance of heat transfer and thermal conductivity compared to conventional fluids. In view of the aforementioned significance, the goal of continuing research is to investigate the fluid flow and thermal efficiency of water-ethylene glycol (EG)-based ternary nanofluids (TiO2, MoS2, and CoFe2O4) past a thin needle that is subjected to a transverse magnetic field along the normal direction of the flow as well as resistive heating. The governing transport flow equations for ternary nanofluid have been converted into a system of ordinary differential equations using self-similarity variables and solved with the use of the BVP4C function in MATLAB. The significance of each flow factor on temperature and velocity profiles is illustrated using graphs, and the local Nusselt number, and skin friction parameters are computed. The study reveals that the addition of nanoparticles exerts a greater adverse effect on the exchange of heat, and it is found that the water-ethylene glycol based ternary nanofluid has a rate of heat transfer of up to 16% compared to hybrid nanofluid even at very low volume fractions (0.0025–0.03). It is inspected that in the presence of resistive heating, the ternary nanofluid has greater heat transfer than hybrid nanofluids. It is also observed that as the volume proportion of nanoparticles increases, the Nusselt number rises and wall friction decreases.

Flow Characteristics of Casson Nanofluid Over a Moving Wedge

Objectives: Analysis of Cassion nanofluid over a wedge is carried out for magnetohydrodynamics (MHD), wedge parameter, thermal radiation parameter, non-uniform heat source or sink and suction/injection parameter. Method: With the help of similarity transformations, the governing partial differential equations corresponding to the momentum and heat transfer are reduced to a set of non-linear ordinary differential equations. Numerical solutions of these equations are obtained. Findings: The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and in table form for two flow cases namely for nanofluid and for regular fluid. Novelty: It is experienced that with an escalation of magnetic field parameter, the flow is accelerated. Velocity profile shows growth with enhanced wedge parameter. Nusselt number and Skin friction parameters are discussed with the assistance of the table for base fluid and nanofluid. Keywords: Nanofluid, Suction, Injection, MHD, Casson fluid, Wedge

The influence of magnetic field on entropy generation in a wavy cavity equipped with internal heated plate using Darcy–Brinkman–Forchheimer model

In this study, entropy accumulation during thermal convection of a hybrid nanosuspension in an undulating cavity having an interior heated plate is investigated in relation to magnetic fields. The Darcy-Brinkman-Forchheimer approach is employed to simulate the liquid circulation and energy transport parameters, while the impact of the Lorentz force on the system's thermodynamic properties is analyzed. To better understand the characteristics of this complex phenomenon, best compromise combination of different interacted parameters is needed to be set on. The geometrical parameters are number of cavity waves (N), length (s) and inclination angle of heated plate (γ) and the inclination angle of Lorentz force (δ). These parameters are studied with different volume fractions of compound nanofluid (φ = 0 − 0.02), different Rayleigh numbers (103 − 106), Darcy number changes between (Da = 10−5 − 10−1) and various Hartmann numbers (Ha = 0 − 60). The mean Nusselt number rises with a growth of the Rayleigh number by about three times (≈300%), while the average skin friction parameter reduces with a growth of the number of wall waves approximately to the half (≈50%). Additionally, the average Bejan number reaches its maximum value when the parameter of number of waves equals to (N = 5). Taking into consideration an objective function of maximizing average Nu and minimizing skin frication coefficient (Cf), the best scenario is determined at (N = 3, s = 0.4, γ = π/3 and δ = π/2).

Heat transfer enhancement in a corrugated chamber filled with hybrid nanofluid under an influence of internal heated plate

PurposeThe purpose of this research is to scrutinize numerically the effect of internally equipped nonuniformly heated plate within wavy cavity on heat transfer enhancement in the case of hybrid nanofluid flow.Design/methodology/approachThe two-dimensional, steady, laminar, Newtonian and incompressible thermo-fluid flow phenomenon has been investigated numerically using Galerkin method. The considered parameters including number of waves (3–7), nondimensional length of heated plate (0.4–0.8), plate inclination angle (0º–90º), Rayleigh number (103–106) and concentration of nanoparticles (0.0–2.0) have been investigated in combination with involving hybrid nanofluid as a working fluid to augment thermal properties effectively. Two vertical wavy boundaries have low temperature whilst the other horizontal surfaces are adiabatic.FindingsThe Rayleigh number has a moderate impact on the values of Nusselt number, and skin friction parameter varied from 103 to 105 while it strongly affects them for Ra = 106, where Nu is roughly doubled (approximately 200%) in comparison with its value at Ra = 105 for all cases. Stream function is changed by the orientation of heated plate and Ra values, where its maximum value was 12.9 in horizontal position and 13.6 at vertical one. Results indicate a separation from the wavy walls at low Ra which tends to keep stagnation region at the deep parts of corrugated walls contrary the case at high Ra. The behavior of the isotherm contours tends to be distributed more evenly at lower values of Ra and angle of inclination lower than 45º. The resulting properties from mixing two materials for hybrid nanofluid into one base fluid show a good compromise between thermal capacity and heat conductivity, which is improved by 16% that leads to enhanced convective energy transport in the wavy chamber.Originality/valueThe originality of this work is the considered physical phenomenon where an influence of internal nonuniformly heated plate has been studied for the irregular geometry filled with a hybrid nanofluid. Such analysis allows defining the possible heat transfer enhancement for such an irregular cavity and inner heated plate.

History effects and wall-similarity of non-equilibrium turbulent boundary layers in varying pressure gradient over rough and smooth surfaces

Experimental investigations were conducted on non-equilibrium, turbulent boundary layers over rough and smooth surfaces. A NACA 0012 airfoil was systematically rotated to generate a family of bi-directional pressure fields on the research surface. The rough surface consisted of 2mm tall, staggered, circular cylindrical elements producing flow conditions that were in the fully rough regime. The velocity fields were measured using a custom Pitot-probe boundary layer rake and time-resolved particle image velocimetry (TR-PIV). The primary effect of the roughness was to increase the magnitude of the outer layer and skin friction parameters. Flows over both wall conditions exhibited “history effects” in the integrated boundary layer parameters, which indicates characteristic dependencies on the streamwise flow evolution. Indirect skin friction methods for non-equilibrium rough wall flows were sensitive to the regression fits of the empirical data, which were used in the absence of direct measurements. The effective sandgrain roughness parameter, ks, remained independent of pressure gradient flow history, within the uncertainty of empirical methods used for skin friction determination. Varying levels of wall-similarity were observed in the smooth and rough wall Reynolds stress profiles. Although past evaluations of wall-similarity have suggested that a sufficiently large boundary layer thickness to ks is sufficient for wall-similarity, the present results indicate a need for additional multivariable considerations including matching flow histories and considering local Reynolds numbers measurement resolution.

Dynamics of lorentz force and cross-diffusion effects on ethylene glycol based hybrid nanofluid flow amidst two parallel plates with variable electrical conductivity: A multiple linear regression analysis

This research investigates how the presence of Dufour and Soret parameters affect the properties of hybrid nanofluid flow amidst two parallel plates with temperature dependent electrical conductivity. Heat transport procedure is studied using thermal radiation parameter and Eckert number. Equations that characterize the current problem are turned into a set of ordinary differential equations, which are then solved with the assistance of a built-in function in MATLAB called the bvp4c solver. Multiple linear regression is used to explain physical parameters of interest including Sherwood number. The main conclusions of this study are that the velocity decreases with increasing nanoparticle volume fraction parameter and the concentration profile minifies with the rise in Soret parameter. It is observed that the increase in Dufour number causes a corresponding increase in the fluid temperature. It is discovered that, when the magnetic field parameter (M) is set to 0≤M≤2.5, the decreasing rate in the skin friction parameter is 0.02215. It is observed that, when φ1 is set to 0≤φ1≤0.25, Nusselt number drops by 3.82891. It is detected that, when Sr is set to 0≤Sr≤2.5, Sherwood number increases at a rate of 0.037225.

Impact of thermal-solutal stratifications and activation energy aspects on time-dependent polymer nanoliquid

Nanofluids are used in our daily life and have engineering applications due to their improving energy efficiency and heat transfer in different thermal systems. Nanotechnology and thermal performance have developed a great prospect for global scientists and researchers. In our research work, we have considered time-dependent Sutterby nanofluid by capturing the aspects of thermal radiation and stratification phenomenon. Additionally, features of activation energy and heat source-sink are considered. Transformation variables are used to reduce PDEs into nonlinear ordinary differential equations. To obtain the numerical results, we have used the bvp4c scheme. Through graphs and tables, we have demonstrated a comprehensive analysis for velocity, temperature, concentration profiles, skin-friction parameter, Nusselt number, and Sherwood number. It is analyzed that the temperature profile increases as the thermal biot number raises, also, the concentration profile declines when the Schmidt number raises.

Analytical study of time-dependent Mgnatohydrodynomics flow of hybrid nanofluid around a rotating sphere

The important aim of this study is to deliver the idea of boost of the heat, transfer which is used in the new technology, the energy demand is the key aspect of the researchers in the recent decade and the experts are working to develop new ideas for the rapid gaining of energy at low cost. The present research paper investigates the Analytical study of time-dependent MHD flow of hybrid nanofluid over a rotating sphere. The novelty of present research is that Analytical study of time-dependent MHD hybrid nanofluid over a rotating sphere is considered. To transform the nonlinear partial differential equation to nonlinear ordinary differential, equation we used the defined similarity transformation. By using approximate analytical method to obtain the approximate analytical solution of the nonlinear ordinary differential equations two for velocity profile, one for concentration and other for temperature profile. The influence of different parameter such as magnatic filed parameter, Casson parameter, time dependent parameter, roation parameter, Schmidt number,thermophoresis parameter and prandtl number on velocity, temperature and concentration profile, also the effect of skin friction parameter and Nusalt number are presented in the form of figure, the present research paper shows good similarity with published work.

Magnetohydrodynamic hybrid nanofluid flow with the effect of Darcy–Forchheimer theory and slip conditions over an exponential stretchable sheet

The characteristics of water-based hybrid nanofluid flow when passing over an exponentially stretchable sheet with velocity and thermal slip factors are presented. This article provides a concept for a hybridized fluid comprising copper and cobalt iron oxide nanoparticles (NPs) dispersed into a base fluid (water). In addition, physical observations of the heat absorption behavior, the Darcy effect, the thermal radiation, and viscous dissipation are also taken into account. Because of their strong thermophysical properties, copper and cobalt iron oxide NPs are used in a wide range of applications in the engineering and medical fields. To study the dynamics of these NPs, a system of partial differential equations (PDEs) has been generated that forms a highly nonlinear coupled model. The PDE system is converted into nondimensional ordinary differential equations (ODEs) with the aid of similarity replacements. The semi-analytical homotopy analysis method (HAM) is applied to the set of dimensionless ODEs obtained to find the solution. Two engineering parameters, the Nusselt number and the skin friction, are plotted versus various parameters of the hybridized fluid using bar charts. It was observed that the no-slip condition, the suction parameter, and the Darcy–Forchheimer medium enhanced the thermal profile of the hybridized fluid.

Simulation of Dissipative Hybrid Nanofluid (PEG-Water + ZrO2 + MgO) Flow by a Curved Shrinking Sheet with Thermal Radiation and Higher Order Chemical Reaction

The heat transmission capabilities of hybrid nanofluids are superior to those of mono nanofluids. In addition to solar collectors and military equipment, they may be found in a number of areas including heat exchanger, automotive industry, transformer cooling and electronic cooling. The purpose of this study was to evaluate the significance of the higher order chemical reaction parameter on the radiative flow of hybrid nanofluid (polyethylene glycol (PEG)–water combination: base fluid and zirconium dioxide, magnesium oxide: nanoparticles) via a curved shrinking sheet with viscous dissipation. Flow-driven equations were transformed into nonlinear ODEs using appropriate similarity transmutations, and then solved using the bvp4c solver (MATLAB built-in function). The results of two scenarios, PEG−Water+ZrO2+MgO (hybrid nanofluid) and PEG−Water+ZrO2, (nanofluid) are reported. In order to draw important inferences about physical features, such as heat transfer rate, a correlation coefficient was used. The main findings of this study were that curvature parameter lowers fluid velocity, and Eckert number increases the temperature of fluid. It was observed that the volume fraction of nanoparticles enhances the skin friction coefficient and curvature parameter lessens the same. It was noticed that when curvature parameter (K) takes input in the range 0.5≤K≤2.5, the skin friction coefficient decreases at a rate of 1.46633 (i.e., 146.633%) (in the case of hybrid nanofluid) and 1.11236 (i.e., 111.236%) (in the case of nanofluid) per unit value of curvature parameter. Increasing rates in the skin friction parameter were 3.481179 (i.e., 348.1179%) (in the case of hybrid nanofluid) and 2.745679 (in the case of nanofluid) when the volume fraction of nanoparticle (ϕ1) takes input in the range 0≤ϕ1≤0.2. It was detected that, when Eckert number (Eck) increases, Nusselt number decreases. The decrement rates were observed as 1.41148 (i.e., 141.148%) (in the case of hybrid nanofluid) and 1.15337 (i.e., 153.337%) (in the case of nanofluid) when Eckert number takes input in the range 0≤Eck≤0.2. In case of hybrid nanofluid, it was discovered that the mass transfer rate increases at a rate of 1.497214 (i.e., 149.7214%) when chemical reaction (Kr) takes input in the range 0≤Kr≤0.2. In addition, we checked our findings against those of other researchers and discovered a respectable degree of agreement.

Effects of internal heat generation and Lorentz force on unsteady hybrid nanoliquid flow and heat transfer along a moving plate with nonuniform temperature

AbstractThe aim of the studyThis study aims to explore the transient magnetohydrodynamics (MHD) boundary layer thermal convective flow of a hybrid nanoliquid past a moving vertical plate under the influence of internal heat generation and variable surface temperature.The research methodologyThe problem is modeled by coupled nonlinear partial differential equations with relevant boundary conditions. Formulated control equations are worked out using the robust implicit finite‐difference technique. The current work is validated with existing literature for special cases of the problem. The impact of important characteristics on hydrodynamic and thermal patterns, accompanied by skin friction parameter and Nusselt number, is scrutinized graphically.The major conclusion of the studyImpacts of MHD, inner thermal generation, and variable surface temperature on nanoliquid circulation and energy transport are studied. It has been found that velocity, temperature, and skin friction coefficient increase with the increase in the heat generation parameter, whereas the Nusselt number reduces with such parameter.The significance of the studyObtained results can be used in different engineering devices, including heat exchangers, solar collectors, and chemical reactors.

Numerical Solution of Biomagnetic Power-Law Fluid Flow and Heat Transfer in a Channel

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel.

Temperature-Dependent Viscosity and Prandtl Number Effects on Natural Convection Methanol Boundary Layers about a Vertical Plate with Injection

<p>The present study deals with the effect of temperature-dependent viscosity and Prandtl number on the steady, natural, laminar flow of methanol past a vertical porous plate with injection. The coupled nonlinear partial differential equations governing the non-similar flow have been solved numerically using an implicit finite-difference scheme along with the quasilinearization technique. Numerical results indicate that temperature-dependent viscosity and Prandtl number, both have a major role on skin friction and heat transfer parameters as well as velocity and temperature fields.</p>

Impact of chemical reaction and double stratification on heat and mass transfer characteristics of nanofluid flow over porous stretching sheet with thermal radiation

ABSTRACT This article analyses heat and mass transfer characteristics of the steady and unsteady cases of nanofluid flow over a stretched surface embedded in a porous medium by taking chemical reaction, thermal radiation, magnetic field, thermal stratification and solutal stratification into account. Partial differential equations representing the boundary layer flow, heat and mass transfer are reduced into ordinary differential equations using the similarity variable technique and solved numerically using the Galerkin finite element method. A parametric analysis of all pertinent parameters is accompanied and a descriptive set of numerical results for the velocity, temperature and concentration profiles, as well as the skin-friction parameter, Nusselt number and Sherwood number are demonstrated through graphs and tables. It is determined that temperature profiles deteriorate as thermal stratification parameter (S t) raises; furthermore, the concentration profiles also decline when the solutal stratification parameter (S m) escalates.

HEAT AND MASS TRANSFER ANALYSIS OF STEADY AND UNSTEADY NANOFLUID FLOW OVER A STRETCHING SHEET WITH DOUBLE STRATIFICATION

Attention is focused on heat and mass transfer by a stretched surface over a nanofluid in a steady and unsteady state in the presence of a magnetic field, thermal stratification, and solutal stratification. The proper partial differential equations governing the boundary-layer flow, heat and mass transfer are reduced to ordinary differential equations by using the similarity variable technique and solved numerically by using the Galerkin finite-element method. A parametric analysis of all pertinent parameters is carried out and a descriptive set of numerical results for the velocity, temperature, and concentration profiles as well as the skin-friction parameter, Nusselt number, and Sherwood number is demonstrated through graphs and tables. It is determined that temperature profiles deteriorate as thermal stratification parameter St increases, furthermore, the concentration profiles also decline when solutal stratification parameter Sm increases.

Effects of lubricated surface in the oblique stagnation point flow of a micro-polar fluid

In this investigation, we have considered steady, two-dimensional, oblique flow of a micro-polar fluid towards a stagnation point over a lubricated plate. A power-law fluid is utilized for the purpose of lubrication. To derive the slip condition in the present flow situation, continuity of shear stress and velocity has been imposed at the fluid lubricant interface. The set of non-linear coupled ordinary differential equations subject to boundary conditions is solved by a powerful numerical technique called the Keller-box method. Some important flow features have been analyzed and discussed under the influence of slip parameter $\lambda$ , the material parameter K, a free parameter $\beta$ and ratio of micro-rotation to the skin friction parameter n . The main purpose of the present article is to analyze the reduction in the shear stress and shift of stagnation point in the presence of lubrication as compared to the viscous fluid that may be beneficial during polymeric processing.

MHD unsteady GO–water-squeezing nanofluid flow—heat and mass transfer between two infinite parallel moving plates: analytical investigation

Investigation for unsteady squeezing viscous flow is one of the most important research topics due to its wide range of engineering applications such as polymer processing and lubrication systems. The aim of the present paper is to study the unsteady squeezing viscous graphene oxide–water nanofluid flow with heat transfer between two infinite parallel plates. The governing equations, continuity, momentum and energy for this problem are reduced to coupled nonlinear ordinary differential equations using a similarity transformation. The transmuted model is shown to be controlled by a number of thermo-physical parameters, viz., moving parameter, graphene oxide nanoparticles solid volume fraction, Eckert and Prandtl numbers. Nusselt number and skin friction parameter are obtained for various values of GO solid volume fraction and Eckert number. Comparison between analytical results and numerical ones achieved by fourth order Runge–Kutta method revealed that our analytical method can be a simple, powerful and efficient technique for finding analytical solutions in science and engineering nonlinear differential equations.

MHD Convection Fluid Flow and Heat Transfer in an Inclined Microchannel with Heat Generation

The problem of fully developed free convection flow of electrically conducting fluid in an inclined microchannel in the presence of transverse magnetic field and internal heat generation is investigated. The analytical solution for velocity profile and temperature profile have been obtained, considering the velocity slip and temperature jump conditions at the wall of the microchannel. The effect of different parameters involved in the problem on the velocity and temperature profile along with the skin friction parameter and Nusselt number has been discussed graphically.

An analytical solution of MHD flow of two visco-elastic fluids over a sheet shrinking with quadratic velocity

The steady laminar boundary layer flow of two classes of incompressible visco-elastic and electrically conducting fluids over a nonlinearly shrinking sheet with appropriate wall transpiration under the influence of a magnetic field is analyzed. It is shown that the problem permits an analytical solution of two classes of visco-elastic fluids, namely the second grade fluid and fluid obeying Walters’ liquid B model. The effects of visco-elasticity, suction/blowing parameter and magnetic parameter on both the skin friction parameter and velocity profiles are studied. It is shown that dual solution exists for certain range of physical parameters.