Local Skin Friction Coefficient Research Articles

An analytical approach to entropy production in MHD mixed convection micropolar fluid flow over an inclined porous stretching sheet

This analytical analysis examines the MHD micropolar fluid flow and mixed convection features using entropy production analysis of an inclined porous stretching sheet. Flow field and heat transfer analysis are presented to consider thermal radiation, heat source/sink, Lorentz, and buoyancy forces. The PDEs system is transformed by appropriate similarity variables, turned into a system of high non-linearity coupling ODEs, and then solved with the help of an analytical approach. An analytical approach can provide exact explicit solutions for the flow field, heat transport, entropy production, the local skin friction coefficient, the local couple stress coefficient, and the local Nusselt number. It is shown that the magnetic field, mixed convection, and sheet inclination effects can be incorporated together into a single parameter, which is called the magneto-buoyancy-inclination parameter here. In other words, this parameter controls the boundary layer flow. In addition, an experimental procedure called Box-Behnken design (BBD) was employed to analyze the influence of material (K), radiation (Rd), and buoyancy (Λ) parameters on entropy production in MHD micropolar fluid flow over the sheet. In order to estimate accurately the optimum entropy generation containing K, Rd, and Λ, we used a quadratic regression model. Based on the results of this investigation, the value of the entropy generation number became larger by decreasing the magneto-buoyancy-inclination parameter. Further, the magnitude of the local couple stress coefficient is reduced as the heat source parameter increases.

Silver–ethylene glycol and copper–ethylene glycol based thermally radiative nanofluid characteristics between two rotating stretchable disks with modified Fourier heat flux

AbstractIn the present analysis, our aim is to investigate the mass and heat transport of silver (Ag)–ethylene glycol (EG) and copper (Cu)–EG‐based nanofluids between two rotating stretchable disks under the convective boundary conditions. We have also incorporated Cattaneo–Christov heat flux, thermal radiation, and chemical reaction in the fluid flow. The system of coupled partial differential equations is transformed into ordinary differential equations by using similarity transformations. The finite element method has been accomplished to find numerical solutions to transformed equations. The behavior of radial and tangential velocity, temperature fields, and concentration fields influenced by the various parameters are sketched through graphs. The local skin friction coefficient, Nusselt number, and Sherwood number are also calculated for the pertinent parameters and displayed the results through tables. It is perceived that velocity sketches of both nanoliquids degenerate with larger values of thermal relaxation parameters. Also, the values local Nusselt number of both Ag–EG, and Cu–EG based Cattaneo–Christov nanofluid intensifies with improving values of stretching parameter at the lower disk, whereas, it impedes at the upper disk.

MHD Boundary Layer Flow Past an Exponentially Stretching Sheet with Darcy-Forchheimer Flow of Nanofluids

Objectives: To investigate an exponentially stretched sheet with a magnetic force to explore the Darcy-Forchheimer flow of a two-dimensional blood-based nanofluid and the effect of different relevant parameters of the fluid flow assumption for velocity and temperature profiles. Methods: Nanoparticles such as Ag, TiO2 and Fe with base fluid blood are being investigated. The governing equations of the problem, such as continuity, motion, and energy, are derived and translated into ordinary differential equations by employing appropriate optimization techniques. The bvp4c technique is used to perform numerical computations. The impacts of non-dimensional governing factors like the prandtl number (Pr), magnetic field parameter (M), Forchheimer number (Fr), porosity parameter (b ) and nanofluid volume fraction (ϕ ) are determined numerically and displayed through graphs. Tables illustrate and explain the local Nusselt number and skin friction coefficient. Findings: Velocity profile of Ag-blood, TiO2-blood and Fe-blood decreases and temperature profile increases for increasing values of Pr, b , M and Fr. For rising values of M, b , and Fr, the skin friction coefficient increases and the Nusselt number decreases, but the accelerating trend of ϕ exhibits a reversible trend. Novelty: The Darcy-Forchheimer flow of a two-dimensional blood-based nanofluid with a magnetic field is novel in the model. The (Ag-Blood, TiO2-Blood, Fe-Blood) nanofluid flow past an exponentially stretching surface is considered in the present study, while no one has considered these nanofluids for the same model. Keywords: MHD; Bloodbased nanofluid; Nanoparticles; Exponentially stretching surface; Darcy Forchheimer flow; Blood based nanofluid

ANALYSIS STUDY OF BOUNDARY LAYER OF AIR FLOWING ON A FLAT PLATE

When the real liquid flows through a solid object or solid wall, the particles of the liquid stick to the boundary and a non-slip state occurs. In this paper, a practical and theoretical study was conducted to calculate and show the effect of fluid velocity on the thickness of the boundary layer and the local skin friction coefficient and a comparison between the theoretical and experimental results of laminar flow and turbulence along the flat plate at (5,10,15,20, cm). The results showed that the coefficient of skin friction decreases with the increase in the velocity of the liquid and that the velocity increases until it is constant (1m/sec) at the dimension x = 20 cm. The distribution of the velocity, friction coefficient, and thickness of the boundary layer are obtained analytically and experimentally and compared with the previously reported results, where good agreements are observed also the results also showed that there is an error ratio between the theoretical and practical values

Dual solutions for double diffusion and MHD flow analysis of micropolar nanofluids with slip boundary condition

The present communication is designed to elucidate the flow attributes of micro-polar non-Newtonian liquid over stretching/shrinking surfaces. In addition, we have observed the stagnation aspect along with the velocity slip condition on the momentum field. The Fourier law of heat conduct, along with a physical aspect of stratified and heat generation absorption, are then used to model the temperature equation. The Buongiorno nanofluid model is used to study additional transport features. After a discussion of PDEs using similarity transformation, mathematical formulations of the given problem are supported in the form of an ordinary differential system. The solution of modeled governing equations containing physical effects is simulated by using the shooting method in conjunction with RK- Method. The significant effects of flow parameters that are associated with velocity, temperature, and concentration distribution for low and upper branch solutions are revealed through graphs and tables. Quantities of engineering concerns like skin friction coefficient and Nusselt number are also compared with previous results of critical values. Furthermore, it should be considered that as the micro-pole parameters are increased, the local skin friction coefficient and the local Nusselt number amplitude also rise.

The mathematical model for heat transfer optimization of Carreau fluid conveying magnetized nanoparticles over a permeable surface with activation energy using response surface methodology

AbstractThe sensitivity analysis and response surface methodology (RSM) is performed for the key parameters governed by the magneto‐flow and heat transport of the Carreau nanofluids model toward a stretching/shrinking surface in the presences Arrhenius activation energy and chemical reaction. Nanofluid that displayed Brownian motion and thermophoresis was considered with the permeable condition. The effects of different physical parameters were analyzed by employing appropriate similarity transformations in nonlinear partial differential equations and converted to the dimensionless system of ordinary differential equations. The finite difference method in bvp4c code solves the equations numerically. Associated parameters are presented graphically and interpreted against local Nusselt number, Sherwood number, and skin friction coefficient. An increase in the activation energy factor leads to increased concentration in permeable flow. The higher the activation energy lower the temperature and causes the reaction rate constant to decrease. In addition, it slows down the chemical reaction and increases the concentration characteristics. The increase of radiation and Prandtl number leads to an increase in heat transfer for the permeable surface. Furthermore, the Schmidt number and the binary reaction rate parameter increase the mass transfer for suction/injection flow. As a result, the Nusselt number's highest sensitivity is the Eckert number and the lowest to the thermophoresis parameter. The Sherwood number's positive sensitivity is observed for the Eckert number and Brownian motion parameter, whereas negatively sensitive to thermophoresis.

Statistical Modelling for the Darcy–Forchheimer Flow of Casson Cobalt Ferrite-Water/Ethylene Glycol Nanofluid under Nonlinear Radiation

Current research is focused on the utilization of a numerical solution of Casson cobalt ferrite nanofluid flow by taking two forms of base fluid. This investigation includes the gradual influence of nonlinear thermal radiation on the improvement of heat transfer related to the flow of nanofluids over a stretched rotating surface by the Darcy–Forchheimer law. The model constructed by a Casson nanoliquid in the boundary layer’s flow is studied for its symmetric behaviour, including cobalt ferrite nanomaterials. Two base liquids named as ethylene glycol and water are considered. The rate of heat transport is examined by considering Newtonian heating conditions. By utilizing similarity transformations, a partial differential system that governs the said model has been transformed into a highly nonlinear ordinary differential system, and numerical outcomes are obtained by implementing the RK4 via shooting methodologies. All obtained results, including local skin friction coefficients and local Nusselt number, are defined and discussed in the paper. The study’s findings ensure that the Casson cobalt ferrite nanofluid flowing towards a stretching plate has a unique solution: A variation of the solid volume fraction corresponds to the decrease in various values of the Casson nanofluid parameter for both type of nanofluid. Furthermore, a similar behaviour is noted for various values of the solid volume fraction, which corresponds to various values of the inertia coefficient parameter. Moreover, for the highest values of the solid volume fraction and all values of R1 and Ni taken into account, the rate of heat transfer upsurges. The data from the local skin friction coefficient (LSFC) and local Nusselt number (LNN) have been analysed using various statistical distributions, and it has been determined that both datasets generally fit the exponentiated Weibull distribution for various values of considered parameters. The findings would serve as a starting point for the manufacture of devices.

Nonsimilar modeling and numerical convective transport analysis of forced flow of radiative Carreau nanofluid with zero mass flux boundary condition

AbstractPresent research focuses on nonsimilar analysis of the flow of a non‐Newtonian Carreau nanofluid against different geometrical configurations affected by thermal radiations. The flow is induced by stretchable surface with the implementation of zero‐net mass‐flux conditions on the surface. This considered model is commonly known as Kuznetsov and Nield's proposed updated model for nanoparticles. The derived flow equations are first nondimensionalized by employing appropriate nonsimilar transformations. The transformed system is analytically tackled by employing the local nonsimilarity (LNS) approach up to the second‐truncation level in association with the numerical algorithm bvp4c. The consequences of appropriate parameters, such as the suction parameter, wedge angle parameter, Weissenberg number, Prandtl number, constant velocity parameter, temperature ratio, Brownian motion, Lewis number, thermophoresis and radiation parameters, on fluid velocity, thermal, and concentration profiles are calculated and graphed. Drag coefficient, Nusselt, and Sherwood numbers are also computed and presented in tabular form. It is observed that intensification in the suction parameter shows augmentation in the local skin friction coefficient. Enhancement in the wedge angle parameter increases both the Sherwood and Nusselt numbers. Enhancement in velocity profile of the nanofluids is noticed with the increasing estimations of suction parameter. Thermophoresis parameter enhances both thermal and concentration profiles, however increasing Lewis number leads to a decline in the concentration boundary layer. With judgment, a comparative assessment is made of the present and previous results. This research may be helpful for the researchers that are interested in studying prospective industrial and engineering nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, and many others.

Linking supersonic boundary layer separation to structural deformation using the Kármán–Pohlhausen momentum-integral equation

A first-order link between local separation of supersonic turbulent boundary layer flow and structural deformation is established. First, mathematical analysis of the Kármán–Pohlhausen momentum integral equation is carried out with the assumption of spatially varying surface topology in order to identify fluid-centric representations of structural deformation. Next, a data-driven approach is used to identify the dominant fluid-centric parameters. This ultimately yields a simple linear correlation between local skin friction coefficient and surface curvature, which is the unifying parameter relating deformation and separation. This link represents a key step toward deep understanding of the nuanced interplay between turbulent boundary layers and structural deformation and significantly improves fundamental understanding of fluid-structure interaction problems with prominent turbulent boundary layer dynamics.

Free convection boundary layer correlations for a vertical plate with nonuniform heating

An analytical study of a free convection boundary layer (BL) for a laminar and steady flow over a vertical flat plate (VFP) having nonuniform thermal conditions has been investigated. The plate is subjected to a variable wall heat flux of where is the distance along the VFP from the leading edge and is a reference heat flux. The boundary layer equations for nonuniform wall heat flux conditions have been formulated. These equations are then solved numerically for the range of exponents and Prandtl numbers () of −0.25 to 1 and 0.01 to 1000 respectively. The effects of two physical parameters and on the characteristic of thermal boundary layer (TBL) and hydrodynamic boundary layer (VBL) are described. Moreover, correlations of TBL and VBL thicknesses have been presented as a function of Pr and The TBL and VBL thickness are more influenced by Pr as compared to These correlations are reasonably accurate for uniform heat flux (n = 0) proposed by A. Bejan using a scale analysis and no other such correlations are available for nonuniform heat flux for a wide range of Prandtl numbers (Pr). It has been found that when both the BL thicknesses decrease with the Pr till a value of is reached. For the growth of VBL and TBL thickness over the VFP increases and decreases respectively. Consequently, the local skin friction coefficient decreases and the local Nusselt number increases with the increase in and at a fixed value of modified Rayleigh number.

Analysis of Heat Transfer of Power-Law Fluid Along a Vertical Stretching Cylinder

The aim of this paper is to study the heat transfer enhancement of power-law fluid over a vertical stretching cylinder. The model is governed by partial differential equations (PDEs) which is then converted into a coupled system of non-linear ordinary differential equations (ODEs). Here both velocity and temperature profiles have been constructed for different physical parameters such as, Reynold number, Prandtl number, Eckert number, unsteadiness, mixed convective and magnetic-parameters. The obtained results have been compared with the existing literature that reveals the accuracy of the proposed scheme. Moreover, it has been noticed during the study that the power-law energy is getting enhanced corresponding to these parameters, which can be viewed in graphical simulations. In addition, the numerical computations of local-skin friction coefficient and Nusselt number are tabulated.

Dynamics of ternary-hybrid nanofluids due to dual stretching on wedge surfaces when volume of nanoparticles is small and large: forced convection of water at different temperatures

Management of heat energy and control of temperature distribution are major problems in the industry. With emphasis on the heat and mass transfer when the volume of nanoparticles is small and large, nothing is known on forced convection flow of water at different temperatures conveying platelet aluminum nanoparticles, cylindrical magnesium oxide nanoparticles, and titanium dioxide nanoparticles due to dual stretching on wedge surfaces. The mathematical model for the problem mentioned above is presented in this report, transformed using similarity variables, and solved numerically using the approach of shooting technique together with fourth order Runge-Kutta integration scheme. The analysis of results, justification, and discussion of results was established after the positive outcome of the reliability and validity. It is worth concluding that as time goes on in all the four cases of water at different temperature as in the case of four ternary-hybrid nanofluid flows, the local skin friction coefficients increases at the rate of 0.07 when the volume of nanoparticles is small and at a most minimum rate of 0.008 when the volume of nanoparticles is large. At 80°C temperature of water-based ternary hybrid nanofluid, as time grows large, the heat transfer decreases at the optimal rate of −0.354681119 when the volume of nanoparticles is small but the same heat transfer increases at the minima rate of 0.159722534 when the volume of nanoparticles is large.

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.

Numerical investigation of heat transfer characteristics for blood/water-based hybrid nanofluids in free convection about a circular cylinder

This paper investigates hybrid nanofluids flowing around a circular cylinder of free convection under the constant surface heat flux. Nanoparticles of copper oxides, Gold, and Aluminum (CuO, Au, Al) are considered to support the heat transfer performance of blood/water-based hybrid nanofluids. The governing model for hybrid nanofluids which is in form of non-linear partial differential equations (PDEs) are first transformed to a more convenient form by similarity transformation approach then approximated numerically by the Keller box method. Several comparatives are performed in this work resulting in the superiority of the hybrid-nanofluid over regular nanofluid in terms of heat transfer rate, velocity, and local skin friction coefficient. Findings confirmed that the surface temperature and temperature field are augmented, with increasing volume fraction for nanoparticles. Also, Gold nanoparticles give a higher result for all examined physical properties than Aluminum and copper oxides nanoparticles.

Thermal Radiation Effect on Unsteady Magneto-Convective Heat-Mass Transport Passing in a Vertical Permeable Sheet with Chemical Reaction.

The unsteady magneto-convective heat-mass transport passing in a vertical porous sheet with the thermal radiation and the chemical reaction effects has been examined numerically. The governing PDEs have been transferred into ODEs by applying the local similarity transformation. The nondimensional governing equations including the boundary conditions are solved by applying the superposition method with the help of the “MATLAB ODE45” software numerically. The influence of emerging nondimensional numbers/parameters, for example, the Prandtl number (Pr), thermal radiation parameter (R), Schmidt number (Sc), and chemical reaction parameter (Kr), on fluid velocity, concentration, and thermal radiation within the boundary layer has been examined. The outcomes indicate that enhancing values of the Soret and Dufour numbers reduce the thermal boundary layer thickness. Uplifting values of the thermal radiation (0.5-3.5) enhance the local skin friction coefficient and mass transfer rate by approximately 15% and 78% but decrease the heat transfer rate by 47%. The local skin friction coefficient enhances about 21%, and the mass transfer rate reduces about 64% due to an increase in the chemical reaction parameter (0.5-2.0). Finally, we compared our numerical results with previously published literature and observed them to have a good agreement.

Dual solution of MHD mixed convection flow and heat transfer over a shrinking sheet subject to thermal radiation

In this paper, the steady-state two-dimensional incompressible, magnetohydrodynamics, stagnation point flow and heat transfer of viscous fluid having mixed convection over the linearly shrinking porous sheet is studied. The governing non-linear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by exercising the pertinent similarity variables. Numerical results are obtained by using the bvp4c solver in MATLAB to solve the resulting ODEs. The dual solution is obtained for a certain range of shrinking and mass suction parameters. The resulting dual solution projects that local skin friction coefficient and Nusselt number escalates in the upper branch solution and decelerates in the lower branch solution with the increase in the mass suction and magnetic parameter. However, the heat transfer rate is diminishing in both the upper and lower branch solutions due to an escalation of the radiation parameter. In addition, temporal stability analysis has been performed by which the upper branch solution is physically trustworthy and stable while the lower branch solution is not physically stable (unstable).

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 .

Heat transmission in Darcy-Forchheimer flow of Sutterby nanofluid containing gyrotactic microorganisms

PurposeThis paper aims to deal with the heat transmission of Sutterby fluid-containing gyrotactic microorganism by incorporating non-Darcy resistance law. The mathematical modeling is based on nanoparticle concentration, energy, momentum and motile microorganism equations.Design/methodology/approachThe governing nonlinear coupled equations are first rendered into nonlinear ordinary equations using appropriate transformation and are then solved analytically by using the optimal homotopy.FindingsGraphical illustration of results depict the behavior of flow involved physical parameters on temperature, gyrotactic microorganism, concentration and velocity. Additionally, local Nusselt number and skin friction coefficient are computed numerically and validated through comparison with existing literature as a special case of proposed model. It is found that the temperature profile decreases by increasing values of Brownian-motion parameter and Prandtl number. An increase in thermophoresis parameter and Schmidt number results in decrease in concentration of nanoparticles. Bioconvection Peclet number corresponds to decreasing behavior of nondimensional gyrotactic microorganism field is observed. Finally, a comparison with the existing literature is made, and an excellent agreement is seen.Originality/valueTo the best of the authors’ knowledge, this study is reported for the first time.

Estimation of chemical properties of single- and multi-wall carbon nanotubes (SWCNT/MWCNT) in the suspended nanofluids flow over a thin moving needle

ABSTRACT The aim of the current study is to analyze the flow and heat transport mechanism in carbon nanotubes (CNTs) in the suspended nanofluids flow due to a thin needle. The influence of MHD, activation energy, and thermal radiation are also incorporated while developing boundary layer equations governing the nanofluid flow. The governing partial differential equations (PDEs) problem are reduced into a set of nonlinear ordinary differential equations (ODEs) using an appropriate similarity transformation and then computed numerically through the Runge–Kutta–Fehlberg fifth-order (RKF-5) numerical method with a shooting scheme. The sway of significant parameters on velocity, temperature, and concentration evaluations are examined in detail, and the results are shown graphically. The quantities of physical interest, such as local skin friction coefficient, local Nusselt number, and local Sherwood number, are also investigated for pertinent parameters. When the size of needle thickness expands, the surface drag force increases for single- and multi-wall carbon nanotubes. Furthermore, heat transfer rate enhances by rising values of Eckert number for first and second branch solutions. The results also revealed that the higher values of the chemical reaction parameter diminish the concentration distribution for both solutions.

Analysis of Transient MHD Flow Past a Vertical Plate with Periodic Temperature

A mathematical model is used to simulate the effect of the magnetic field on the temporary free convection flow of electrically conductive fluid past a vertical plate under periodic temperatures. Analyzing momentum and energy equations using homotopy perturbations. The analysis of the temperature profile with a constant temperature plate is presented using Homotopy perturbation method and Laplace transform. There is an analysis of the significance of different physical parameters, such as Grashof number, magnetic parameter, Prandtl number, and temperature frequency, on transient velocity and temperature. Additionally, the local Skin-friction and local Nusselt number coefficients are determined and analyzed.