Local Skin Friction Coefficient Research Articles

Non-Newtonian Cross fluid flow through a porous medium with regard to the effect of chemical reaction and thermal stratification phenomenon

A comprehensive study encompassing a general development and a presentation of results for the influence of the chemical reaction on the laminar Cross fluid flow and heat mass transfer is made here. The motion of the fluid is assumed due to the stratified stretching sheet which embedded in a porous medium. Some of important characteristics of the fluid such as the variable thermal conductivity and its dependence on the temperature field are mentioned. Accordingly, some account of the possible effects of heat generation on heat mass transfer in fluid flows is given. Numerical treatments have been introduced for the resulting coupled ordinary differential equations. Then, the results of the variation in the velocity profile, the temperature profile and the concentration profile due to porous parameter, thermal conductivity parameter, heat generation parameter, thermal stratification parameter and chemical reaction parameter are presented graphically. At the proposed physical conditions for the problem, the Sherwood number, the Nusselt number or the temperature gradient and the local skin friction coefficient were measured. It is interesting to observe that, both the solutal and the thermal stratification phenomena plays a dominant role in the mechanism of heat and mass transfer. Also, regarding the warming factors within the thermal boundary layer, both Darcy parameter and heat generation parameter have been proposed which are of special interest in heat transfer problems. Finally, the results pointed out the efficiency of the proposed numerical method, where it gives a good representation describing the mechanism of the flow, heat and mass transfer.

Unsteady magnetohydrodynamic stagnation point flow of a nanofluid past a permeable shrinking sheet

In this study, the flow and heat transfer behavior of a magnetohydrodynamic nanofluid past over an unsteady permeable shrinking sheet are investigated. The governing equations of such a flow are transformed into a set of nonlinear ordinary differential equations utilizing similarity transformations. Using the well-known shooting method along with sixth order Runge-Kutta method, the resulting equations are numerically solved. A comparison with available solutions is made which provides a good agreement. The noticeable findings are that the local skin friction coefficient and the local Nusselt number are significantly increased with the increase of volume fraction of nanoparticles, mass transfer parameter, magnetic field parameter and velocity ratio parameter. Moreover, all of these parameters significantly enhance the domain of the occurrence of dual solutions. The velocity and temperature are increased by a higher volume fraction of nanoparticles. When the mass transfer and magnetic field parameters are increased the velocity of the fluid is augmented, whereas the temperature decreases. However, a converse scenario is recognized for increasing the velocity ratio parameter.

RETRACTED: Development of Nusselt number correlation in natural convection over the walls of a blast furnace: A CFD approach

Blast furnaces are large and costly devices, and contribute enormous wealth to world economy. A tiny improvement of furnace performance can translate to huge saving not only in cost of operation but also in air pollution. It presents a numerical solution of the continuity, momentum, and energy equations for a fluid domain surrounding the outer cylindrical surface of a vertical cylinder with the specific longitudinal section using ANSYS FLUENT 18. The main parameters of this study are the dimensionless ratio of cylinder length to the maximum diameter varying between 3.24 and 5.4, the Rayleigh number ranging between 104 and 107, and the cylinder surface temperature ([Formula: see text]) varying between 375 K and 600 K, the ambient temperature being taken as 300 K. These parameters have been varied during the simulation to determine their influence on the free convection characteristics. The study clearly shows that the computed Nusselt number increases with increase of Rayleigh number and surface temperature, the increment being minimal for high values of length to the maximum diameter. It is also observed from the simulation that the rate of heat transfer goes down with increase of length to the maximum diameter. The results present local heat transfer and skin friction coefficients over the outer cylindrical surface of the blast furnace of chosen dimensions. The thermal plume and the velocity vector field around the furnace are displayed. An empirical Nusselt number to Rayleigh number relationship has been proposed for the blast furnace of any size within range of Rayleigh numbers covered in this study. This formula derived is correct within ±5%, and is expected to be very useful to field engineers.

Significance of viscosity and thermal conductivity variation parameters on the dynamics of Newtonian fluid conveying tiny particles over a convectively heated surface

The significance of viscosity and thermal conductivity variation parameters on the dynamics of Newtonian fluid conveying tiny particles over a convectively heated surface is examined. The dimensional partial differential equations controlling the flow are remodeled to ordinary differential equations via suitable similarity variables in conjunction with the rescaled Nusselt, Sherwood and density number of motile microorganisms. The resulting nonlinear coupled ordinary differential equations are consequently scaled down to a system of first order ordinary differential equations. The system of equations are evaluated arithmetically via shooting technique along with fourth order Runge–Kutta integration scheme for different boundary conditions. The result was found to be in excellent agreement when compared with available records in the literature. The major highlights of the problem are analyzed and discussed thoroughly. It is seen that increase in viscosity variation parameter is capable to cause a decline in the local skin friction coefficients at the rate of − 0 . 04985 and the Nusselt number is an increasing function of the thermal conductivity variation parameter.

Dual solutions of magnetohydrodynamic mixed convection flow of an Oldroyd-B nanofluid over a shrinking sheet with heat source/sink

In this study, the dual solutions for mixed convection flow of an Oldroyd-B fluid containing alumina nanoparticles over a shrinking sheet are investigated taking into account the effects of magnetic field and heat source/sink. By utilizing the similarity transformations, the governing equations are reduced to ordinary differential equations which have been solved by the well-known shooting method. The present investigation reveals that some published results are not realistic. It is remarkable that for higher Deborah numbers for relaxation and retardation times, suction parameter and magnetic field parameter, the domain of the occurrence of dual solutions becomes wider and the local skin friction coefficient and local Nusselt number are found to increase. On the other hand, dual solutions exist in a broader domain as long as the volume fraction of alumina nanoparticles is less than or equal to 0.05 and after that it decreases. The critical values of the shrinking parameter relating to the existence of dual solutions are rendered in approximate functions. These characteristics of an Oldroyd-B nanofluid are not reported yet and might be useful in the development of the existing technology.

Regression modelling of hybrid nanofluid flow past an exponentially stretching/shrinking surface with heat source-sink effect

Regression model for thermal characteristics of nanofluid, hybrid nanofluid are presented in this current communication. The main focus in this theoretical study is to identify the most suitable nanoparticle volume fraction which gives better heat transfer rate fitting regression model for Nusselt number which is one of the important quantity to understand heat exchange rate. Momentum, energy equations are converted into system of algebraic equations with the help of self-similarity variable and solved by shooting method. Importance of each fluid flow parameter on velocity, temperature profile has been explained through graphs and local skin friction coefficient, local Nusselt number are computed. Three different regression models have been developed with variable volume fraction of nanoparticle (ϕ1=0.005, ϕ1=0.01, ϕ1=0.1) and compared to predict the heat transfer rate. It is observed that there is no significant improvement in Nusselt number with ϕ1=0.005, 0.01⩽ϕ2⩽0.04 and ϕ1=0.01, 0.01⩽ϕ2⩽0.04 but for ϕ1=0.1, 0.01⩽ϕ2⩽0.04 Nusselt number increases.

A Study of Flow and Heat Transfer of a Nanofluid Over a Vertical Cone With Heat Generation Using Legendre-Galerkin Method

An efficient Legendre-Galerkin method was applied to describe the nanofluid flow along an upward cone and how the heat transfers under the impacts of heat generation and thermal radiation. A strong uniform transverse magnetic field subjects to the flow and perpendicular to the cone surface. Suitable transformations with appropriate variables are presented to put the administering equations and the boundary conditions in a helpful structure for calculation. The arising sets of nonlinear system are settled using a Galerkin method with the Legendre function as a base. The study on the impacts of magnetic, Eckert number, heat source, and Hall parameters on fluid temperature, velocity profiles, local skin-friction coefficient, and Nusselt number are analyzed and introduced in tables and graphs forms. The volume fraction parameter of nanoparticles and their type assumed a significant part to fundamentally decide the stream behavior. Upon validation of the proposed study with special cases from other previous studies in the literature, an excellent agreement is obtained.

Buoyancy driven flow of a couple stress fluid from an isothermal vertical plate: the role of spatially periodic magnetic field

The present article deals with the analysis of the buoyancy-driven flow of a non-Newtonian couple stress fluid from an isothermal vertical plate under the influence of a spatially periodic magnetic field. We consider, in this work, the applied magnetic field to be a sinusoidal function of axial coordinate. We solve the coupled nonlinear governing equations numerically consistent with the help of an implicit Crank-Nicolson finite difference scheme. We analyse the impact of periodic magnetic field on the flow velocity of couple stress fluid and its eventual consequence on the convective transport of heat. The flow variables governing the underlying thermo-magneto-hydrodynamics are examined graphically in terms of velocity, temperature distribution, and friction-factor coefficients. The result indicates that the magnitude of the velocity and temperature increases for increasing the magnitude of the couple stress parameter, attributed primarily to the enhanced resistance due to larger degree collision of couple stress fluid particles. On the other hand, the local skin friction coefficient and heat transfer rate reduces owing to the adverse effect of the Lorentz force due to the applied magnetic field.

Optimal hydro-thermal characteristics of a porous annular elliptic pipe using response surface method

Natural convection of pure water within an annular condensed elliptic pipe fully filled with saturated porous metal foam is computationally evaluated. A single-phase fluid with the Darcy-Forchheimer model and Local-Thermal-Equilibrium between fluid and solid is implemented for water flow through the porous zone. The outer and inner surfaces of the annular pipe are exposed to constant cold temperature and variable hot temperatures, respectively. The desirable hydraulic-thermal features for the hot surface temperature of the inner pipe (Th) and contraction ratio (CR) are considered. After achieving the optimum of Th and CR, the response surface method (RSM) is conducted to maximize heat transfer rate and minimise skin friction coefficient by utilising the multi-objective optimum design for porous metal foam properties such as porosity (ε), viscous resistance (1/K) and inertial resistance (C) simultaneously. The key results show that the local and average Nusselt number and heat transfer rate are enhanced, while the local and average skin friction coefficients have been increased with hot surface temperature increase and contraction ratio decrease. In addition, RSM shows that porosity (ε) and viscous resistance of metal foam (1/K) have a major effect on hydro-thermal efficiency enhancement, while inertial resistance (C) has a minor effect on the desired responses. Consequently, for any value of inertial resistance (C), the optimal values of porous media properties are ε = 0.95, 1/K = 106. This investigation provides an original method and useful guidance for the optimum design of the annular condensed elliptic pipe.

Heat Transfer Enhancement and Boundary Layer Separations for a Hybrid Nanofluid Flow past an Isothermal Cylinder

Unsteady magnetohydrodynamic mixed convection flow of an incompressible hybrid nanofluid (Cu-Al2O3/water) past an isothermal cylinder with thermal radiation effect has been studied. Appropriate non-dimensional variables are initiated to reduce the governing equations into a convenient form. By utilizing the procedure of finite difference, reduced equations are then solved for all time. Besides, series solutions are obtained using perturbation technique for short time and asymptotic method for long time which agree with the acquired numerical solution up to a good accuracy. When the mixed convection parameter Ri, radiation conduction parameter Rd, magnetic field parameter M and the volume fractions of nanoparticles ϕ1 and ϕ2 are increased, the local skin friction coefficient and the local Nusselt number are found to increase. Results revealed that the hybrid nanofluid (Cu-Al2O3/water) enhances the heat transfer about 28.28% in comparison to the Al2O3-water nanofluid and about 51.15% than the pure fluid. Contrary to this, the heat transfer of hybrid nanofluid is augmented about 41.76% than the Cu-water nanofluid and 71.41% than the base fluid. The streamlines and isotherms reveal that higher values of Ri, M and Rd delay the boundary layer separation and accordingly shrink the vortices. Moreover, the thermal boundary layer is thickened for the increment of aforesaid quantities. The surface temperature parameter augments the local skin friction coefficient, however, the reverse characteristic is observed for the local Nusselt number.

Unsteady radiative nanofluid flow near a vertical heated wavy surface with temperature-dependent viscosity

In the present contribution, a numerical treatment is provided to describe unsteady nanofluid flow near a vertical heated wavy surface. A memorable feature of the present work is the investigation of nanofluid flow associated with thermal radiation that acts as a catalyst for heat transfer rates. Likewise, the effectiveness of variable viscosity is examined as it controls fluid flow as well as heat transfer. It is necessary to study heat and mass transfer for complex geometries because predicting heat and mass transfer for irregular surfaces is a topic of fundamental importance, and irregular surfaces frequently appear in many applications, such as flat-plate solar collectors and flat-plate condensers in refrigerators. A simple coordinate transformation from the wavy surface into a flat one is employed. The non-dimensional boundary layer equations that governing both heat transfer and nanofluid flow phenomena along the wavy surface are solved via a powerful numerical approach called the implicit Chebyshev pseudospectral (ICPS) method with Mathematica code. A comparison graph of the current numerical computation and the published data shows a perfect match. Figures depict the effect of various physical parameters on nanofluid velocities, temperature, salt concentration, nanoparticle concentration, skin friction, Sherwood, nanoparticle Sherwood, and Nusselt numbers. According to the numerical results, increasing the variable viscosity parameter value causes a drop in the local skin friction coefficient value and an increase in the steady-state axial nanofluid velocity profile near the wavy surface. Furthermore, as heat radiation is increased, the local Nusselt number decreases but the nanoparticle Sherwood number increases.

Williamson hybrid nanofluid flow over swirling cylinder with Cattaneo–Christov heat flux and gyrotactic microorganism

This is a numerical study of gyrotactic microorganism, heat and mass transfer futures of hybrid Williamson nanofluid made up of water − Ag / MWCNT nanoparticles over swirling cylinder with Cattaneo–Christov heat flux. Suitable similarity transformations are presented to convert the governing partial differential equations into ordinary differential equations. The set of ordinary differential equations along with boundary conditions are solved by using the finite element technique. The sketches of swirling velocity, axial velocity, temperature, concentration and density of microorganism with individual pertinent quantities, such as volume fraction parameter of Ag nanoparticle ( 0.01 < ϕ 1 < 0.04 ) , volume fraction parameter of MWCNT nanoparticle ( 0.01 < ϕ 2 < 0.04 ) , Magnetic field parameter ( 0.1 < M < 0.7 ) , Weissenberg number ( 0.5 < We < 0.8 ) , Prandtl number ( 2.2 < Pr < 8.2 ) , Reynolds number ( 0.5 < Re < 2.0 ) , Chemical reaction parameter ( 0.1 < Cr < 0.7 ) , Peclet number ( 0.1 < Pe < 0.7 ) , Bio-convection Lewis number ( 1.0 < Sb < 1.6 ) , Biot number ( 0.2 < Bi < 0.8 ) , thermal relaxation parameter ( 0.5 < γ < 2.0 ) and Suction parameter ( 0.1 < V 0 < 0.7 ) , are depicted through graphs. Moreover, the numerical estimates of local density number of microorganisms, heat and mass transfer rates for different parameters are specified in a tabular form. The calculations show that local skin friction coefficient, Sherwood number and local density of microorganism intensify with increasing values of both volume fraction parameters ( ϕ 1 ) and ( ϕ 2 ) . Also, the density of microorganisms and profiles of concentration are elevated in the fluid region with rising values of Weissenberg number. Temperature of hybrid nanofluid deteriorates with increasing values of thermal relaxation parameter.

Unsteady MHD three-dimensional flow of nanofluid over a stretching surface with zero nanoparticles flux and thermal radiation

The unsteady three-dimensional flow of nanofluid over a stretching surface in the presence of a magnetic field and thermal radiation are investigated. Zero nanoparticle flux at the wall has been considered. Buongiorno’s model for nanofluid has been used in this study. Employing similarity transformations, the governing partial differential equations are transformed to ordinary ones and the transformed equations are then solved numerically by using the shooting technique with the help of Runge–Kutta method. The computed results are compared with previously reported work and found in excellent agreement. Fluid velocity initially decreases with the increase of the unsteadiness parameter. Temperature and nanoparticle volume fraction both increase with the increase of unsteadiness parameter. Due to the increase of thermal radiation temperature increases, nanoparticle volume fraction decreases initially but increases away from the surface. The effect of the other governing parameters on velocity, temperature and concentration fields are discussed through their graphical representations. Besides, the local skin friction coefficient, local Nusselt number and local Sherwood number are presented through graphs.

Thermodiffusion, chemical reaction, and Hall and ion‐slip impacts on MHD rotating flow past an infinite vertical porous plate

AbstractThe current scrutiny explores the impacts of thermodiffusion, chemical reaction, and Hall and ion‐slip impacts lying on unsteady heat and mass transport of free convective hydromagnetic flow enclosed past a semi‐infinite porous plate within a gyratory frame under the accomplishment of a transverse magnetic field and convective boundary conditions. The nondimensional governing equations are solved systematically by means of the finite element method. Through the facilitation of graphical profiles, the outcomes of a variety of significant parameters within the boundary layer are addressed. In addition, the local skin friction coefficient and rates of heat and mass transports in expressions of the local Nusselt number and local Sherwood number are presented digitally in tabulation form, although it is originated that the Nusselt number and Sherwood number remain constant with varying all pertinent parameters. It is found that the porous medium impact on the boundary layer growth is significant due to the increase in the thickness of the hydrodynamic boundary layer and the decrease in the thickness of the thermal and concentration boundary layers. The resultant velocity enhances with increasing rotation, Hall and ion‐slip parameters.

On Numerical Thermal Transport Analysis of Three-Dimensional Bioconvective Nanofluid Flow

In this paper, a numerical study is presented for the 3D mathematical model of bioconvective boundary layer flow having nanoparticles and motile microorganisms on a curved sheet under isothermal conditions. Using an appropriate choice of similarity transformations, the problem reduces to coupled ordinary nonlinear equations, and this system is then treated with bvp4c (a MATLAB-based solver) to get the desired solution with good accuracy. The repercussion of distinct important dimensionless numbers such as thermophoresis, buoyancy ratio, Lewis number, and Brownian number on the velocity, temperature, and volume fraction of nanoparticles is presented graphically and is discussed in context with their importance on flow dynamics. Moreover, the physical impact of various parameters on motile microorganism density, the local Sherwood number, the local Nusselt number, and the local skin friction coefficients is analyzed and presented in tables. Qualitative analysis also reveals that the Brownian motion parameter, Peclet number, and Schmidt number have an inverse impact on the density microorganisms.

Effectiveness of Magnetized Flow on Nanofluid Containing Gyrotactic Micro-Organisms over an Inclined Stretching Sheet with Viscous Dissipation and Constant Heat Flux

The bioconvection phenomenon, through the utilization of nanomaterials, has recently encountered significant technical and manufacturing applications. Bioconvection has various applications in bio-micro-systems due to the improvement it brings in mixing and mass transformation, which are crucial problems in several micro-systems. The present investigation aims to explore the bioconvection phenomenon in magneto-nanofluid flow via free convection along an inclined stretching sheet with useful characteristics of viscous dissipation, constant heat flux, solutal, and motile micro-organisms boundary conditions. The flow analysis is addressed based on the Buongiorno model with the integration of Brownian motion and thermophoresis diffusion effects. The governing flow equations are changed into ordinary differential equations by means of appropriate transformation; they were solved numerically using the Runge–Kutta–Fehlberg integration scheme shooting technique. The influence of all the sundry parameters is discussed for local skin friction coefficient, local Nusselt number, local Sherwood number, and local density of the motile micro-organisms number.

Effect of Hall current on the flow and heat transfer of non-Newtonian power-law nanofluid in the presence of Cattaneo–Christov heat flux and free stream

The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid [Formula: see text] and dilatant fluid [Formula: see text] are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid [Formula: see text] gives higher values of [Formula: see text] and [Formula: see text] compared to the pseudoplastic fluid [Formula: see text].

Gyrotactic microorganisms mixed convection flow of nanofluid over a vertically surfaced saturated porous media

In the current study, a mathematical model is developed to visualize the mixed convection boundary layer flow of a nanofluid containing gyrotactic microorganisms past a permeable vertical surface saturated in a porous medium with variable viscosity and velocity slip effects. Suction/injection impact is taken into detail through the flow with heat and mass transfer analysis. Appropriate transformations are applied to transform the governing partial differential equations into non-linear ordinary differential equations, before being solved numerically using Runge-Kutta procedure is used with shooting technique. A parametric study focusing the influence of involved parameters on various fields such as the local skin friction coefficient, local Nusselt number are graphed via plots along with the local Sherwood number and motile microorganisms density number. The present results indicate that the motile microorganism number is enhanced for increasing Peclet number estimations. Moreover, the growing in the thermophoresis parameter leads to sufficient enhancement in the skin friction coefficient, Sherwood number and the density of the motile microorganism number for injection case, while the opposite behavior occurred with suction case.

Stagnation Point Heat Flow and Mass Transfer in a Casson Nanofluid with Viscous Dissipation and Inclined Magnetic Field

Influence of slip and inclined magnetic field on stagnation-point flow with chemical reaction are studied. Implementation of the similarity transformations, transformed the fluid non-linear ordinary differential equations and numerical computation is performed to solve those equations using Spectral Collocation Method. Various pertinent parameters on fluid flow, temperature and concentration distributions of the Casson nanofluid flow as well as the local skin friction coefficient, local Nusselt number, and Sherwood number are graphically displayed. The results indicate that thermophoresis parameter N_t enhanced the temperature and nanoparticle concentration profiles, because a rise in thermophoresis parameter enhances the thermophoresis force within the flow regime. Values of both local Nusselt and Sherwood numbers are enhanced with an increase in Hartman number (magnetic field parameter). The present results are compared with previously reported ones and are found to be in excellent agreement.

Heat Transmission of Engine-Oil-Based Rotating Nanofluids Flow with Influence of Partial Slip Condition: A Computational Model

This particular research was conducted with the aim of describing the impact of a rotating nanoliquid on an elasting surface. This specific study was carried out using a two-phase nanoliquid model. In this study engine oil is used as the base fluid, and two forms of nanoparticles are used, namely, titanium oxide and zinc oxide (TiO2 and ZnO). Using appropriate similarity transformations, the arising system of partial differential equations and the related boundary conditions are presented and then converted into a system of ordinary differential equations. These equations are numerically tackled using powerful techniques. Graphs for nanoparticle rotation parameter and volume fraction for both types of nanoparticles present the results for the velocity and heat transfer features. Quantities of physical significance are measured and evaluated, such as local heat flux intensity and local skin friction coefficients at the linear stretching surface. Numerical values for skin friction and local heat flux amplitude are determined in the presence of slip factor.