Skin Friction Factor Research Articles

Theoretical analysis of convective heat flux structure in the incompressible turbulent boundary layer on a porous plate with uniform injection and suction

Although many experimental and numerical studies on thermal convection exist for turbulent transpiration boundary layer flows on a porous structure, the general convective heat flux formula is urgently needed to clarify the influence of injection or suction on the energy transfer mechanism of turbulent heat convection. The two-dimensional (2D) theoretical convective heat flux structure obtained previously is therefore applied to the incompressible turbulent thermal boundary layer on a porous flat plate with uniform injection and suction. The energy balance relationship between the streamwise and wall-normal heat flux components is established and the effects of injection and suction on turbulent convective heat fluxes are analyzed. The explicit analytical expressions of turbulent skin friction factor, convective heat transfer coefficient and Stanton number are obtained based on the heat flux theory and verified by the previously experimental measurements. The turbulence characteristics of convective heat transfer with uniform injection and suction are revealed by the proposed key parameters. A hybrid control volume analysis for energy transfer inside the porous media plate is performed and applied to the cases of transpiration cooling and enhancing heat transfer, respectively, and a novel calculation formula for convective heat transfer is proposed in the form of heat flux instead of the heat transfer coefficient. It is also found that the direction of the resultant convective heat flux combining the conduction with advection is not always to remain that of the negative temperature gradient, and it depends not only on the temperature difference direction as well as velocity direction, but also on the magnitude contrast of the conductive and advective heat fluxes.

The improved thermal efficiency of Maxwell hybrid nanofluid comprising of graphene oxide plus silver / kerosene oil over stretching sheet

An analysis for heat transfer enhancement of Graphene oxide (Go)/Kerosene oil and Go + silver (Ag)/Kerosene oil hybrid nanofluid is made theoretically when the fluids flow through a porous medium over a stretching sheet in the presence of an applied magnetic field. The heat energy is augmented with thermal dissipation, heat source, and convective boundary conditions. The mass transpiration at the wall of the sheet is taken into account. The model equations are transmuted to ordinary differential form. The roles of controlling parameters are observed numerically by hiring Runge-Kutta method in Matlab coding. The flow speed becomes faster with Maxwell fluid parameter. The growing strengths of magnetic field and porosity resistance make the flow slower but cause to raise in temperature. Further, the additive volume fraction of silver with Graphene oxide becomes responsible to decelerate the flow and enhance heat transportation. The skin friction factor declines in magnitude against exceeding inputs of magnetic characteristic parameter M and porosity parameter Kp.

A computational model for hybrid nanofluid flow on a rotating surface in the existence of convective condition

The current work aims to study heat transfer properties within the flow. A newly developed idea regarding hybrid nanofluid is utilized to obtain the desired outcomes. This study focused on hybrid base nano liquid flow past an exponentially stretching rotating surface in the presence of the convective condition. Ethylene glycol-water (50%–50%) mixture is taken as base fluid. Thermophysical properties are discussed. The probe of emerging parameters indicates that hybrid base nanofluid gives a preferable rating as compared to nanofluid. Appropriate choice of composition plays a vital role. Physical characteristics of essential parameters such as Prandtl number, convective parameter, stretching ratio, rotation parameter, and temperature exponent are evaluated. Graphical depiction reveals that the velocity curve decline by increasing rotation parameter for CuO-hybrid base fluid and TiO2 hybrid base fluid. By expanding the values of the stretching ratio the velocity profile p′(η) is decreasing while the velocity curve q′(η) increased for CuO as well as TiO2 hybrid base fluid. Concentration boundary layer thickness growing by enlarging rotation parameters for both types of nanofluid. Moreover, the influence of various parameters on skin friction factor and Nusselt numbers are also evaluated.

A numerical model for analysis of binary chemical reaction and activation energy of thermo solutal micropolar nanofluid flow through permeable stretching sheet: nanoparticle study

The mechanism of nanofluid to improve heat transfer features has received great consideration due to their wide applications in chemical engineering and industry. In light of these facts, a numerical simulation for the flow of a micropolar nanofluid with suspended nanoparticles has been analyzed past a permeable stretching sheet with non-uniform heat source/sink, Binary chemical reaction and activation energy. In modeling micropolar nanofluid quantifies and qualifies the thermal phenomena caused by convective heat transfer in the presence of non-uniform heat source/sink and reaction rate. The formulated equations are altered to ordinary differential equations by employing similarity transformations which are then solved by utilizing shooting technique and RKF-45 method. The potentialities of all the representatives are put into graphs and are elucidated. Furthermore, the skin friction coefficient and Nusselt number in the boundary layer regime, are exhibited through graphs and tables and are deliberated with proper physical justification. The significant outcomes of the current investigation are that increment in the suction parameter declines the flow velocity and temperature while the injection is uplift the temperature. The skin friction factor is trigger considerable decrease with the stretching parameter. The heat transfer rate increases with the increased values of the radiation parameter.

A Numerical Study of MHD Carreau Nanofluid Flow with Gyrotactic Microorganisms over a Plate, Wedge, and Stagnation Point

This article addresses the numerical exploration of steady and 2D flow of MHD Carreau nanofluid filled with motile microorganisms over three different geometries, i.e., plate, wedge, and stagnation point of a flat plate. The influence of magnetic field, viscous dissipation, thermophoresis, and Brownian motion is considered for both cases, i.e., shear thinning and shear thickening. A set of relevant similarity transformations are utilized to obtain dimensionless form of governing coupled nonlinear partial differential equations (PDEs). The transformed system of ordinary differential equations (ODEs) is then numerically solved by bvp4c via MATLAB based on shooting technique and Runge–Kutta–Fehlberg (RKF) scheme via MAPLE. Also, a numerical analysis has been made for skin friction factor, heat, and mass transfer rates. Results elucidate that all the profiles except velocity show decreasing behavior for higher values of magnetic field parameter. Among all three flow geometries for both shear thinning and shear thickening cases, the flow over a plate has lesser skin friction factor. The nanoparticle concentration and density of motile microorganism decrease in both the shear thinning and shear thickening cases, for increasing values of Brownian motion (Nb), but reverse trend is observed for rising values of thermophoresis parameter (Nt). Furthermore, it is observed that, as we increase the values of suction/injection parameter (S), the velocity of fluid increases but decreases the fluid temperature, concentration of mass and density of motile organisms over a plate, wedge, and stagnation point of a flat plate. Also, we observed that shear thinning nanofluid has higher rate of heat, mass, and motile microorganisms mass transfers than shear thickening fluid. Both shear thinning and thickening nanofluid have a low rate of heat/mass and gyrotactic microorganisms mass transfer over plate among wedge and stagnation point flow.

On solution existence of MHD Casson nanofluid transportation across an extending cylinder through porous media and evaluation of priori bounds

It is a theoretical exportation for mass transpiration and thermal transportation of Casson nanofluid over an extending cylindrical surface. The Stagnation point flow through porous matrix is influenced by magnetic field of uniform strength. Appropriate similarity functions are availed to yield the transmuted system of leading differential equations. Existence for the solution of momentum equation is proved for various values of Casson parameter beta , magnetic parameter M, porosity parameter K_p and Reynolds number Re in two situations of mass transpiration (suction/injuction). The core interest for this study aroused to address some analytical aspects. Therefore, existence of solution is proved and uniqueness of this results is discussed with evaluation of bounds for existence of solution. Results for skin friction factor are established to attain accuracy for large injection values. Thermal and concentration profiles are delineated numerically by applying Runge-Kutta method and shooting technique. The flow speed retards against M, beta and K_p for both situations of mass injection and suction. The thermal boundary layer improves with Brownian and thermopherotic diffusions.

G-Jitter impact on magnetohydrodynamic non-Newtonian fluid over an inclined surface: Finite element simulation

The consequences of microgravity and micropolarity are assessed on mixed convection flow associated with magnetic and heat sources. The flow fields take place on a stretching vertical sheet. This communication therefore addresses oscillating convective flow driven by g-Jitter forces to facilitate guidelines for upper atmospheric aerodynamic designs through operating thermal fields. The field equations are reframed as ordinary differential types to be resolved numerically by finite element discretization. Matlab code is developed for Glariken formulation to evaluate parametric simulations for reduced skin friction factor, the velocity of fluid, microrotation, heat transfer rate, and thermal characteristics. The oscillating trends of physical outputs are notably influenced by the parameters of micropolarity, the amplitude of modulation, frequency parameter, magnetic and thermal sources. The oscillatory pattern of reduced skin friction factor −f″(τ,0) becomes stronger for progressive inputs of amplitude parameter and magnetic parameter, but the fluid temperature rises up with increasing strength of the magnetic field. The fluid speed f′(τ,η) responds reciprocal to the magnetic parameter, but it behaves directly with material parameter.

Analytical solutions for the incompressible laminar pipe flow rapidly subjected to the arbitrary change in the flow rate

A one-dimensional mathematical model is developed for an unsteady incompressible laminar flow in a circular pipe subjected to a rapid change in the flow rate from an initial flow with flow rate, Qi, to a final flow with flow rate, Qf, in a step-like fashion at an arbitrary time, tc. The change in the flow rate may either be an increment, Qf > Qi, or a decrement, Qf < Qi. The change time, tc, may either belong to the initial flow remaining in a temporally developing state or temporally developed state. The developed model is solved using the Laplace transform method to deduce generalized analytical expressions for the flow characteristics, viz., velocity, pressure gradient, wall shear stress, and skin friction factor, CfRe, where Re is Reynolds number based on the cross-sectional area-averaged velocity and pipe radius. Exact solutions for λa=Qi/Qf=0 and λd=Qf/Qi=0 with tc≥tsi are available in the literature and the present generalized analytical solutions fill the remaining range of parameters, 0<λa<1 and 0<λd<1 with 0<tc<tsi and tc≥tsi, where tsi is the time at which the initial flow reaches the temporally developed state. Exact solutions for canonical pipe flow problems reported in the literature are deduced as subsets of the derived generalized solutions. The parametric study reveals the effects of varying λa or λd and tc on the quantities of practical importance, viz., τs and CfRe, where τs is the time required for the final flow to reach the temporally developed state.

Combined magnetic and porosity effects on flow of time-dependent tangent hyperbolic fluid with nanoparticles and motile gyrotactic microorganism past a wedge with second-order slip

This research explores the time-dependent heat transport phenomena for the MHD flow of nanofluids containing motile microorganisms via porous matrix. The fluid flows through a porous stretched wedge with second-order slip and Nield boundary. Different physical and geometric parameters are included to achieve more practicable effects. The developed equations are converted into a non - dimensional form through the use of appropriate similarity functions. The mathematical formulation is built for these transmuted equations using the built-in Matlab software bvp4c. Differences in physical quantities namely skin friction coefficient −f″(0), local Nusselt number −θ′(0), Sherwood number φ′(0)and microorganism organism density −χ′(0) have also been identified under the influences of emerging parameters. Bioconvection caused by microorganisms stabilized nanomaterials, resulting in effective thermal delivery. The findings showed good consistency as compared to the current literature. The higher mixed convection parameter contributes to the quantities of flow viscosity, temperature, and nanoparticle concentration in boundary conditions. The incremented slip parameter γ precedes the flow speed. The skin friction factor −f″(0) reduces against unsteadiness parameter A, Hartree pressure gradient β, velocity ratio parameterλ, bouancy ratio parameterNr but it develops progressively when the parameters M, We, n, λ and bioconvection Rayleigh number Nc are incremented. The elaborated discussion is also presented with graphical and tabular illustrations.

Predicting the effect of the rib pitch on thermal performance factor of small channels plate heat exchangers fitted with Y and C shapes obstacles

This study presents a numerical analysis of a laminar counter flow inside small channels plate heat exchanger fitted with Y and C shape obstacles. Using the Computational Fluid Dynamics CFD, an advanced and modern simulation technique, the influence of the geometrical parameters (such as geometry, rib pitch) on the flow characteristics, the thermal and the hydrodynamics performance of the PHE (plate heat exchanger) is investigated numerically. The main goal of this work is to increase the flow turbulence, enhance the heat transfer and the thermal efficiency by inserting new obstacles forms. The computational domain is a conjugate model which is developed by the Computer Aided Design CAD software Solidworks. The results, obtained with Ansys Fluent, show that the presence of the shaped ribs provides enhancement in heat transfer and fluid turbulence. The CFD analysis is validated with the previous study. The non-dimensional factors such as the Nusselt number Nu, the skin friction factor Cf and the thermo-hydraulic performance parameter THPP are predicted with a Reynolds number Re range of 200–800. The temperature and the velocity distribution are presented and analyzed. The Y ribs and the C ribs offer as maximum THPP values respectively about 1.44 and 2.6 times of a smooth duct.

Internal energy activation stimulus on magneto-bioconvective Powell-Eyring nanofluid containing gyrotactic microorganisms under active/passive nanoparticles flux

Influence of Stephan blowing on a three-dimensional hydro magneto-bioconvective Eyring-Powell nanofluid containing Gyrotactic microorganisms under active and passive nanoparticle flux conditions is investigated in this paper. The presence of non-linear radiation along a bidirectional stretched surface is also deliberated throughout this analysis. A comparative study is made up for active and passive nanoparticle volume control. The study is relevant to novel microbial fuel cell technologies combining the nanofluid with bioconvection phenomena. The Prandtl’s boundary layer equations, approximated by Oberbeck-Boussinesq’s are studied under suitable boundary conditions. Similarity transformation is used to transform the governing boundary layer equations to dimensionless nonlinear ordinary differential equation model. The non-linear model is then resolved by combining the Runge–Kutta method and the MATHEMATICA software. The dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms together with the wall shear stress, Nusselt, Sherwood and density of motile microorganism number are graphically presented to visualize the effects of particular parameters. A novel idea of Stefan blowing on three-dimensional space taking into consideration the non-linear radiation is implemented in the investigation of Eyring-Powell flow over a deformable sheet under the effects of slip and activation energy for the first time. Axial Newtonian slip decreases the momentum of the nanoflow while tangential slip augments the flow. Bio-convection parameter reduces the nanoparticle concentration of the rescaled density of motile microorganisms. Skin friction factor is dominant in passive nanoparticles flux rather than active nanoparticles flux. Passive nanoparticles help in smooth delivery of drugs which is seen here for zero mass flux. Energy transfer rate is high compared to active nanoparticle volume control. A zero mass flux acts as a cooling agent in this study by diffusing more heat from the system.

Darcy–Forchheimmer flow of MHD Jeffrey nanoliquid over a permeable cone with Cattaneo–Christov heat and mass flux theories

Objective of the present study is to magnify the effects of Cattaneo–Christov heat and mass flux models on the phenomena of heat and mass transfer aspects for single-phase Jeffrey nanoliquid above a permeable cone in the occurrence of Darcy–Forchheimmer, Brownian motion and thermophoresis effects. The primitive governing equations for Jeffrey fluid flow are formulated with the aid to boundary layer approximations. The non-dimensional forms of the corresponding equations are elucidated by the optimal homotopy analysis method (OHAM). Some elementary features as velocity, temperature and nanoparticles concentrations with respect to the various critical parameters like magnetic parameter, porosity, Darcy–Forchheimmer, Prandtl number, thermophoresis parameter, Brownian motion, Deborah number of first and second kind, Schmidt number and Jeffrey fluid parameter are investigated via plots. The study also divulges the investigation of the skin friction factor, the Nusselt number and the Sherwood number through tables. A comparative study between the OHAM with the previously published results justifies the salient features of OHAM.

Effects of Variable Thermal Conductivity and Grashof Number on Non-Darcian Natural Convection Flow of Viscoelastic Fluids with Non Linear Radiation and Dissipations

Effects of variable thermal conductivity, porosity and Grashof number on natural convection of viscoelastic fluid flow and heat transfer are studied and discussed. The nonlinear radiation and dissipations are taken into consideration. The fluid flows through non-Darcy porous medium which lies between two heated vertical plates that are kept at constant, but different, temperatures. High order accurate finite difference schemes are introduced to solve the governing equations. The coupled nonlinear differential equations are linearized and iterations are used to approximate that linearized terms. The finite difference method transforms the coupled linearized differential (momentum and energy) equations to a linear system of algebraic equations. An error analysis is introduced by refinement of mesh size and comparisons with available previous results. Effects of fluid and heat parameters on the velocity field, temperature, skin friction factor and Nusselt number are tabulated and plotted. The present results and comparisons show that the numerical solution is of excellent agreement with previous analytical and numerical solution.

Penetration and retrieval forces during sampling in a very soft clay

Three series of sampling with thin-walled samplers, with and without inside clearance and without a piston, have been performed in a very soft organic clay deposit. The penetration and retrieval forces were measured throughout the operation, thus contributing to a clearer understanding of the sampling process. The measured forces show the importance of proper borehole cleaning conditions, and also identify when samples were lost during retrieval. This occurs when the underpressure at the sampler bottom does not appear in the retrieval force versus time chart. The obtained values have been compared to the sleeve friction measured by piezocone tests. Direct simple shear (DSS) tests and vane shear tests have been used as references to back-calculate the dimensionless skin friction factor from both sample penetration and retrieval. The measurement of force during sampling proved useful for controlling sampling operation, also providing further information with respect to the regular procedure.

Effect of suction or blowing on velocity and temperature distribution of flow over a flat plate

In this paper, laminar, incompressible flow with constant pressure gradient and constant wall temperature over a flat plate for several values of fluid suction and blowing parameters at β = −0.1978, m = −0.09 and β = 0.66, m = 0.5 respectively were studied numerically. The governing nonlinear partial differential equations are transformed to ordinary differential equations by using a similarity variable and then solved numerically adopting Runge–Kutta integration method. Effects of continuous suction and blowing with very low ratio of constant velocity to free stream neglecting the mass transfer on the velocity, temperature profiles and skin friction are presented. The results indicated that the skin friction factor is increased with increase the value of the suction for given Reynolds number. In order to reduce the skin friction, the laminar flow and avoid transition the blowing have been applied. The effect of fluid blowing parameter on velocity profile in hydrodynamic boundary layer are the certain incidence angles. Results show that the hydrodynamic boundary layer thickness is increased due to the blowing. It can be noted that the delaying separation is led to increase of the maximum lift. It was observed that increasing the maximum lift by maintain laminar flow to avoid transition and delaying separation to reduce skin friction is existing by suitable magnitude of suction or blowing. It is concluded that the skin friction is decreasing due to apply the blowing over a flat plate.

Conjugate Heat and Mass Transfer on Steady MHD Mixed Convection Flow along a Vertical Slender Hollow Cylinder with Heat Generation and Chemical Reaction Effects

This paper studies the effects of heat generation and chemical reaction on the coupled conjugate heat and mass transfer by MHD laminar mixed convective flow along a vertical slender hollow cylinder. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a non similar transformation and the resulting equations are then solved by the finite difference method using Matlab@ following the code bvp4c. Numerical results of the velocity, temperature and concentration for different values of the conjugate heat transfer parameter p, the magnetic parameter M, the heat generation Q, and the chemical reaction K are studied. The local skin friction, Nusselt number and Sherwood number are also analyzed and presented graphically. In the numerical ranges of the main parameters, it is found mainly that working with strong conjugate heat transfer or/and all others parameters affects negatively the Nusselt and Sherwood numbers. The same trend is revealed for the skin friction factor.

Magnetohydrodynamic nonlinear mixed convection flow of reactive tangent hyperbolic nano fluid passing a nonlinear stretchable surface

The intent of this paper is to unravel the transport of a nonlinear mixed convection tangent hyperbolic nanofluid along a nonlinear stretchable sheet in the neighbourhood of a stagnation point. The impacts of magnetohydrodynamic, thermophoresis, Brownian motion and activation energy together with non-uniform heat source associated with varying thermal conductivity are scrutinized. The outlining transport equations are mutated into a system of nondimensional ordinary differential equations by the use of similarity transformations and then tackled with the Runge–Kutta Fehlberg coupling shooting method. The impact of all essential parameters in respect of the dimensionless quantities are graphically exhibited and deliberated. The significant consequences of the investigation are that increment in the Darcy with magnetic term declines the flow velocity while that uplift the fluid temperature. The skin friction factor triggers a considerable increase with the power-law exponent and magnetic field parameters. The intensity of heat and mass transfer shrink with hike in the values of the thermophoresis parameter. The vetting of the numerical solution is done with earlier related studies in the limiting position and presented in tabular form showing perfect correlation.

Performance assessment of longitudinal flow through rod bundle of ETRR-2 Cobalt/Iridium irradiation device

In the present paper, three dimension CFD analysis was presented for longitudinal flow through rod bundle of ETRR2 Cobalt/Iridium irradiation device. Study of optimal performance for both heat transfer and flow characteristics was performed by the determination of the conditions at which minimum entropy generation exist. The study was performed for Reynolds number (Re) in the range 2 × 104 ≤ Re ≤ 5.5 × 105, and Prandtl number (Pr) in the range 3.2 ≤ Pr ≤ 5.2 under both the conditions of uniform and non uniform (cosine shape) heat flux. Contours of fluid temperature and fluid velocity at irradiation box outlet as well as temperature contours of Ir rods at different values of inlet velocity were illustrated. Two correlations one relating the Nusselt number (Nu) with Re and Pr and the other relating skin friction factor with Re was presented in the studied range of Re and Pr. Determination of the applicability of the existing correlations for turbulent forced convection heat transfer and friction coefficient are also presented. Comparison between the flow and heat transfer characteristics through Ir rods of different locations in the irradiation box is presented.

Entropy analysis of Powell–Eyring hybrid nanofluid including effect of linear thermal radiation and viscous dissipation

Hybrid nanofluids are introduced as heat transfer fluids with greater surface stability, diffusion and dispersion capabilities compared to traditional nanofluids. In this work, flow, convective heat transport and volumetric entropy generation in Powell–Eyring hybrid nanofluid are investigated. Hybrid nanofluid occupies the space over the uniform horizontal porous stretching surface with velocity slip at the interface. Effect of viscous dissipation and linear thermal radiation are also included in the simplified model. Mathematical equations for conservation of mass, momentum, energy and entropy are simplified under assumptions of boundary layer flow of Powell–Eyring hybrid nanofluid. Similarity solutions are obtained by transformation of governing partial differential equations to ordinary differential equations, using similarity variables. Keller box finite difference scheme is then adopted to find the approximate solutions of reduced ordinary differential equations. Numerical computations are performed for alumina–copper water ( $${\mathrm{Al}}_2{\mathrm{O}}_3$$ – $${\mathrm{Cu/H}}_{2}{\mathrm{O}}$$ ) hybrid nanofluid and conventional copper water ( $${\mathrm{Cu}}$$ – $${\mathrm{H}}_{2}{\mathrm{O}}$$ ) nanofluid. Graphs are produced for velocity, temperature and entropy profiles to study the effect of governing parameters. Skin friction factor and the local Nusselt number are also calculated at the boundary. The notable findings indicate that the hybrid Powell–Eyring nanofluid is better thermal conductor when compared with the conventional nanofluid. The rate of heat transfer at the boundary is greatest for smallest value of the shape factor parameter. The increase in Reynolds number and Brinkman number increases the overall entropy of the system.

Heat and mass transfer analysis in unsteady MHD flow of aluminum alloy/silver‐water nanoliquid due to an elongated surface

AbstractThe current article presents an analytical study of an unsteady magnetohydrodynamic flow of Al50Cu50/Ag‐water nanofluid over an elongated surface with thermal radiation and thermal diffusion effects. The flow is caused by an elongated plate, and the flow governing partial differential equations are transmuted into ordinary differential equations using suitable similarity transmutations. The regular perturbation technique is employed to resolve the transmuted equations. The results obtained describe the influence of pertinent parameters over usual flow fields, which are presented via plots, and the expressions procured for skin friction factor and rate of thermal and diffusion transport are comprehensibly portrayed in a tabular mode. The outcomes stipulate that the thermal transport performance of Al50Cu50‐water nanofluid is moderately high as compared with Ag‐water nanofluid. Also, the thermal radiation and chemical reaction parameters have a tendency to augment the rate of mass transfer.