Local Skin Friction Coefficient Research Articles

Nonsimilar numerical analysis for the mixed convective flow of Casson fluid with thermal radiations and chemical reactions

The focus of this nonsimilar study is to implore the effects of thermal radiations and chemical reactions on the boundary layer flow of Casson fluid over an exponentially stretching sheet. The appropriate nonsimilar transformations are implemented to convert convection differential equations into a set of coupled dimensionless partial differential equations (PDEs). The dimensionless nonsimilar system is analytically approximated by local nonsimilarity methods up to two truncations levels. The numerical simulations of the local nonsimilar truncations are obtained via Matlab-built-in solver bvp4c. The effects of several parameters, such as, radiation parameter, Schmidt and Prandtl numbers on local skin friction coefficient, local Nusselt and local Sherwood numbers, are given in a table, while velocity, temperature, and concentration distributions are numerically calculated and expressed through graphs. From numerical experiments, it can be concluded that the temperature flow profile escalates by enhancing the radiation parameter and the concentration profile de-escalates by rising values of the reaction rate parameter.

Thermal aspects of radiation in Casson fluid with nonlinear stretching surface: non-similar solutions

A mathematical model is established to peruse the effects of viscous dissipation and thermal radiation on non-Newtonian, incompressible, steady, mixed convective flow next to a nonlinear vertical stretching surface. The Rosseland approximation is used in the energy equation to describe the radiative heat flux. Non-similarity transformation has been used to convert coupled partial differential equations (PDEs) into dimensionless PDEs. For dealing with non-similar problems, the non-similarity method is more effective as compared to similarity transformation. First, this method utilizes transformations to reduce governing equations into dimensionless systems of PDEs, and further, it utilizes different truncation levels to get a detailed set of PDEs. MATLAB built-in solver bvp4c is used to solve obtained dimensionless PDEs. Parameters describing the nature of flow like local Sherwood number, local Nusselt number and local skin friction coefficient are explored in detail after finding the numerical solution. The effects of Casson number, Radiation number, Eckert number, Schmidt number, Prandtl number and Grashof number for heat and mass transfer on concentration, temperature and velocity profiles are specified with the aid of graphs.

Unsteady Heat and Mass Transfer Slip Flow over an Exponentially Permeable Stretching Sheet

In this paper, the problem of unsteady two-dimensional boundary layer heat and mass transfer flow over an exponentially stretching sheet embedded in a porous medium in the presence of a uniform magnetic field with thermal radiation, heat generation/absorption, and suction/blowing is analyzed numerically. Instead of no-slip boundary conditions, velocity slip, thermal slip, and mass slips at the boundary are considered. Using a suitable similarity transformation, the governing partial differential equations are transformed to a system coupled with nonlinear ordinary differential equations. The reduced equations are solved numerically by using bvp4c with the MATLAB package. A detailed parametric study is performed to illustrate the physical parameters on the velocity, temperature, and concentration profile and the local skin-friction coefficient and Nusselt and Sherwood number. Then the results are exhibited in both graphical and tabular forms. It is observed that the present results have been in close agreement with the previously published studies under some special cases.

Combined Effect of Radiant Heat, Local Nusselt Number and Skin Friction Coefficient of a Third Grade Fluid through a Channel Flow in a Saturated Porous Medium

This paper investigates the combined effects of radiant heat, local Nusselt number and Skin friction coefficient on a channel flow of third grade fluid in the presence of saturated porous medium. It is assumed that the fluid has temperature-dependent variable viscosity and thermal conductivity. The non-linear governing differential equations are obtained and tackled numerically using Spectral element technique and C++ programming language. Increase in the values of radiation parameter and third grade material parameter consequently increase the local Nusselt number and skin friction coefficient. Graphical results showing the effects of various physical parameters are presented and discussed quantitatively. It is concluded that Williamson’s fluid parameter served as a cooling factor in diverse improved technological processes in order to avoid different machines from overheating and enhance their efficiencies.

Theoretical Analysis of MHD Mixed Convection From A Vertical Plate Embedded in a Porous Medium with a Convective Boundary Condition

An analytical approach has been used to study the heat and mass transfer from a vertical plate embedded in a porous medium experiencing a first-order chemical reaction and exposed to a transverse magnetic field. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved analytically a highly accurate and thoroughly tested using Homotopy Perturbation Method. The effects of Biot number, thermal Grashof number, permeability parameter, Hartmann number, Eckert number, Sherwood number and Schmidt number on the velocity, temperature, and concentration profiles are illustrated graphically. Proportional to the plate surface temperature, the local skin-friction coefficient, the local Nusselt number and the local Sherwood number were also presented analytically. The discussion focuses on the physical interpretation of the results as well their comparison with the results of previous studies.

Entropy generation on the variable magnetic field and magnetohydrodynamic stagnation point flow of Eyring–Powell hybrid dusty nanofluid: Solar thermal application

The prime intention of this study is to analyse the significance of the variable magnetic field and magnetohydrodynamic stagnation point flow of Eyring–Powell hybrid dusty nanofluid over a Darcy–Forchheimer sheet. The hybrid nanofluid was formulated by suspending the nanoparticles of copper ( Cu) and zirconium dioxide ( ZrO2) into a base fluid mixture of ( C2 H6 O2) ethylene glycol (50%) + ( H2 O) water (50%). The mixture of two different base fluid properties has notable results compared to using a single base fluid. Because when we used the mixture of both base fluids, we obtained better heat conductivity than pure ethylene glycol and a lower freezing point than water. Glycol water has several applications in solar heating installation and antifreeze in automobiles. The suitable self-similarity transformations are employed to convert the hybrid and dusty nanofluids transport equations into ordinary differential equations and then resolved using the Runge–Kutta fourth order with the shooting method in the MATLAB solver. The calculated results are plotted graphically through velocity, temperature, entropy generation, local skin friction coefficient and rate of heat transfer. The velocity profile enhances with the higher values of the Eyring–Powell fluid parameter. Entropy generation ( N G) and Bejan number ( Be) have an opposite nature on the Brinkman number ( Br). The rate of heat transfer rises for the higher values of the radiation parameter and opposite behaviour is observed to the magnetic field parameter. It is noticed that hybrid nanofluids have a higher heat transfer process than dusty nanofluids.

Transient separation and fluctuation of turbulent flow in an axisymmetric U-turn channel perturbed by periodically passing gust inflow

The flow in the vane-less diffuser bend and return the channel of radial turbo-machines which is perturbed by the time-periodic and circumferentially passing jet-wake structure exited from the upstream impeller, and the transient characteristics of separation and fluctuation occurring in these stationary components determine the operational stability and performances of the turbo-machines especially for the next stage. In this work, we present a numerical investigation on the transient separation and fluctuation behaviors of turbulent flow in a sector of a 180° bended axisymmetric U-turn channel subjected to time-periodic gust inflow which passes in the circumferential direction. The objective is to explore the effect of period of gust inflow, in simulating the non-dimensional blade passing frequency (BPF*) in turbo-machines, on the characteristics of flow in the whole U-turn channel. Numerical results reveal that flow separation occurs in the curved section for about half the cycle at BPF* = 1 and 2, and earlier separation is observed for BPF* = 2, while there is no separation for BPF* = 5 and 10. There is a phase lag between the local skin friction coefficient in the channel and gust inflow, and the magnitude of the phase lag is related to BPF*. As BPF* increases, the thickness of the boundary layer on both walls decreases.

Natural Convection Flow over a Vertical Permeable Circular Cone with Uniform Surface Heat Flux in Temperature-Dependent Viscosity with Three-Fold Solutions within the Boundary Layer

The aim of this study is to investigate the effects of temperature-dependent viscosity on the natural convection flow from a vertical permeable circular cone with uniform heat flux. As part of numerical computation, the governing boundary layer equations are transformed into a non-dimensional form. The resulting nonlinear system of partial differential equations is then reduced to local non-similarity equations which are solved computationally by three different solution methodologies, namely, (i) perturbation solution for small transpiration parameter (ξ), (ii) asymptotic solution for large ξ, and (iii) the implicit finite difference method together with a Keller box scheme for all ξ. The numerical results of the velocity and viscosity profiles of the fluid are displayed graphically with heat transfer characteristics. The shearing stress in terms of the local skin-friction coefficient and the rate of heat transfer in terms of the local Nusselt number (Nu) are given in tabular form for the viscosity parameter (ε) and the Prandtl number (Pr). The viscosity is a linear function of temperature which is valid for small Prandtl numbers (Pr). The three-fold solutions were compared as part of the validations with various ranges of Pr numbers. Overall, good agreements were established. The major finding of the research provides a better demonstration of how temperature-dependent viscosity affects the natural convective flow. It was found that increasing Pr, ξ, and ε decrease the local skin-friction coefficient, but ξ has more influence on increasing the rate of heat transfer, as the effect of ε was erratic at small and large ξ. Furthermore, at the variable Pr, a large ξ increased the local maxima of viscosity at large extents, particularly at low Pr, but the effect on temperature distribution was found to be less significant under the same condition. However, at variable ε and fixed Pr, the temperature distribution was observed to be more influenced by ε at small ξ, whereas large ξ dominated this scheme significantly regardless of the variation in ε. The validations through three-fold solutions act as evidence of the accuracy and versatility of the current approach.

EFFECT OF BROWNIAN MOTION AND THERMOPHORESIS ON NANOFLUID PAST A STRETCHING SURFACE WITH VARIABLE VISCOSITY AND NEWTONIAN COOLING INSPIRED BY THERMAL RADIATION

We analyze the combined influence of Brownian motion, thermophopresis, with past a stretching surface with variable viscosity and thermal radiation. The governing equations have been solved by employing fifth-order Runge-Kutta-Fehlberg method along with shooting technique. The effects of various parameters on the velocity, temperature and concentration as well as on the local skin-friction coefficient, local Nusselt number and local Sherwood number are presented graphically and discussed. It is observed that a velocities component increases with Hall parameter(m), Brownian motion parameter (Nb), Radiation parameter (Rd), Viscosity parameter (r), Convective heat transfer constant(h1), reduces with thermophoresis parameter (Nt). Nusselt number increase in r and reduces Nu and Sh, increase in r/h1 reduces rate of heat transfer and enhances mass transfer.

Entropy optimized radiative heat transfer of hybrid nanofluid over vertical moving rotating disk with partial slip

Hybrid nanofluids are a mixture of two types of nanomaterials in the base fluid. These nanofluids have novel characteristics that benefit many industrial applications like fuel cells, refrigerators, heat exchangers, etc. The present study examined entropy optimized Cu−TiO2/Water flow over vertically moving rotating disk with thermal radiation and partial slip. Also, Dufour and Soret’s effects are utilized in the modeling of the energy equation. The highly non-linear system of differential equations is solved by the BVP Midrich scheme employed in Maple software. The effects of embedded non-dimensional parameters on velocity, concentration, and temperature profiles are analyzed graphically along with the examination of entropy generation. It is observed that vertical disk movement and rotation have a contrasting impact on velocity, concentration, and temperature profiles compared to existing literature. Also entropy rate rises with radiation parameter, diffusion factor and temperature ratio parameter but declines with slip coefficient. The local skin friction coefficients, Nusselt number and Sherwood number are plotted with respect to different involved parameters. The current work can be utilized in various engineering applications to improve their efficiency.

Triple diffusion with heat transfer under different effects on magnetized hyperbolic tangent nanofluid flow

The core objective of the presented analysis is to explore the mixed convection and magnetohydrodynamics effects on tangent hyperbolic nanofluid flow generated by elongating surface. Mechanisms of thermal radiation and chemical reaction are incorporated in energy and concentration equations respectively. Moreover, the Soret-Dufour phenomenon is also taken into consideration. Mathematical formulation is floated under the assumption of boundary layer theory. Formulated partial differential (PD) system reduces into nonlinear ordinary differential (OD) system with the help of suitable transformations which has been solved with a technique named finite element method (FEM) and outcomes are justified through grid-free and convergence phenomenon. The characteristics of numerous effective parameters are displayed graphically and discussed. Furthermore, the physical quantities like local Nusselt number, Sherwood number and skin friction coefficient are tabulated numerically and analyzed. Solute concentration profile [Formula: see text] shown reverse trend for distinct values of [Formula: see text] and [Formula: see text] [Formula: see text] diminishes whereas [Formula: see text] boosted the [Formula: see text].

Numerical Study of Unsteady Boundary Layer Flow of a Biomagnetic Fluid over a Horizontal Stretching Sheet with Magnetic Dipole

This paper focuses on the theoretical and numerical investigation of the unsteady, viscous, incompressible, two-dimensional laminar boundary layer flow of a Newtonian biomagnetic fluid over a stretching sheet under the influence of an applied magnetic field in the presence of heat transfer. The magnetic field is induced by a magnetic dipole placed below the stretching sheet. The magnetic field intensity represents the magneto-thermo-mechanical coupling. This allows exclusion of the biofluid that is distant from the sheet at Curie temperature to avoid further magnetization. The unsteadiness of the flow is discernible in the fluid flow properties. The mathematical model of the problem conforms to the principles of Magnetohydrodynamics (MHD) and Ferrohydrodynamics (FHD). In this work, the study is performed on a specific biofluid, human blood. The modified Stokes principle is used to implement the model under the assumption that along with the three thermodynamic variables P, ρ, and T, the Biomagnetic Fluid Dynamics (BFD) fluid behavior can be characterized as a function of magnetization M. To describe the physical problem, a coupled non-linear system of ordinary differential equations subject to appropriate boundary conditions is derived from Navier-Stokes and thermal energy equations by performing non-dimensionalization of the considered variables. To solve these equations, the dsolve routine in the MAPLE software is used. Numerical results for flow profiles and the local skin friction coefficient (Cfx) and the local Nusselt number (Nux) are discussed for different values of unsteadiness parameter (A), biomagnetic interaction parameter (B) and a rational quantity (ϵ). The achieved results are compared with previously published work for steady state flow, and they seem to be in good agreement. It is found that MHD and FHD interaction parameters affect significantly on the velocity, temperature and pressure field. A successful completion will bring interesting results for better understanding of the biomagnetic fluid flow characteristics and can be beneficial to medical and bioengineering applications; particularly for estimating the characteristics of blood flow in stenosed arteries.

Bödewadt Flow and Heat Transfer in Nanofluid over a Permeable and Radially Stretching Disk

A Bödewadt boundary layer flow and heat transfer problem in nanofluid was investigated in this study for suction/injection as well as combined effects of suction/injection and radial stretching disk. Similarity variables were introduced to transform the three-dimensional flow into a system of ordinary differential equations. Moreover, similar to the Bödewadt heat transfer problem in a viscous fluid, adequate suction is also required so that similarity solutions exist for nanofluid problems with no other boundary effects such as a partial slip or stretching disk. Both the suction and stretching disk effects can suppress the natural oscillatory behavior of flow apart from reducing the momentum and thermal boundary layer thicknesses. As expected, injection acts oppositely. However, the skin friction coefficient and heat transfer rate for Bödewadt flow increase with the increasing suction and stretching parameters. As for stagnant disk, increasing the nanoparticle volume fraction can enhance the wall shear stress, whereas nanofluid can only enhance the heat transfer when both the suction and nanoparticle volume fraction are sufficiently small. For radially stretching disk, both the local skin friction coefficient and local Nusselt number increase as the nanoparticle volume fraction increases. However, for larger suction, a smaller volume fraction of nanoparticles yielded enhanced heat transfer than the larger volume fraction of nanoparticles.

Dynamics of ethylene glycol-based graphene and molybdenum disulfide hybrid nanofluid over a stretchable surface with slip conditions

In this research study, numerical and statistical explorations are accomplished to capture the flow features of the dynamics of ethylene glycol-based hybrid nanofluid flow over an exponentially stretchable sheet with velocity and thermal slip conditions. Physical insight of viscous dissipation, heat absorption and thermal radiation on the flow-field is scrutinized by dissolving the nanoparticles of molybdenum disulfide (MoS2) and graphene into ethylene glycol. The governing mathematical model is transformed into the system of similarity equations by utilizing the apt similarity variables. The numerical solution of resulting similarity equations with associated conditions are obtained employing three-stages Lobatto-IIIa-bvp4c-solver based on a finite difference scheme in MATLAB. The effects of emerging flow parameters on the flow-field are enumerated through various graphical and tabulated results. Additionally, to comprehend the connection between heat transport rate and emerging flow parameters, a quadratic regression approximation analysis on the numerical entities of local Nusselt numbers and skin friction coefficients is accomplished. The findings disclose that the suction and thermal radiation have an adverse influence on the skin friction coefficients and heat transport rate. Further, a slight augmentation in the thermal slip factor causes a considerable variation in the heat transport rate in comparison to the radiation effect.

Slip Effect on Stagnation Point Flow and Heat Transfer Over a Shrinking/Stretching Sheet in A Porous Medium with Suction/Injection

The effects of thermal and velocity slip on Newtonian fluid steady boundary layer stagnation-point flow and heat transfer through a porous shrinking sheet with suction effect are investigated in the present research. By using a similarity transformation, the partial differential equation (PDE) is converted to an ordinary differential equation (ODE) and solved using the shooting technique to get numerical results. The flow characteristics for various values of the physical parameters are discussed, taking into consideration the effects of suction/injection as well as velocity and thermal slip. The local Nusselt number and skin friction coefficient, as well as the temperature and the velocity profiles, are presented as results. It is noticed that when the suction and velocity slip increase, the skin friction coefficient and local Nusselt number rise, as does the range of solutions that exist.

Stability Solution of Unsteady Stagnation-Point Flow and Heat Transfer over a Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect

Computational of unsteady flow with slip condition is essential since physically the heat transfer process is time-dependent and there may exist slip between fluid and surface. Therefore, this study aims to investigate the unsteady stagnation-point flow and heat transfer over a stretching/shrinking sheet immersed in nanofluid in the presence of slip velocity. By applying boundary layer theory and Tiwari-Das model, the governing equations are developed and transformed into a system of ordinary differential equations using similarity transformation, which are then solved numerically using bvp4c solver in MATLAB. The influence of slip velocity, stretching/shrinking parameters, nanoparticle volume fraction and unsteadiness parameter on the local skin friction coefficient, local Nusselt number, as well as velocity and temperature profiles are analysed. There are three types of nanoparticles considered, namely Copper (Cu), Alumina (Al203), Titania (TiO2) and water (H20) is the base fluid. It is found that dual solutions occur for certain parameters and the stability analysis is performed. The analysis shows that the first solutions are found to be stable than the second solution. The local skin friction coefficient and local Nusselt number are increasing with slip velocity, nanoparticle volume fraction for shrinking case; however, the opposite trend is observed for stretching case. By raising 20% of nanoparticle volume fraction for the shrinking sheet ( the friction at the surface increases 24% and 15.5% for heat transfer rate for the first solution. Moreover, for 10% of nanoparticle volume fraction for the shrinking sheet (and the first solution, varying slip parameters from 0 to 0.2, give rise to approximately 21% of the friction at the surface and 68% of the heat transfer rate.

Non-similarity method for heat and mass transfer of MHD radiative flow over exponentially stretching sheet

In this paper a modification of existing mathematical model of MHD radiative incompressible fluid-flow over exponentially stretching sheet is given by accumulating equation of mass transfer under an influence of chemical reaction. Using local non-similarity variables method, governing equations for heat and mass transfer of viscous fluid-flow are efficiently remodeled into the system of dimensionless PDE, and later on the obtained system of dimensionless PDE is tack?led numerically using MATLAB built in solver bvp4c. Graphs of temperature, velocity and concentration profiles are explained through variation of different values of physical parameters. Significant effects of several parameters, for example radiation and magnetic parameters, Eckert and Prandtl numbers on local skin-friction coefficient, local Nusselt and Sherwood numbers are computed in tabular form.

ASSESSMENT OF CONJUGATE AND CONVECTIVE HEAT TRANSFER PERFORMANCE OVER A PARTITIONED CHANNEL WITHIN BACKWARD-FACING STEP USING THE LATTICE BOLTZMANN METHOD

This research concerns the quality of heat transfer across a two-dimensional backwards-facing step in the presence of vertical or inclined partitions in a rectangular channel. Convective and conjugate heat transfer input using constant temperature and heat flux were successfully achieved for low Reynolds number values. The actual code based on the double multiple relaxation time of the lattice Boltzmann method was employed to model numerically the physical problems related to the fluid flow and heat transfer, where the obtained results had a good agreement with previous experimental research. During this study, parametric variations were carried out according to the inclination and position of the partitions, as well as the thermal conductivity ratio in the case of the conjugate heat transfer problem. The numerical results show that the involvement of the partitions and the thermal conductivity ratio has a significant effect on the fluid flow and heat transfer. This impact controls the evolution of local Nusselt number, bulk temperature, and skin friction coefficient. The improvement of heat transfer is remarkable by the introduction of vertical or inclined partitions such that the quality of heat exchange reaches about 7%. While the presence of two inclined partitions increases the heat transfer by about 6% in case of constant temperature of studied hot wall. The implementation of constant heat flux for the hot wall increases the quality of heat transfer by about 9%-10% by the presence of inclined or vertical walls, 11%-13% with double inclined partitions.

Dissipative Williamson fluid flow with double diffusive Cattaneo-Christov model due to a slippery stretching sheet embedded in a porous medium

<abstract><p>A numerical analysis of the incompressible two-dimensional flow of a non-Newtonian Williamson fluid is offered by expanding the sheet embedded in a porous medium and combining it with the Cattaneo-Christov model. Additionally, it is considered that the thermal conductivity and fluid viscosity both change as a linear function of temperature and an exponential function, respectively. The velocity, temperature and concentration field are all affected by thermal radiation, viscous dissipation, fluid variable properties, chemical reactions, and the slip velocity phenomenon. When the appropriate variables are employed, a system of non-linear, non-dimensional parameters emerges. The shooting method is used to numerically address this system. To better comprehend the impact of dimensionless parameters on dimensionless velocity, concentration, and temperature profiles, physical descriptions are prepared and justified using graphical representations. The values of the local skin-friction coefficient, the rate of heat transfer, and the rate of mass transfer are also investigated using tables. The behavior of changing fluid properties, on the other hand, establishes the link between Williamson fluid flow and the rate of heat mass transfer. According to the results, increasing the slip velocity and viscosity factors lowers both the Nusselt number and the Sherwood number. Also, due to an increase in Deborah number and the chemical reaction parameter, the temperature profiles decrease.</p></abstract>

Significance of nanoparticle radius, inter‐particle spacing, inclined magnetic field, and space‐dependent internal heating: The case of chemically reactive water conveying copper nanoparticles

AbstractSequel to the biocompatibility, physicochemical properties, high electrical conduction of copper nanoparticles over an inclined surface, little is known on the significance of nanoparticle radius, and inclined magnetic field on the dynamics of chemical reactive water conveying copper nanoparticles through a porous medium in the presence of Joule heating and spacing heating. In this case, there exists convective heating of the inclined surface due to thermal and significant concentration at the wall. The similarity solution of the problem was obtained using a suitable similarity solution and a numerical solution of the corresponding boundary value problem of the ordinary differential equation was sought for using MATLAB‐based bvp4c package. Based on the analysis, it is worth concluding that inter‐particle spacing not only exists but is also capable to increase the viscosity thus causing a decline in the velocity. The temperature distribution is an increasing function of the inclined magnetic field parameter. The rate of decrease in the local skin friction coefficients due to enhancement in the angle of inclination of the magnetic field is optimal when the radius of nanoparticles is large.