Numerical approach for stagnation point flow of Sutterby fluid impinging to Cattaneo–Christov heat flux model

This paper presents a comprehensive modelling and simulation study on the optimum parameters that control the distortion and noise of semiconductor lasers (SLs) subject to multichannel modulation for use in analog cable television (CATV) fibre links. The study is based on numerical integration of the rate equation model of the semiconductor laser. The parameters comprise the modulation index per channel (m / ch), number of loaded channels (N) and fibre length \((L_{F})\). The signal distortions include the composite second-order (CSO) and composite triple beat (CTB) distortions. The noise is assessed in terms of the relative intensity noise (RIN) and carrier-to-noise ratio (CNR). In order to achieve acceptable CNR values for SL, m / ch should be less than 7.5 and 2% when loading 12 and 80 channels, respectively. For the CATV fibre link with \(L_{F} = 10 \hbox { km}\), the increase in the number of channels from 12 to 80 corresponds to lowering the optimum value of m / ch from 7 to 1%. The increase of \(L_{F}\) to 50 km limits the optimum value of m / ch between 1.4 and 1%, which corresponds to loading between 12 and 17 channels only.     

Effects of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo–Christov heat flux model

The aim of this research is to analyze the effects of mass transfer on second grade fluid flow subjected to the heat transfer incorporated with the relaxation time to reach the state of equilibrium on or after the state of upheaval. A new heat model namely Cattaneo–Christov heat flux comprising the relaxation time is employed instead of very commonly used mundane model based on classical theory of heat flux. Flow is considered towards stretching cylinder in the existence of external magnetic field. Suitable transformations are first used to deduce the momentum, heat and concentration equations and are then solved analytically. The effects of physical quantities such as fluid parameter, magnetic field, Schmidt number, relaxation time, curvature parameter, Prandtl number and chemical reaction on momentum, temperature and concentration profile are examined graphically whereas for validation of results convergence analysis along with residual error are obtained numerically. A comparison of obtained results is also given with the existing literature as a limiting case of reported problem and are found an excellent agreement. The temperature profile indicates thinning effect for higher values of Prandtl number and relaxation time. It is also noted that the velocity increases with increasing values of fluid parameter whereas it declines for the case of magnetic field. This study can be used an application of central heating system and to measure the fast chemical reactions rates.     

Hybrid nanofluid flow over two different geometries with Cattaneo–Christov heat flux model and heat generation: A model with correlation coefficient and probable error

The authors scrutinize the steady, MHD flow of SiO₂−MoS₂/water hybrid nanofluid towards two different geometries i.e. a wedge and a cone. The Tiwari and Das model is implemented with a generalized–Fourier's model, popularized as Cattaneo-Christov heat flux model. Analysis of heat transfer also incorporates the effects of suction, heat generation and thermal radiation. To showcase the relationship between engineering quantities and pertinent parameters involved in the study, the correlation coefficient for heat transfer coefficient and the skin friction coefficient is computed followed by the computation of probable error and statistical declaration. Similarity transformations are utilized to remodel the constitutive laws of flow in non-dimensional form. Numerical computation of non-linear, coupled O.D.E.’s is performed with the support of the Runge-Kutta-Fehlberg scheme and shooting method. Graphical and tabular illustrations of computed results are provided to report the variation in flow properties with the fluctuation in physical parameters. In both cases, i.e. flow close to a wedge and a cone, the temperature of hybrid nanofluid enhances on intensifying the thermal radiation and experiences a decrement with thermal relaxation parameter and magnetic field. Rising values of the suction parameter, thermal relaxation parameter, and thermal radiation cause increment in heat transfer coefficient. Interestingly, it was spotted that the heat generation parameter has contrary effects on temperature distribution over the two geometries.     

Erratum to “Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux”

We would like to acknowledge the misprinted terms in our published paper “Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux” [Chin. Phys. B 23 044702 (2014)]. Since only two misprints exist and the main results of the published paper are correct, we present the correct equations in this erratum.     

Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions

This article investigates the three-dimensional flow of Powell–Eyring nanofluid with thermophoresis and Brownian motion effects. The energy equation is considered in the presence of thermal radiation. The heat and mass flux conditions are taken into account. Mathematical formulation is carried out through the boundary layer approach. The governing partial differential equations are transformed into the nonlinear ordinary differential equations through suitable variables. The resulting nonlinear ordinary differential equations have been solved for the series solutions. Effects of emerging physical parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt and Sherwood numbers are computed and examined.     

Analytical prediction of multiple solutions for MHD Jeffery–Hamel flow and heat transfer utilizing KKL nanofluid model

In this framework, the novel analytical approach is presented to predict the dual solutions of Jeffery–Hamel (JH) transport model utilizing KKL (Koo–Kleinstreuer–Li) Al₂O₃ model with magnetic field, Ohmic heating and viscous dissipation. The predictor homotopy analysis method (PHAM) is applied to realize the existence of multiple solutions (bifurcation) for stretching/shrinking parameter and channel angle. It is observed that the dual solutions exist only for convergent channel. The eigenvalue problem is constructed to perform stability analysis which shows the physically stability of the upper branch. A numerical validation with Runge–Kutta–Fehlberg (RKF) shooting method using MATLAB is also carried out for verification. The Reynolds number is responsible to increase the velocity of fluid for both branches of the solution. For the increasing values of Ec and M, the Nusselt number decreases and increases respectively.     

β-distribution for Reynolds stress and turbulent heat flux in relaxation turbulent boundary layer of compression ramp

A challenge in the study of turbulent boundary layers(TBLs) is to understand the non-equilibrium relaxation process after separation and reattachment due to shock-wave/boundary-layer interaction. The classical boundary layer theory cannot deal with the strong adverse pressure gradient, and hence, the computational modeling of this process remains inaccurate. Here, we report the direct numerical simulation results of the relaxation TBL behind a compression ramp, which reveal the presence of intense large-scale eddies, with significantly enhanced Reynolds stress and turbulent heat flux. A crucial finding is that the wall-normal profiles of the excess Reynolds stress and turbulent heat flux obey a β-distribution, which is a product of two power laws with respect to the wall-normal distances from the wall and from the boundary layer edge. In addition, the streamwise decays of the excess Reynolds stress and turbulent heat flux also exhibit power laws with respect to the streamwise distance from the corner of the compression ramp. These results suggest that the relaxation TBL obeys the dilation symmetry, which is a specific form of self-organization in this complex non-equilibrium flow. The β-distribution yields important hints for the development of a turbulence model.     

On the boundary slip of fluid flow

For hundreds of years, in all the textbooks of classical fluid mechanics and lubrica- tion mechanics it is assumed that there was no wall slip (boundary slip) at a liquid-solid interface, i.e. no relative motion between liquid and solid at the interface. This is the no-slip boundary condition. It has been widely applied to engineering and experiments and to almost all the rheology or viscosity measurements of fluids. Rheology is one of the most important bases for fluid mechanics and lubricati…     

Experimental study for frequency spectrum of turbulent boundary layer pressure fluctuation

1IntroductionTBL(tUIbulelltboundarylayer)pressurefluctuationisamainsourceofstructurevibra-tinn,soitisanimportantsubjectforthegenerationofacousticradiation.Uptonow,ithasbeenshownaforIIildableundertakingtheexperimentalandtheoreticalelucidationofTBLpressurefiuctuation.Mostofinvestigationsonthissubjectareconcelltratedonexperimenta-leffert.Amodelofeddy-convectingwaspresentedbySkudrzkl1].Hepointedoutthatthefre-quencyspectrtnnofTBLpressurefiuctuation,di.(f),maybeconsideredtobeconstantuptoaconve…     

A novel fluid–wall heat transfer model for molecular dynamics simulations

The ‘fluid–wall thermal equilibrium model’, to numerically simulate heating/cooling of fluid atoms by wall atoms, is used to compare molecular dynamics simulation results to the analytical solution of 1-D heat equation. Liquid argon atoms are placed between two platinum walls and simultaneous heating and cooling is simulated at the walls. Temperature gradient in liquid argon is evaluated and the results are found to match well with the analytical solution showing the physical soundness of the proposed model. Additional simulations are done where liquid argon atoms are heated by both the walls for two different channel heights and it is shown that in such cases, heat transfer occurs at a faster rate than predicted by heat equation with decreasing channel heights.     

Impact of melting heat transfer in the time-dependent squeezing nanofluid flow containing carbon nanotubes in a Darcy-Forchheimer porous media with Cattaneo-Christov heat flux

This study aims to investigate the time-dependent squeezing of nanofluid flow, comprising carbon nanotubes of dual nature, e.g. single-walled carbon nanotubes, and multi-walled carbon nanotubes,between two parallel disks. Numerical simulations of the proposed novel model are conducted,accompanied by Cattaneo-Christov heat flux in a Darcy-Forchheimer permeable media. Additional impacts of homogeneous–heterogeneous reactions are also noted, including melting heat. A relevant transformation procedure is implemented for the transition of partial differential equations to the ordinary variety. A computer software-based MATLAB function, bvp4c, is implemented to handle the envisioned mathematical model. Sketches portraying impacts on radial velocity, temperature, and concentration of the included parameters are given, and deliberated upon. Skin friction coefficient and local Nusselt number are evaluated via graphical illustrations. It is observed that the local inertia coefficient has an opposite impact on radial velocity and temperature field. It is further perceived that melting and radiation parameters demonstrate a retarding effect on temperature profile.     

Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux

The aim of this paper is to investigate numerically the boundary layer forced convection flow of a Casson fluid past a symmetric porous wedge. Similarity transformations are used to convert the governing partial differential equations into ordinary ones. With the help of the shooting method, the reduced equations are then solved numerically. Comparisons are made with the previously published results in some special cases and they are found to be in excellent agreement with each other. The results obtained in this study are illustrated graphically and discussed in detail. The velocity is found to increase with an increasing Falkner-Skan exponent whereas the temperature decreases. With the rise of the Casson fluid parameter, the fluid velocity increases but the temperature is found to decrease in this case. Fluid velocity is suppressed with the increase of suction. The skin friction decreases with the increasing value of Casson fluid parameter. It is found that the temperature decreases as the Prandtl number increases and thermal boundary layer thickness decreases with the increasing value of Prandtl number. A significant finding of this investigation is that flow separation can be controlled by increasing the value of the Casson fluid parameter as well as by increasing the amount of suction.     

Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.     

Magnetohydrodynamic flow of burgers fluid with heat source and power law heat flux

Here magnetohydrodynamic (MHD) two-dimensional (2D) flow of an incompressible Burgers material bounded by a permeable stretched surface is addressed. The boundary layer flow equations are modelled. Heat transfer is discussed for power law heat flux at the surface and heat source. Convergent series solutions are constructed. Clarification of different emerging variables is presented through graphs of velocity, temperature and local Nusselt number. The present solutions are matched with the available published work in a limiting case.     

Effects of Thermal Radiation on a 3D Sisko Fluid over a Porous Medium Using Cattaneo-Christov Heat Flux Model

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter, thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Stability of thermal convection of an Oldroyd-B fluid in a porous medium with Newtonian heating

A linear stability analysis determining the onset of oscillatory convection of an Oldroyd-B fluid in a bounded two-dimensional rectangular porous medium generated by Newtonian heating is conducted. Influences of viscoelastic parameters and Biot number on the onset of oscillatory convection, preferred modes and patterns of disturbed temperature contours are discussed.     

Casson fluid flow and heat transfer over a nonlinearly stretching surface

A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.     

Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation

This Letter presents a numerical study of the flow and heat transfer of an incompressible FENE-P fluid over a non-isothermal surface. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of the thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient, as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Moreover, the mechanical characteristics of the corresponding flow are also presented.