Wavelet strategy for flow and heat transfer in CNT-water based fluid with asymmetric variable rectangular porous channel

In the present work, the characteristics of physical model unsteady nanofluid flow and heat transfer in an asymmetric porous channel are analyzed numerically using wavelet collocation method. Using similarity transformation, unsteady two-dimensional flow model of nanofluid in a porous channel through expanding or contracting walls has been transformed into a system of nonlinear ordinary differential equations (ODEs). Then, the obtained nonlinear system of ODEs is solved via wavelet collocation method. The effect of various emerging parameters, such as nanoparticle volume fraction, Reynolds number (Re), and expansion ratio have been analyzed on velocity and temperature profiles. Numerical results have been presented in form of figures and tables. For some special cases, the obtained numerical results are compared with exact one and found that the results are good in agreement with exact solutions.

     

MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions

The flow of a radiative and electrically conducting micropolar nanofluid inside a porous channel is investigated. After implementing the similarity transformations, the partial differential equations representing the radiative flow are reduced to a system of ordinary differential equations. The subsequent equations are solved by making use of a well-known analytical method called homotopy analysis method (HAM). The expressions concerning the velocity, microrotation, temperature, and nanoparticle concentration profiles are obtained. The radiation tends to drop the temperature profile for the fluid. The formulation for local Nusselt and Sherwood numbers is also presented. Tabular and graphical results highlighting the effects of different physical parameters are presented. Rate of heat transfer at the lower wall is seen to be increasing with higher values of the radiation parameter while a drop in heat transfer rate at the upper wall is observed. Same problem has been solved by implementing the numerical procedure called the Runge–Kutta method. A comparison between the HAM, numerical and already existing results has also been made.

     

Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a Darcy–Forchheimer medium

This article explores the influence of thermal radiation on the flow and heat transfer of single-walled carbon nanotubes over both a convergent and divergent channel. Flow is induced due to a Darcy–Forchheimer medium. Further, the heat transfer mechanism is analyzed in the presence of a thermal radiation process. Guided by some appropriate similarity transformations, the fundamental PDEs are converted into a self-similar system of coupled non-linear ODEs. The findings are obtained with the help of the Runge–Kutta-45-based shooting method. The roles of the Reynolds number, porosity parameter, inertia coefficient parameter, Prandtl number and radiation parameter are presented graphically. Results are displayed and show that the rate of heat transfer is higher in a divergent channel as compared to a convergent channel.

     

Analytical solution for suction and injection flow of a viscoplastic Casson fluid past a stretching surface in the presence of viscous dissipation

In this study, steady two-dimensional flow of a viscoplastic Casson fluid past a stretching surface is considered under the effects of thermal radiation and viscous dissipation. Both suction and injection flows situations are considered. The partial differential governing equations are transformed into ordinary differential equations and solved analytical. Analytical solutions for velocity and temperature are obtained in terms of hypergeometric function and discussed graphically. Moreover, numerical results are also obtained by Runge–Kutta–Fehlberg fourth–fifth-order (RKF45) method and compared with the analytical results. The results showed that the injection and suction parameter can be used to control the direction and strength of flow. The effects of Casson parameter on the temperature and velocity are quite opposite. The effects of thermal radiation on the temperature are much more stronger in case of injection. The heat transfer coefficient shows higher value for Casson fluid while for Newtonian fluid is the lowest.

     

Buoyancy effects on gaseous slip flow in a vertical rectangular microchannel

Consideration is given to the buoyancy effects on the fully developed gaseous slip flow in a vertical rectangular microduct. Two different cases of the thermal boundary conditions are considered, namely uniform temperature at two facing duct walls with different temperatures and adiabatic other walls (case A) and uniform heat flux at two walls and uniform temperature at other walls (case B). The rarefaction effects are treated using the first-order slip boundary conditions. By means of finite Fourier transform method, analytical solutions are obtained for the velocity and temperature distributions as well as the Poiseuille number. Furthermore, the threshold value of the mixed convection parameter to start the flow reversal is evaluated. The results show that the Poiseuille number of case A is an increasing function of the mixed convection parameter and a decreasing function of the channel aspect ratio, whereas its functionality on the Knudsen number is not monotonic. For case B, the Poiseuille number is decreased by increasing each of the mixed convection parameter, the Knudsen number, and the channel aspect ratio.     

Effect of wall roughness on performance of microchannel applied in microfluidic device

The influence of wall roughness on flow and heat transfer performance in microchannels at low Reynolds number is investigated in this paper. Two sizes of PMMA microchannels are fabricated by microinjection molding and the width is 20 μm and 800 μm respectively. The surface profile of bottom wall is described by the two-dimensional fractal geometry method and it is found there is error within 5% between surface roughness obtained by the fractal geometry method and actual roughness. Then, the effects of dimensionless relative roughness (5–7.5%), fractal dimension (1.5–1.8), aspect ratio (0.025–4) on the flow resistance and heat transfer performance are analyzed by numerical and experimental method respectively. Reynolds number considered here are 10–60. The results show that the better flow performance and heat transfer performance can be obtained with high aspect ratio of rectangular microchannel. However, increasing surface roughness not only increases the heat transfer performance, but also introduces a large flow resistance, which makes the friction coefficient rise sharply. As a result, surface roughness has great influence on the flow and heat transfer performance, and the most suitable surface morphology should be obtained according to the specific application.

     

Analysis of magnetohydrodynamic flow and heat transfer of Cu–water nanofluid between parallel plates for different shapes of nanoparticles

The present study analyzes the heat transfer in the flow of copper–water nanofluids between parallel plates. For effective thermal conductivity of nanofluids, Hamilton and Crosser's model has been utilized to examine the flow by considering different shape factors. By employing the suitable similarity transformations, the equations governing the flow are transformed into a set of nonlinear ordinary differential equations. The resulting set of equations is solved numerically with the help of Runge–Kutta–Fehlberg numerical scheme. The graphical simulation presents the analysis of variations, in velocity and temperature profiles, for emerging parameters. A comprehensive discussion also accompanies the graphical results. Moreover, the effects of relevant parameters, on skin friction coefficient and Nusselt number, are highlighted graphically. It is noticed that the velocity field is an increasing function of all the parameters involved. Furthermore, the temperature of the fluid is maximum for the platelet-shaped particles followed by the cylinder- and brick-shaped particles.

     

An investigation of turbulent open channel flow with heat transfer by large eddy simulation

Large eddy simulation of fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. Two typical temperature boundary conditions, i.e., constant temperature and constant heat flux being maintained at the free surface, respectively, are used. The objective of this study is to explore the behavior of heat transfer in the turbulent open channel flow for different temperature boundary conditions and to examine the reliability of the LES technique for predicting turbulent heat transfer at the free surface, in particular, for high Prandtl number. Calculated parameters are chosen as the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel depth. Some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures based on the velocity, vorticity and temperature fluctuations, are analyzed.     

Darcy–Forchheimer flow and heat transfer augmentation of a viscoelastic fluid over an incessant moving needle in the presence of viscous dissipation

The main focus of the present study is to analyse the effect of viscous dissipation Darcy–Forchheimer flow and heat transfer augmentation of a viscoelastic fluid over an incessant moving needle. The governing partial differential equations of the defined problem are reduced into a set of nonlinear ordinary differential equations using adequate similarity transformations. Obtained set of similarity equations are then solved with the help of efficient numerical method fourth fifth order RKF-45 method. The effects of different flow pertinent parameters on the flow fields like velocity and temperature are shown in the form of graphs and tables. The detailed analysis of the problem is carried out based on the plotted graphs and tables.

     

Convective Poiseuille flow of Al2O3-EG nanofluid in a porous wavy channel with thermal radiation

In current article, convective Poiseuille boundary layer flow of ethylene glycol (C₂H₆O₂)-based nanofluid with suspended aluminum oxide (Al₂O₃) nanoparticles through a porous wavy channel has been examined. The impact of thermal radiation, Ohmic dissipation, electric field, and magnetic fields are also considered. The flow is due to constant pressure gradient in a wavy frame of reference. The governed momentum and thermal boundary layer equations is system of PDE’s, which are converted to system of ODE’s via suitable similarity transformations. The homotopy analysis method is applied to solve the governed flow problem. Convergence of series solutions is inspected through h-curves and residual errors norm, whereas the optimal value of convergence control parameter is obtained by means of genetic algorithm Nelder–Mead approach. The influence of numerous involving parameters like Hartmann number, Grashof number, Eckert number, electric parameter, radiation parameter, and porosity parameter on flow, heat transfer, skin friction coefficient and Nusselt number are illustrated through graphs and discussed briefly.

     

Effect of temperature gradient orientation on the characteristics of mixed convection flow in a lid-driven square cavity

The effect of temperature gradient orientation on the fluid flow and heat transfer in a lid-driven differentially heated square cavity is investigated numerically. The transport equations are solved using the high-order compact scheme. Four cases are considered depending on the direction of temperature gradient imposed. The differentially heated top and bottom walls result in gravitationally stable and unstable temperature gradients. While the differentially heated left and right side walls lead to assisting and opposing buoyancy effects. The governing parameters are Pr = 0.7 and Ri = 0.1, 1, and 10. It is found that both Richardson number and direction of temperature gradient affect the flow patterns, heat transport processes, and heat transfer rates in the cavity. Computed average Nusselt number indicates that the heat transfer rate increases with decreasing Ri regardless the orientation of temperature gradient imposed. And the assisting buoyancy flows have best performance on heat transport over the other three cases.     

The impact of side walls on the MHD flow of a second-grade fluid through a porous medium

The magnetohydrodynamic flow through a porous medium of a second-grade fluid between two side walls induced by an infinite plate that exerts an accelerated shear stress to the fluid over an infinite plate is examined. Expressions for velocity and shear stress are determined with the help of integral transforms. In the absence of side walls, all the solutions that have been obtained are reduced to those corresponding to the motion over an infinite flat plate. The Newtonian solutions are also obtained as limiting case of the general solution. Finally, influence of magnetic and porosity parameter is graphically highlighted.

     

Impacts of gold nanoparticles on MHD mixed convection Poiseuille flow of nanofluid passing through a porous medium in the presence of thermal radiation,thermal diffusion and chemical reaction

Impacts of gold nanoparticles on MHD Poiseuille flow of nanofluid in a porous medium are studied. Mixed convection is induced due to external pressure gradient and buoyancy force. Additional effects of thermal radiation, chemical reaction and thermal diffusion are also considered. Gold nanoparticles of cylindrical shape are considered in kerosene oil taken as conventional base fluid. However, for comparison, four other types of nanoparticles (silver, copper, alumina and magnetite) are also considered. The problem is modeled in terms of partial differential equations with suitable boundary conditions and then computed by perturbation technique. Exact expressions for velocity and temperature are obtained. Graphical results are mapped in order to tackle the physics of the embedded parameters. This study mainly focuses on gold nanoparticles; however, for the sake of comparison, four other types of nanoparticles namely silver, copper, alumina and magnetite are analyzed for the heat transfer rate. The obtained results show that metals have higher rate of heat transfer than metal oxides. Gold nanoparticles have the highest rate of heat transfer followed by alumina and magnetite. Porosity and magnetic field have opposite effects on velocity.

     

Double-diffusive and Soret-induced convection of a micropolar fluid in a vertical channel

This paper reports an investigation of the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel. Asymmetric temperature and concentration boundary conditions are applied to the walls of the channel. The cases of double diffusion and Soret-induced convection are both considered. The governing parameters for the problem are the buoyancy ratio and the various material parameters of the micropolar fluid. The resulting non-dimensional boundary value problem is solved analytically in closed form using MAPLE software. A numerical solution of the time dependent governing equations is demonstrated to be in good agreement with the analytical model. The influence of the governing parameters on the fluid flow as well as heat and solute transfers is demonstrated to be significant.     

Numerical investigation on 2D viscoelastic fluid due to exponentially stretching surface with magnetic effects: an application of non-Fourier flux theory

Two-dimensional flow of Casson fluid toward an exponentially stretched surface in view of Cattaneo–Christove flux theory is discoursed in current communication. Flow pattern within boundary layer under the effectiveness of magnetic field is also contemplated in the communication. Non-dimensionalized governing expressions are attained through transformation procedure. To anticipate the fascinating features of present work, solution of resulted nonlinear differential system is computed with the collaborated help of shooting scheme and Runge–Kutta method. The influence of involved variables on velocity and temperature fields is scrutinized. Contribution of thermal relaxation is explicitly pointed out. Evaluation of convective heat transfer and friction factor in the fluid flow is visualized through graphs and tables. Additionally, the assurance of present work is affirmed by developing comparison with previous findings in the literature which sets a trade mark for the implementation of numerical approach. It is inferred from the thorough examination of the analysis that present formulation reduces to classical Fourier’s problem by considering \(\varLambda = 0\). Furthermore, decreasing pattern in temperature distribution is depicted in the presence of Cattaneo–Christove flux law as compared to heat transfer due to the Fourier’s law.

     

Lattice Boltzmann computations of incompressible laminar flow and heat transfer in a constricted channel

A multi-population thermal lattice Boltzmann method (TLBM) is applied to simulate incompressible steady flow and heat transfer in a two-dimensional constricted channel. The method is validated for velocity and temperature profiles by comparing with a finite element method based commercial solver. The results indicate that, at various Reynolds numbers, the average flow resistance increases and the heat transfer rate decreases in a constricted channel in comparison to a straight channel. The effect of the constriction ratio is also investigated. The results show that the presented numerical model is a promising tool in analyzing simultaneous solution of fluid flow and heat transfer phenomena in complex geometries.     

Analytical solution of mixed electromagnetic/pressure driven gaseous flows in microchannels

The influences of wall-slip/jump conditions on the fluid flow and heat transfer for hydrodynamically and thermally fully developed electrically conducting gaseous flow subject to an electromagnetic field inside a parallel plate microchannel with constant heat flux at walls are studied under the assumptions of a low-magnetic Reynolds number. The governing equations are non-dimensionalized and then analytical solutions are derived for the friction and the heat transfer coefficients. The fluid flow and the heat transfer characteristics obtained in the analytical solutions are discussed in detail for different parameters such as the Knudsen, Hartmann, and Brinkman numbers. The velocity profiles verify that even with a constant Knudsen number, applying a stronger electromagnetic field gives rise to an increase in the slip velocity. The results also reveal that on increasing the Hartmann number, the heat transfer rate as well as the friction factor is enhanced, whereas it tends to suppress the movement of the fluid. Further, it is found that the Nusselt and the Poiseuille numbers are less sensitive to the electromagnetic field effects with increase in rarefaction.     

Numerical study of unsteady hydromagnetic Generalized Couette flow of a reactive third-grade fluid with asymmetric convective cooling

Unsteady hydromagnetic Generalized Couette flow and heat transfer characteristics of a reactive variable viscosity incompressible electrically conducting third grade fluid in a channel with asymmetric convective cooling at the walls in the presence of uniform transverse magnetic field is studied. It is assumed that the chemical kinetics in the flow system is exothermic and the convective heat transfer at the channel surface with the surrounding environment follow the Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using an unconditionally stable and convergent semi-implicit finite difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system.     

Eduction of near wall flow structures responsible for large deviations of the momentum-heat transfer analogy and fluctuations of wall transfer rates in turbulent channel flow

In this paper we analyze the flow structures responsible for large local instantaneous deviations of the conventional momentum-heat transfer analogy and large fluctuations of the wall shear stress and the wall heat flux in a forced convection turbulent channel flow at low-Reynolds numbers (Re = 4570, Pr = 0.7). The analysis was carried out using a database obtained from a direct numerical simulation performed with a second-order finite volume code. The ensemble averaged velocity and temperature profiles and profiles of the turbulence intensities and turbulent heat fluxes agree well with direct numerical simulations available in the literature. When the flow was statistically fully developed, we recorded the time evolution of the velocities and temperatures near one wall of the channel. The near wall structures responsible for the extreme values of the deviations were educed by a conditional sampling technique. Results show that extreme values of the wall shear stress and wall heat transfer rates, as well as departures from the conventional analogy between momentum and heat transfer, occur within the high-speed streaks on the wall and are associated with fluctuations of the streamwise pressure gradient. These large fluctuations on the wall are produced by the combined effect of two quasi-parallel counterrotating streamwise vortices.     

Mixed convective heat and mass transfer in a vertical wavy channel with traveling thermal waves and porous medium

We investigate the problem of mixed convection heat and mass transfer through a vertical wavy channel with porous medium. The flow is generated by the periodic thermal waves prescribed at the wavy walls of the channel. The equations of momentum energy and concentration are solved subject to a set of appropriate boundary conditions by assuming that the solution consists of a mean part and a perturbed part. The effects of various pertinent parameters on flow, heat and mass transfer characteristics are discussed numerically and explained graphically.