Numerical study of dynamic thermal conductivity of nanofluid in the forced convective heat transfer

In this work, forced convective heat transfer of nanofluid in the developing laminar flow (entrance region) in a circular tube is considered. The nanofluid thermal conductivity, as an important parameter, is considered as two parts: static and dynamic part. Simulated results show that the dynamic part of nanofluid thermal conductivity due to the Brownian motion has a minor effect on the heat transfer coefficients, on the other hand, static part of thermal conductivity including nanolayer around nanoparticle has an important role in heat transfer.     

Simulation of turbulent dispersion using a simple random model of the flow field

A method is devised to simulate the movement and spreading of a patch of contaminant in two-dimensional turbulent flow. The turbulent motion is exponentially divided into components of differing wave number, adjacent components being made to have correlation times differing by a factor of two. The turbulent motion is then reconstructed by replacing each component with a sinusoidal advection field having a randomly directed wave number. Contaminant particles are advected by each of the reconstructed components, the smallest scale components being applied first. A computer simulation was performed, using a Kolmogorov k^{-$\text{5}\text{3}$} turbulent energy spectrum. Batchelor's σ ∝ t^{$\text{3}\text{2}$} law for the spreading of a contaminant patch was reproduced, approximately, as was Richardson's non-Gaussian asymptotic form of the distance-neighbour function.     

Lie symmetry group analysis of magnetic field effects on free convective flow of a nanofluid over a semi-infinite stretching sheet

We investigate the steady two-dimensional flow of an incompressible water based nanofluid over a linearly semi-infinite stretching sheet in the presence of magnetic field numerically. The basic boundary layer equations for momentum and heat transfer are non-linear partial differential equations. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations for this investigation are solved numerically using Nachtsheim–Swigert shooting iteration technique together with fourth order Runge–Kutta integration scheme. Effects of the nanoparticle volume fraction ϕ, magnetic parameter M, Prandtl number Pr on the velocity and the temperature profiles are presented graphically and examined for different metallic and non-metallic nanoparticles. The skin friction coefficient and the local Nusselt number are also discussed for different nanoparticles.     

Viscous fluid flow at all speeds: analysis and numerical simulation

In [43] a finite volume method for reliable simulations of inviscid fluid flows at high as well as low Mach numbers based on a preconditioning technique proposed by Guillard and Viozat [14] is presented. In this paper we describe an extension of the numerical scheme for computing solutions of the Euler and Navier-Stokes equations. At first we show the high resolution properties, accuracy and robustness of the finite volume scheme in the context of a wide range of complicated transonic and supersonic test cases whereby both inviscid and viscous flow fields are considered. Thereafter, the validity of the method in the low Mach number regime is proven by means of an asymptotic analysis as well as numerical simulations. Whereas in [43] the asymptotic analysis of the scheme is focused on the behaviour of the continuous and discrete pressure distribution for inviscid low speed simulations we prove both the physical sensible discrete pressure field for viscous low Mach number flows and the divergence free condition of the discrete velocity field in the limit of a vanishing Mach number with respect to the simulation of inviscid fluid flow.     

Mathematical modeling and computation of fire induced turbulent flow in partial enclosures

The purpose of this paper is to understand the growth and spread of fires in ceiling vented enclosures. The transport phenomena due to fire have been modeled as buoyancy-induced turbulent flow in partial enclosures. The governing equations comprises the Reynolds averaged Navier–Stokes (RANS) equations with k–?$k''–''?$ turbulence model in stream function–vorticity formulation approach. The governing equations are solved by high accuracy compact finite difference schemes with four stage Runge–Kutta method for time integration. Results are reported for Grashof numbers varied from 10⁸${10}^8$ to 10¹⁰${10}^{10}$. The effects of multiple heat sources in rectangular enclosure and ceiling vent aspect ratio in square enclosure are investigated. The thermal plume growth rate, ambient entrainment flow rate and the oscillatory nature at the vent opening are reported. As the Grashof number increases the effect of entrained ambient air is significant with higher volume flow rates through ceiling vent. A bidirectional flow is visualized at the ceiling opening. The distance between two heat sources governs the unified and independent behavior of thermal plumes. Present results are matching very well with the numerical and experimental results available in literature.     

Numerical simulation of pollutant dispersion in street canyons: Geometric and thermal effects

Numerical investigations on pollutant dispersion in street canyons with emission sources located near the ground level are performed in the present work. Pollutant dispersion problems in urban areas are usually studied considering the street canyon model, which consists of long streets laterally confined by buildings. Significant changes can be observed in wind flow patterns and pollutant concentration fields when thermal and geometric effects are considered. Thus, the objective of this study is to investigate numerically the wind flow and pollutant dispersion for the following cases: (a) a two-dimensional street canyon model considering three different aspect ratios and four different wall heating configurations; (b) a flow domain with two immersed buildings arranged in two distinct configurations; (c) a three-dimensional urban area model composed of a building set and street intersections. Expected flow structures were obtained inside the canyon when different aspect ratios and wall heating configurations were considered. Flow phenomena such as separation/reattachment were observed when two-buildings models were analyzed. Finally, three-dimensional flow structures, with some characteristic that are not observed in two-dimensional models, affecting the pollutant removal, were simulated in the last case, highlighting the relevance of model dimensionality. The wind flow and pollutant dispersion are investigated using a numerical model based on the finite element formulation utilized by some of the authors of this work, which is extended here to deal with problems of heat and mass transport in the urban micro-scale. Turbulence is reproduced using Large Eddy Simulation (LES) and thermal effects on the momentum equations are considered as a buoyancy force, according to Boussinesq approximation.     

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions.     

Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity,non-uniform heat source and radiation

An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Performance comparison of the NWF and DC methods for implementing High-Resolution schemes in a fully coupled incompressible flow solver

This paper reports on the use of the Normalized Weighting Factor (NWF) method and the Deferred Correction (DC) approach for the implementation of High Resolution (HR) convective schemes in an implicit, fully coupled, pressure-based flow solver. Four HR schemes are realized within the framework of the NWF and DC methods and employed to solve the following three laminar flow problems: (i) lid-driven flow in a square cavity, (ii) sudden expansion in a square cavity, and (iii) flow in a planar T-junction, over three grid systems with sizes of 10⁴, 5 × 10⁴, and 3 × 10⁵ control volumes. The merit of both approaches is demonstrated by comparing the computational costs required to solve these problems using the various HR schemes on the different grid systems. Whereas previous attempts to use the NWF method in a segregated flow solver failed to produce converged solutions, current results clearly demonstrate that both methods are suitable for utilization in a coupled flow solver. In terms of CPU efficiency, there is no global and consistent superiority of any method over another even though the DC method outperformed the NWF method in two of the three test problems solved.     

Numerical simulation of a continuum model for bi-directional pedestrian flow

An algorithm for an extended reactive dynamic user equilibrium model of pedestrian counterflow as a continuum is developed. It is based on a cell-centered high-resolution finite volume scheme with a fast sweeping method for an Eikonal-type equation on an orthogonal grid. A high-order total variation diminishing Runge-Kutta method is adopted for the time integration of semi-discrete equations. The numerical results demonstrate the rationality of the model and efficiency of the algorithm. Some crowd pedestrian flow phenomena, such as dynamic lane formation in bi-directional flow, are observed which are helpful for a global comprehension of pedestrian dynamics. Also, the model can be utilized with different potential applications.     

Magnetic effect on the formation of longitudinal vortices in natural convection flow over a rotating heated flat plate

A numerical study of magnetic effect on the formation of longitudinal vortices in natural convection flow over a rotating heated flat plate is presented. The onset position characterized by the local Grashof number, depends on the rotational Reynolds number, the Prandtl number, the Hartmann number, and the wave number. The Coriolis force and the Lonertz force have significant effects on the formation of longitudinal vortices and the associated instability. Positive rotation stabilizes the flow on the rotating flat surface. On the contrary, a negative rotation destabilizes the flow. The flow is found more stable as the value of Hartmann number increases. The numerical data show reasonable agreement with the experimental results with the case of thermal instability in natural convection over a flat plate heated from below.     

Mixed convection of heat generating nanofluid in a lid-driven cavity with uniform and non-uniform heating of bottom wall

Steady state two-dimensional mixed convection in a lid-driven square cavity filled with Cu  –water nanofluid is investigated numerically in the presence of internal heat generation. In the present investigation, bottom wall is uniformly and non-uniformly heated while two vertical walls are fixed and they are thermally insulated. The top wall is moving from left to right at a constant speed. The governing equations are normalized and solved numerically with boundary conditions by finite volume approach using third order accurate upwinding scheme (deferred QUICK). Effects of the pertinent physical parameters are investigated in terms of the flow and temperature fields, as well as Nusselt number distributions. The presented results show that the solid volume fraction plays a significant role on the flow and thermal fields and the Nusselt number distributions for different flow configurations. It is found that Richardson number strongly affect the fluid flow and heat transfer in the cavity. For Ri<1$\mathit{Ri}<1$, the forced convection becomes dominant in the entire cavity, the natural convection relatively weak.     

Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium

The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.     

A new approach to the nonlinear stability of viscous flow in a coplanar magnetic field

We present a new Lyapunov function for laminar flow, in the x‐direction, between two parallel planes in the presence of a coplanar magnetic field for three‐dimensional perturbations with stress‐free boundary planes that provides conditional nonlinear stability for all Reynolds numbers(R_e) and magnetic Reynolds numbers(R_m) below π²/2M. Compared with previous results on the nonlinear stability of this problem, the radius of stability ball and the energy decay rate obtained in this paper are independent of the magnetic field. Copyright © 2016 John Wiley & Sons, Ltd.     

The material parameter design and finite element simulation of the quadrilateral thermal cloak device

In this paper, we first design a coordinate transformation and derive the anisotropic material parameters of the quadrilateral thermal cloak according to the transformation thermodynamics principle. Then, since the derived parameters are inherently anisotropic, we eliminate its anisotropy by considering the effective medium theory and use a layered structure of metamaterials composed of only two isotropic materials to design the cloak device. Finally, we simulate the performance of a perfect and layered thermal cloak by the finite element method. To the best of our knowledge, this is the first work to design and simulate the performance of this quadrilateral thermal cloak by the finite element method(FEM).     

Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

Modelling of processes in fractured rock using FEM/FVM on multidimensional domains

The paper deals with a new approach to the numerical modelling of groundwater flow in compact rock massifs.     

Triple diffusive mixed convection flow in a duct using convective boundary conditions

The motivation of the current article is to explore a numerical investigation on steady triply diffusive convection in a vertical channel. Heat is exchanged from the external fluid with the plates. The reference temperature is taken as equal and also as different for the external fluid. Solutions in the absence of viscous dissipation and buoyancy forces are also obtained as special cases. General solutions including the effects of viscous dissipation and buoyancy forces are obtained analytically using the method of perturbation. The analytical solutions can be used only if the Brinkman number is small. Hence to know the flow properties for all values of Brinkman number, we resort to numerical solutions. The effects of thermal Grashof number, solutal Grashof number, and the chemical reaction parameter on the flow field are evaluated numerically. The obtained results are validated against previously published results for special case of the problems.     

Heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation in presence of external magnetic field

This paper presents a mathematical analysis of MHD flow and heat transfer to a laminar liquid film from a horizontal stretching surface. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of non-linear ordinary differential equations. Numerical solution of resulting non-linear differential equations is found by using efficient shooting technique. Boundary layer thickness is explored numerically for some typical values of the unsteadiness parameter S and Prandtl number Pr, Eckert number Ec and Magnetic parameter Mn. Present analysis shows that the combined effect of magnetic field and viscous dissipation is to enhance the thermal boundary layer thickness.     

Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A Lie group analysis

In this paper, heat and mass transfer analysis for boundary layer stagnation-point flow over a stretching sheet in a porous medium saturated by a nanofluid with internal heat generation/absorption and suction/blowing is investigated. The governing partial differential equation and auxiliary conditions are converted to ordinary differential equations with the corresponding auxiliary conditions via Lie group analysis. The boundary layer temperature, concentration and nanoparticle volume fraction profiles are then determined numerically. The influences of various relevant parameters, namely, thermophoresis parameter Nt, Brownian motion parameter Nb, Lewis number Le, suction/injection parameter S, permeability parameter k₁, source/sink parameter λ and Prandtl parameter Pr on temperature and concentration as well as wall heat flux and wall mass flux are discussed. Comparison with published results is presented.