Abstract: Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302–307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Abstract: Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. A laterally heated square enclosure, filled with air, was studied. A FORTRAN code based on the lattice Boltzmann method (LBM) was developed for this purpose. The finite difference method was applied to discretize the LBM equations. Furthermore, for comparison purpose, the commercially available CFD package FLUENT, which uses finite volume Method (FVM), was also used to simulate the same problem. Different discretization schemes, being the first order upwind, second order upwind, power law, and QUICK, were used with the finite volume solver where the SIMPLE and SIMPLEC algorithms linked the velocity-pressure terms. The results were also compared with existing experimental and numerical data. It was observed that the finite volume method requires less CPU usage time and yields more accurate results compared to the LBM. It has been noted that the 1st order upwind/SIMPLEC combination converges comparatively quickly with a very high accuracy especially at the boundaries. Interestingly, all variants of FVM discretization/pressure-velocity linking methods lead to almost the same number of iterations to converge but higher-order schemes ask for longer iterations.

Abstract: We develop a Fluctuating Immersed Boundary (FIB) method for performing Brownian dynamics simulations of confined particle suspensions. Unlike traditional methods which employ analytical Green's functions for Stokes flow in the confined geometry, the FIB method uses a fluctuating finite-volume Stokes solver to generate the action of the response functions “on the fly.” Importantly, we demonstrate that both the deterministic terms necessary to capture the hydrodynamic interactions among the suspended particles, as well as the stochastic terms necessary to generate the hydrodynamically correlated Brownian motion, can be generated by solving the steady Stokes equations numerically only once per time step. This is accomplished by including a stochastic contribution to the stress tensor in the fluid equations consistent with fluctuating hydrodynamics. We develop novel temporal integrators that account for the multiplicative nature of the noise in the equations of Brownian dynamics and the strong dependence of the mobility on the configuration for confined systems. Notably, we propose a random finite difference approach to approximating the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. Through comparisons with analytical and existing computational results, we numerically demonstrate the ability of the FIB method to accurately capture both the static (equilibrium) and dynamic properties of interacting particles in flow.

Abstract: We study locally mass conservative approximations of coupled Darcy and Stokes flows on polygonal and polyhedral meshes. The discontinuous Galerkin (DG) finite element method is used in the Stokes region and the mimetic finite difference method is used in the Darcy region. DG finite element spaces are defined on polygonal and polyhedral grids by introducing lifting operators mapping mimetic degrees of freedom to functional spaces. Optimal convergence estimates for the numerical scheme are derived. Results from computational experiments supporting the theory are presented.

Abstract: Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) beams are analyzed in this research. All thermomechanical properties of the beam are assumed to be temperature and position dependent. Beam is subjected to thermal shock on the ceramic-rich surface whereas the metal-rich one is kept at reference temperature or thermally insulated. The one-dimensional transient heat conduction equation is established and solved via a hybrid iterative central finite difference method and Crank–Nicolson method. Total functional of the beam is obtained under the assumptions of uncoupled thermoelasticity laws, first order beam theory, and the von Karman type geometrical non-linearity. The conventional multi-term p-Ritz method appropriate for arbitrary in-plane and out-of-plane boundary conditions is applied to the total functional of the system which results in the matrix representation of the equations of motion. Non-linear coupled equations of motion are solved via the iterative Newton–Raphson method accompanied with the β-Newmark time approximation technique. Numerical results are well validated with the available results for the case of isotropic homogeneous beams. Some parametric studies are conducted to examine the influences of beam geometry, material composition, temperature dependency, in-plane and out-of-plane mechanical and thermal boundary conditions. It is shown that, thermally induced vibrations indeed exist especially for the case of sufficiently thin beams.

Abstract: In this work, three-dimensional numerical simulations of acoustically excited flow through a millimeter-size circular orifice are conducted to assess its noise damping performance, with particular emphasis on applying the lattice Boltzmann method (LBM) as an alternative computational aeroacoustics tool. The model is intended to solve the discrete lattice Boltzmann equation (LBE) by using the pseudo-particle based technique. The LBE controls the particles associated with collision and propagation over a discrete lattice mesh. Flow variables such as pressure, density, momentum, and internal energy are determined by performing a local integration of the particle distribution at each time step. This is different from the conventional numerical investigation attempting to solve Navier-Stokes (NS) equations by using high order finite-difference or finite-volume methods. Compared with the conventional NS solvers, one of the main advantages of LBM may be a reduced computational cost. Unlike frequency domain simulations, the present investigation is conducted in time domain, and the orifice damping behavior is quantified over a broad frequency range at a time by forcing an oscillating flow with multiple tones. Comparing the numerical results with those obtained from the theoretical models, large eddy simulation, and experimental measurements, good agreement is observed.

Abstract: Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcy's law with variable order Riemann-Liouville fractional derivatives; this leads to a new variable-order fractional percolation equation.In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

Abstract: 1. Finite difference equations 2. Spatial discretization in wave number space 3. Time discretization 4. Finite difference scheme as dispersive waves 5. Finite difference solution of the Euler equations 6. Radiation, outflow, and wall boundary conditions 7. The short wave component of finite difference schemes 8. Nonlinear acoustic waves and shocks 9. Advanced numerical boundary treatments 10. Time domain impedance boundary condition 11. Extrapolation and interpolation 12. Multi-scales problems 13. Complex geometry 14. Continuation of a near field acoustic solution to the far field 15. CAA code design and applications.

Abstract: In this paper, a new powerful numerical hydrodynamic in-house model is presented and tested. The model simulates flood routing in two dimensions. It is based on the solution of Shallow Water Equations using the Finite Difference Method according to the explicit McCormack numerical scheme which has shock capturing capability. The innovation of the proposed model lies in the modification of McCormack scheme by incorporating artificial viscosity through a diffusion factor in order to avoid oscillations as proposed by various researchers. Additionally, a threshold of water depth is introduced in order to distinguish the wet and dry cells of the computational domain. The model is capable of producing maps for the inundation extent, water depths and depth-averaged water velocities. Finally, the paper presents extensive testing of the model by comparison with analytical solution, experimental results and with the output of another software package in real world flood simulation studies.

Abstract: Based on the uncoupled thermoelasticity assumptions, axisymmetric thermally induced vibrations of a circular plate made of functionally graded materials (FGMs) are analyzed. Each thermomechanical property of the circular plate is assumed to be functions of temperature and thickness coordinate. Solution of the transient one-dimensional heat conduction equation with the arbitrary type of time-dependent boundary conditions is carried out employing the central finite difference method combined with the Crank–Nicolson time marching scheme. Afterwards, with the establishment of the associated Hamilton's principle and the accountancy of the von Karman type of geometrical non-linearity, the motion equations are obtained with the aid of the conventional multi-term Ritz method. The solution of highly coupled non-linear motion equations is obtained utilizing a hybrid iterative Newton–Raphson–Newmark scheme. After validating the developed computer code, some parametric studies are accomplished to show the influences ...

Abstract: Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Ra...

Abstract: In this article, the generalized finite-difference method (GFDM), one kind of domain-type meshless method, is adopted for analyzing inverse biharmonic boundary-value problems. In inverse problems governed by fourth-order partial differential equations, overspecified boundary conditions are imposed at part of the boundary, and, on the other hand, part of the boundary segment lacks enough boundary conditions. The ill-conditioning problems will appear when conventional numerical simulations are used for solving the inverse problems. Thus, small perturbations added in the boundary conditions will result in problems of instability and large numerical errors. In this article, we adopt the GFDM to stably and accurately analyze the inverse problems governed by fourth-order partial differential equations. The GFDM is truly free from time-consuming mesh generation and numerical quadrature. Six numerical examples are provided to validate the accuracy and the simplicity of the GFDM. Furthermore, different levels of n...

Abstract: In this article, laminar forced convection of nanofluids in a parallel plate microchannel under constant wall temperature is numerically investigated. A Eulerian–Lagrangian two-phase method is employed to simulate the flow and heat transfer of nanofluid in the microchannel. Navier–Stokes equations were solved using a finite difference method based on the projection algorithm while a Runge–Kutta method have been used to solve Lagrangian equations of the particle phase. A parallel code is developed on a cluster of processors which indicates a good performance to solve an Eulerian–Lagrangian problem. The convective heat transfer coefficient of nanofluids is better than the base fluid particularly in the entrance region. The results based on two phase modelling, show a slightly greater improvement in the heat transfer coefficient in comparison to the homogeneous single-phase nanofluid method. The obtained results show that the heat transfer enhancement increases as the nanoparticles volume fraction increases, and decreases with the Reynolds number for Cu–water nanofluid, while the alumina–water nanofluid have a different behaviour. A comparison of two different nanofluids showed the importance considering all of the nanofluid's properties not just thermal conductivity.

Abstract: We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-H\"uckel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.