A computational method for geometric optimization of enhanced heat transfer devices based upon entropy generation minimization

A computational fluid dynamics‐based optimization methodology is developed, appropriate for the geometric optimization of enhanced heat transfer devices based upon the principle of entropy generation minimization, in which the objective function is evaluated from a flow field obtained by computational simulation. A quasi‐Newton optimization procedure is employed, with computation of the objective function gradients based upon a finite difference approach. The optimization procedure is developed to be general with regard to the choice of objective function, the details of the problem under consideration, and the computational methodology employed in solving the fluid flow and heat transfer problems. A novel implementation of a Taylor series‐based procedure for the fast solution of nearby problems is presented, which is found to greatly benefit the efficiency of the present methodology. Finally, a numerical experiment is presented, illustrating the use of the present method in the geometric optimization of a practical enhanced heat transfer device on the basis of the criterion of entropy generation minimization. The optimization of the fin spacing of a simple plate fin heat sink is considered, and a comparison of the computational results with results obtained by analytical optimization based upon empirical friction factor and Nusselt number correlations is given. Copyright © 2012 John Wiley & Sons, Ltd.     

A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd.     

Strain gradient plasticity analysis of elasto-plastic contact between rough surfaces

From a microscopic point of view, the real contact area between two rough surfaces is the sum of the areas of contact between facing asperities. Since the real contact area is a fraction of the nominal contact area, the real contact pressure is much higher than the nominal contact pressure, which results in plastic deformation of asperities. As plasticity is size dependent at size scales below tens of micrometers, with the general trend of smaller being harder, macroscopic plasticity is not suitable to describe plastic deformation of small asperities and thus fails to capture the real contact area and pressure accurately. Here we adopt conventional mechanism-based strain gradient plasticity (CMSGP) to analyze the contact between a rigid platen and an elasto-plastic solid with a rough surface. Flattening of a single sinusoidal asperity is analyzed first to highlight the difference between CMSGP and J₂ isotropic plasticity. For the rough surface contact, besides CMSGP, pure elastic and J₂ isotropic plasticity analysis is also carried out for comparison. In all cases, the contact area A rises linearly with the applied load, but with a different slope which implies that the mean contact pressures are different. CMSGP produces qualitative changes in the distributions of local contact pressures compared with pure elastic and J₂ isotropic plasticity analysis, furthermore, bounded by the two.     

A three‐dimensional Cartesian cut cell method for incompressible viscous flow with irregular domains

A three‐dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer‐aided design platform (J. Comput. Aided. Des. 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE‐based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscillations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L₁ and L _∞ norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer patterns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd.     

Implementation of ADER scheme for a bore on an unsaturated permeable slope

The paper details the implementation of the Godunov‐type finite volume Arbitrary high order schemes using Derivatives (ADER) scheme for the case of a large source term in the continuity equation of the nonlinear shallow water equations. The particular application is the movement of a bore on a highly permeable slope. The large source term is caused by the infiltration into the initially unsaturated slope material. Infiltration is modelled as vertical downwards piston‐like flow with Forchheimer quadratic parameterisation of the resistance law. The corresponding ODE is solved using the fourth‐order Runge–Kutta method. The surface and subsurface flow models have been tested by comparison with analytical solutions. Example predictions of surface bore propagation and wetting front propagation are presented for a range of slope permeabilities. The effects of permeability on bore run‐up, water depths and velocities are illustrated. The ADER scheme is capable of handling the source term, including the extreme case when this term dominates the volume balance. Copyright © 2011 John Wiley & Sons, Ltd.     

Approximant crystals of icosahedral Mg–(Ga,Al)–Zn alloys

The zero field cooled (ZFC) and field cooled (FC) low-field magnetic moment m of a dense frozen ferrofluid containing Fe₅₅Co₄₅ particles of size 4.6nm in hexane exhibits irreversibility at temperatures T?T _b≈ 30?K. FC in μ ₀ H ≤ 1?T gives rise to shifted minor hysteresis loops below T _b. At T _c≈ 10?K, sharp peaks of m ^ZFC and of the ac susceptibility χ ′, a kink of the thermoremanent magnetic moment m ^TRM, a sizeable reduction of the coercive field H _c, and the appearance of a spontaneous moment m ^SFM indicate a phase transition with near mean-field critical behaviour of both m ^SFM and χ ′ . These features are explained within a core-shell model of nanoparticles, whose strongly disordered shells gradually become blocked below T _b, while their soft ferromagnetic cores couple dipolarly and become superferromagnetic (SFM) below T _c.     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

Experiment on relationship between the magnetic gradient of low-carbon steel and its stress

In geomagnetic field, a series of tensile experiments on the low-carbon steel sticks were carried out. A special homemade detector was used to measure the magnetic gradient on the material surface. The results showed that the relationship between the magnetic gradient and the stress varied with different conditions of measurement. There was no obvious correlation between the magnetic gradient and the tensile stress if the sample remained on the material test machine. If the sample was taken off from the machine, the measured magnetic gradient was linear with the prior maximum stress. In Nanjing, PR China, a place of 32°N latitude, the slope of the linear relationship was about 67 (uT/m)/MPa. This offered a new method of non-destructive stress testing by measuring the magnetic gradient on the ferromagnetic component surface. The prior maximum applied stress of the sample could be tested by measuring the present surface magnetic gradient. Actually this phenomenon was the metal magnetic memory (MMM). The magnetic gradient near the stress concentration zone of the sample, the necking point, was much larger than other area. Thus, the hidden damage in the ferromagnetic component could be detected early by measuring the magnetic gradient distribution on its surface. In addition, the magnetic memory signal gradually weakened as the sample was taken off and laid aside. Therefore, it was effective for a given period of time to detect the stress or stress concentration based on the MMM testing.