Heat transport in granular materials during cyclic fluid flow

Heat transfer takes place between grains and the fluids that saturate the pore space in granular materials, when the fluid is static or moving. This study explores effective heat transport in granular materials during cyclic fluid flow. Controlled particle-scale experiments, complementary analyses and numerical simulations help us identify the governing variables and ensuing time scales. We show that fluid-grain heat transfer leads to effective heat transport along the granular medium during cyclic fluid flow. At the macro-scale, the process resembles diffusion where the effective diffusion coefficient is proportional to the square of the fluid invasion length in each cycle and inversely proportional to the cycle period. Both experimental and numerical results confirm improved heat transfer by cyclic fluid flow over thermal diffusion under hydrostatic conditions. The formulation can be used to identify optimal operation conditions for maximum transport.     

Natural convection heat transfer of cold water in an eccentric horizontal cylindrical annulus — a numerical study

A numerical study of the natural convection heat transfer of cold water, having the density inversion between two isothermal eccentric horizontal cylinders is studied. A general code is developed for the body fitted coordinate system. This procedure transforms an arbitrarily shaped physical domain into a rectangular (square) domain. The governing equations in this computational domain are solved by the upwind finite difference scheme. The numerical solutions are obtained for a Rayleigh number (Ra) ranging between a Prandtl number (Pr) 12.0 and inversion parameter (γ) 0,−1 and −2. The affect of the radius ratio (R) on the flow patterns and heat transfer coefficients is studied by taking the Radius ratio as 1.5 and 2. The eccentricity affect is studied by moving the center of the inner cylinder horizontally and vertically (both positive and negative directions) with respect to the center of the outer cylinder. For the cases considered in the present study, it is again for the minimum heat transfer is observed like in the case of concentric annulus.     

Three-dimensional flow with heat transfer of a viscoelastic fluid over a stretching surface with a magnetic field

The present research study deals with the steady flow and heat transfer of a viscoelastic fluid over a stretching surface in two lateral directions with a magnetic field applied normal to the surface. The fluid far away from the surface is ambient and the motion in the flow field is caused by stretching surface in two directions. This result is a three-dimensional flow instead of two-dimensional as considered by many authors. Self-similar solutions are obtained numerically. For some particular cases, closed form analytical solutions are also obtained. The numerical calculations show that the skin friction coefficients in x- and y-directions and the heat transfer coefficient decrease with the increasing elastic parameter, but they increase with the stretching parameter. The heat transfer coefficient for the constant heat flux case is higher than that of the constant wall temperature case.     

Numerical Simulation of Thermocapillary Convection in a Shallow Rectangular Cavity Under the Action of Combining Horizontal Temperature Gradient with Vertical Heat Flux

In order to understand the influence of the vertical heat flux on thermocapillary convection, we conducted a series of unsteady two-dimensional numerical simulations of thermocapillary convection in a differently heated shallow rectangular cavity with vertical heat flux on the bottom by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and aspect ratio is 30. It is found that a small vertical heat flux has slightly influence on the flow pattern of stable or unstable thermocapillary convection. However, the critical Marangoni number increases first, and then decreases with the increase of the heat flux. And the flow pattern of the oscillatory thermocapillary convection transits from a series of the rolls rotating clockwise and moving from the cold wall to the hot wall to the single roll near the hot wall and a series of rolls near the cold wall, further, two series of rolls moving from the hot wall and cold wall towards the hot spot with the maximum temperature. With the increase of the Marangoni number, the period and the wavelength of the oscillatory thermocapillary convection increase, but the wave speed decreases.     

An experimental investigation of heat transfer in a pebble bed

An experimental investigation is performed of heat transfer under conditions of longitudinal flow of water moving in a bed of glass pebbles past a flat heated wall. Experiments involving the flow of single-phase liquid are performed in the ranges of variation of filtration velocities from 6 to 60 mm/s and of heat fluxes from 40 to 140 kW/m²; in the case of wall boiling, the experiments are performed in the ranges of variation of filtration velocities from 2 to 50 mm/s and of heat fluxes from 27 to 86 kW/m². The temperature distribution is measured over the height of the heated wall and over the cross section (depth) of the channel at the outlet from the pebble bed. The experimental data are processed for single-phase flow using numerical optimization techniques. The values of the coefficient of “turbulent” thermal conductivity in the pebble bed are obtained as a function of the process parameters     

Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation

We introduce fixed, moving and multiple fixed kernel techniques for the construction of interpolation functions over a scattered set of points. We show that for a particular choice of nodal volumes, the fixed, moving and multiple fixed kernel approaches are identical to the fixed, moving and multiple fixed least squares approaches. A finite cloud method, which combines collocation with a fixed kernel technique for the construction of interpolation functions, is presented as a true meshless technique for the numerical solution of partial differential equations. Numerical results are presented for several one‐and two‐dimensional problems, including examples from elasticity, heat conduction, thermoelasticity, Stokes flow and piezoelectricity. Copyright © 2001 John Wiley & Sons, Ltd.     

Analytical solutions of hydromagnetic boundary-layer flow of a non-Newtonian power-law fluid past a continuously moving surface

Summary The boundary-layer flow of a power-law non–Newtonian fluid over a continuously moving surface in the presence of a magnetic field B(x) applied perpendicular to the surface has been investigated. An analytical solution is obtained and compared with the numerical solution of the resulting non linear ordinary differential equation. The effects of the Stewart number (N) and the power law-index (n) on the velocity profiles and the skin-friction are studied.     

Hydrodynamic interaction of axial turbomachine cascades

Hydrodynamic interaction of mutually moving airfoil cascades is investigated. It is shown that the semi-empirical theory of potential-vortical interaction of two mutually moving cascades in incompressible flow allows one to describe correctly the features of their mutual effect for various gaps between cascades and relations of their pitches. Application of the above theory to a flow around three cascades of the stator-rotor-stator type allows to determine the basic mechanism of the stators’ mutual shift effects (clocking effects). To close the theory regarding the vortical interaction of cascades, a semi-empirical model of turbulent diffusion in a non-uniform flow of the periodic vortices descending from airfoils is proposed. Theoretical results are compared with data from numerical and physical experiments. Comparison with results of numerical modeling is based on the solution of the Reynolds equations for a viscous gas closed by the (q-ω) model of turbulence. Results published here and elsewhere are used for comparison with measurement data     

Piston-driven laminar flow and heat transfer in a plane channel with a sudden expansion

 This paper presents a numerical study of piston-driven heat transfer and fluid flow in a plane channel containing a sudden expansion. The numerical method employed is based on a control-volume-based finite element method for incompressible flow with a staggered and moving grid and SIMPLER algorithm for pressure-velocity coupling. The numerical results show a good agreement with the experimental data reported in the literature. Results concerning time and space evolution of the thermal and flow fields are presented for different values of the expansion ratio, the initial clearance volume, and the piston velocity. Received: 20 April 2002 / Accepted: 23 January 2003     

Forced convection heat transfer from concentrated and distributed thermal sources

Abstract

This paper proposes a novel formulation for the analysis of forced convection heat transfer from both a concentrated thermal source and a uniformly distributed thermal source. The illustrative examples are the wedges of various configurations with dual thermal sources; namely, each of the wedges is imposed with uniform‐flux on the surface and embedded with a line source at the leading edge. By introducing a parameter of relative source strength ξ and a dimensionless temperature based on the two characteristic temperature of the sources, a nonsimilar boundary‐layer energy equation is obtained. The nonsimilar energy equation is readily reducible to the self‐similar equations of adiabatic wedge plumes for ξ=0, and to those of uniform‐flux wedges for ξ=1. Numerical solutions are obtained by employing an effective numerical scheme which has been developed for nonsimilar plumes subject to an integral equation of flux conservation condition. Results are presented for the cases of flat plate, right angle wedge, stagnation point and separating wedge flow for Pr=0.7, 1, 7, 10, and 100. Dimensionless wall temperature for all the cases are proportional linearly to ξ over the entire range of ξ from 0 to 1. Solutions for the limiting cases of ξ=0 and 1 are in excellent agreement with the reported data.     

Effect of moving walls on heat transfer and entropy generation in a nanofluid-filled enclosure

In this work, a numerical investigation of mixed convection has been carried out in a two-sided lid-driven enclosure filled with copper–water nanofluid. Three different cases have been discussed depending on the direction of moving vertical walls to analyze the behavior of fluid flow and heat transfer in nanofluid. The buoyancy effects are incorporated using two discrete heat sources placed on the bottom wall maintaining a fixed distance from both the side walls. The stationary part of the bottom wall is kept insulated while other walls are maintained at constant low temperature. A two-dimensional computational visualization technique has been employed to demonstrate the main findings of the presented work. The effect of higher nanoparticle volume fraction (up to 20%) with variations of Reynolds number and Richardson number is studied to find the rate of heat transfer. The results are presented using streamlines, isotherms, and energy flux vectors. The thermodynamic optimization of the system is analyzed by using Nusselt number and entropy generation.     

Non-uniform temperature gradients and thermal stresses produced by a moving heat flux applied on a hollow sphere

This work presents numerical analyses of transient temperature and thermally-induced stress distributions in a hollow steel sphere heated by a moving uniform heat source applied on a certain zenithal segment (the heated zenithal segment, Θ _H ) of its outer surface (the processed surface) under stagnant ambient conditions. Along the process, the moving heat source (MHS) moves angularly from the first zenithal segment to the last zenithal segment on the processed surface with a constant angular speed, ω, and then returns backward to the first zenithal segment with the same speed. It is assumed that the inner surface is heat-isolated and that the outer surface except the heated segment is under stagnant ambient conditions. The numerical calculations are performed individually for a wide range of thermal conductivity, λ, of steel and for the different Θ _H s. The maximum effective thermal stress ratio calculated as per the heat flux intensity (q ₀) can be reduced in considerable amounts. By increasing λ(∼75%) and ω(∼63%) the maximum effective thermal stress ratio calculated can be significantly reduced.     

CFD simulation on inlet configuration of plate-fin heat exchangers

A computational fluid dynamics (CFD) program FLUENT has been used to predict the fluid flow distribution in plate-fin heat exchangers. It is found that the flow maldistribution is very serious in the y direction of header for the conventional header used in industry. The results of flow maldistribution are presented for a plate-fin heat exchanger, which is simulated according to the configuration of the plate-fin heat exchanger currently used in industry. The numerical prediction shows a good agreement with experimental measurement. By the investigation, two modified headers with a two-stage-distributing structure are proposed and simulated in this paper. The numerical investigation of the effects of the inlet equivalent diameters for the two-stage structures has been conducted and also compared with experimental measurement. It is verified that the fluid flow distribution in plate-fin heat exchangers is more uniform if the ratios of outlet and inlet equivalent diameters for both headers are equal.     

Curing simulation of thermoset composites

This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composite laminates during processing in an autoclave. Darcy's Law and Stokes’ slow-flow equations are used for the flow model and, for approximately isothermal flows, a similarity solution is developed. This permits the decoupling of the velocity and thermal fields. A two-dimensional convection–diffusion heat equation with an internal heat generation term is then solved numerically, together with the equation for the rate of cure, using a finite difference scheme on a moving grid. The simulations are performed with varying composite thicknesses, and a comparison of numerical results with known experimental data confirms the approximate validity of the model.     

Calculation of Heat Transfer and Drag in Tubes under Conditions of Laminar Flow of Gases with Varying Properties

A numerical investigation is performed of the problem on heat transfer and hydraulic drag in the hydrodynamic and thermal initial sections of a round tube heated by the q _w = const law, under conditions of laminar flow of gases with varying physical properties. Monatomic, diatomic, and polyatomic gases and gas mixtures are treated, as well as the range of heat loads Q ⁺ _in up to 20. The obtained results are used to analyze disagreement between the available literature data; methods are suggested for improving the engineering procedure of thermohydraulic design under laminar flow of gases and the known model of stabilized flow and heat transfer.     

Approximate Evaluation of Temperature in a Wheel-Rail Tribosystem

By using the methods of piecewise linear approximation and Green functions, we construct an approximate solution of a two-dimensional quasistationary problem of heat conduction for a half space whose surface is heated by a rapidly moving distributed heat flow. It is assumed that the constructed solution simulates, under certain conditions, the process of heat release caused by friction in a wheel-rail tribosystem. The numerical analysis demonstrates that the maximum temperature in the contact region does not exceed 450°C even for significant values of the slip coefficient (2%) and, hence, is too low for the onset martensitic transformations in steel.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 1, pp. 83–88, January–February, 2005.     

An explicit unconditionally stable variable time-step method for one-dimensional stefan problems

Modelling of heat conduction processes with phase changes benefits from the application of variable time-step methods when the behaviour of the moving boundary is not known a prioiri. Due to convergence and stability constraints only implicit difference equations have been used with these methods. Implicit methods show a significant loss of accuracy and exhibit convergence difficulties when used for relatively slow or rapid moving-boundary problems. To overcome these problems an improved explicit variable time-step method which combines the explicit exponential difference equation and a variable time-step grid network with virtual subspace increments around the moving boundary is presented and tested for both a solidification and a melting problem. A virtual subinterval time-step elimination technique is incorporated to ensure that stability is automatically maintained for any mesh size. Unlike the implicit variable time-step methods, the accuracy of the resulting method is not affected by the velocity of the moving boundary. For both test problems numerical results are in better agreement with known analytical solutions than results predicted by other numerical methods.     

Free convection flow of water near 4 °C past a moving plate

In the present study the unsteady free convection flow of water near 4?^°C in the laminar boundary layer over a vertical moving porous plate is investigated. The effect of the suction/injection parameter at the plate on the velocity is considered. The momentum equation is solved numerically by a fourth-order Runge-Kutta scheme. The numerical results which are obtained for the flow are shown graphically.     

Fourier‐based numerical approximation of the Weertman equation for moving dislocations

This work addresses the numerical approximation of solutions to a dimensionless form of the Weertman equation, which models a steadily moving dislocation and is an important extension (with advection term) of the celebrated Peierls‐Nabarro equation for a static dislocation. It belongs to the class of nonlinear reaction‐advection‐diffusion integro‐differential equations with Cauchy‐type kernel, thus involving an integration over an unbounded domain. In the Weertman problem, the unknowns are the shape of the core of the dislocation and the dislocation velocity. The proposed numerical method rests on a time‐dependent formulation that admits the Weertman equation as its long‐time limit. Key features are (1) time iterations are conducted by means of a new, robust, and inexpensive Preconditioned Collocation Scheme in the Fourier domain, which allows for explicit time evolution but amounts to implicit time integration, thus allowing for large time steps; (2) as the integration over the unbounded domain induces a solution with slowly decaying tails of important influence on the overall dislocation shape, the action of the operators at play is evaluated with exact asymptotic estimates of the tails, combined with discrete Fourier transform operations on a finite computational box of size L; (3) a specific device is developed to compute the moving solution in a comoving frame, to minimize the effects of the finite‐box approximation. Applications illustrate the efficiency of the approach for different types of nonlinearities, with systematic assessment of numerical errors. Converged numerical results are found insensitive to the time step, and scaling laws for the combined dependence of the numerical error with respect to L and to the spatial step size are obtained. The method proves fast and accurate and could be applied to a wide variety of equations with moving fronts as solutions; notably, Weertman‐type equations with the Cauchy‐type kernel replaced by a fractional Laplacian.     

Phase State of a Steel Plate Caused by the Action of Distributed Heat Sources

We propose a procedure for the numerical analysis of the structural state of steel plates caused by the action of moving distributed heat sources. With the help of an additional source whose intensity is five times lower than the intensity of the main source, one can halve the maximum content of martensite and, thus, significantly weaken the undesirable consequences of local heating. The results of the proposed investigation can be used in the development of the optimal technological procedures aimed at the minimization of residual welding stresses.