Radial integration boundary element method for heat conduction problems with convective heat transfer boundary

A new boundary domain integral equation with convective heat transfer boundary is presented to solve variable coefficient heat conduction problems. Green’s function for the Laplace equation is used to derive the basic integral equation with varying heat conductivities, and as a result, domain integrals are included in the derived integral equations. The existing domain integral is converted into an equivalent boundary integral using the radial integration method by expressing the normalized temperature as a series of radial basis functions. This treatment results in a pure boundary element analysis algorithm and requires no internal cells to evaluate the domain integral. Numerical examples are presented to demonstrate the accuracy and efficiency of the present method.     

Combination of the fictitious domain method and the sharp interface method for direct numerical simulation of particulate flows with heat transfer

In this paper, the fictitious domain (FD) method and the sharp interface (SI) method are combined for the direct numerical simulations of particulate flows with heat transfer in three dimensions. The flow field and the motion of particles are solved with the FD method. The temperature field is solved in both fluid and solid media with the SI method. The accuracy of the proposed FD/SI method is validated via two problems: the natural convection in a two- dimensional cavity with fixed solid particles, and the flow over a cold sphere. The method is then applied to the natural convection in a three dimensional cavity with a fixed sphere, the motion of a spherical particle in a non-isothermal fluid, and the rising of spherical catalyst particles in an enclosure. The effects of the thermal conductivity ratio are examined in the first and third problems, respectively, and the significant effects of the thermal expansion coefficient ratio on the particle motion are demonstrated in the second problem.     

Traveling wave solutions to incompressible unsteady 2-D laminar flows with heat transfer boundary

Analytical solutions play important roles in the understanding of fluid dynamics and heat transfer related problems. Some analytical solutions for incompressible steady/unsteady 2-D problems have been obtained in literature, but only a few of those are found under heat transfer conditions (which brings more complexities into the problem). This paper is focused on the analytical solutions to the basic problem of incompressible unsteady 2-D laminar flows with heat transfer. By using the traveling wave method, fluid dynamic governing equations are developed based on classical Navier–Stokes equations and can be reduced to ordinary differential equations, which provide reliable explanations to the 2-D fluid flows. In this study, a set of analytical solutions to incompressible unsteady 2-D laminar flows with heat transfer are obtained. The results show that both the velocity field and the temperature field take an exponential function form, or a polynomial function form, when traveling wave kind solution is assumed and compared in such fluid flow systems. In addition to heat transfer problem, the effects of boundary input parameters and their categorization and generalization of field forming or field evolutions are also obtained in this study. The current results are also compared with the results of Cai et al. (R. X. Cai, N. Zhang. International Journal of Heat and Mass Transfer, 2002, 45: 2623-2627) and others using different methods. It is found that the current method can cover the results and will also extend the fluid dynamic model into a much wider parameter ranges (and flow situations).     

Effective boundary conditions for buoyancy-driven flows and heat transfer in fully open-ended two-dimensional enclosures

The present work achieves an accurate representation of the effective boundary conditions at the aperture plane of a two-dimensional open-ended structure for wide range of pertinent parameters. The presented effective boundary conditions are correlated in terms of Rayleigh number, Prandtl number, and the aspect ratio of the open-ended geometry. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. Comprehensive comparisons between the present investigation using the effective boundary conditions for the anticipated closed-ended model and the results for the fully extended computational domain confirm successful implementation of the proposed model. Implementation of this representation reduces the main difficulties associated with specifying the open-ended boundary conditions and results in very substantial savings in CPU and memory usage. The present work plays an important role on modeling a basic and generic set of effective boundary conditions at the aperture plane for several applications of practical interest.     

Immersed boundary computations of shear- and buoyancy-driven flows in complex enclosures

Cartesian grids used with the immersed boundary method (IBM) offer an attractive alternative for simulating fluid flows in complex geometries. We present a ghost fluid method for incompressible flows solved with staggered grids. The primary feature is the satisfaction of local mass continuity for ghost pressure cells, rather than extrapolating the pressures from within the flow domain. The method preserves local continuity in each cell and also global continuity. As a result, no explicit mass sources or sinks are needed. We have applied the method to study shear- and buoyancy-driven flows in a number of complex cavities.     

边界点法在传热问题数值分析中的应用

将一种新的数值分析方法-边界点法应用于传热问题的研究，对无内热源稳态热传导问题，通过传统边界元法将边界积分方程离散化，发现可以不直接求解影响系数矩阵，而是通过对偶关系，由域外虚源构造方程组的特解场形成边界已知和未知温度，热流密度的系数矩阵，而且域内温度和热流密度的求解将不依赖于边界未知参数的求解，对于有内热源的问题，可以将非齐次方程的解转换为齐次方程的解和某一确定解的叠加，对于非线性问题，可以通过基尔霍夫变换，将非线性问题转化为线性问题求解，这种边界点方法不但具有边界元法降维的优势，而且不须求解奇异积分，大大节约了计算时间，计算精度极高，以有内热源非线性稳态热传导问题的实例印证了这种方法的高效性。     

Optimal homotopy asymptotic method for heat transfer in hollow sphere with robin boundary conditions

In this article, we have investigated heat transfer from a hollow sphere using a powerful and relatively new semi‐analytic technique known as the optimal homotopy asymptotic method (OHAM). Robin boundary conditions are applied on both the inner and outer surfaces. The effects of Biot numbers, uniform heat generation, temperature‐ dependent thermal conductivity, and temperature parameters on the dimensionless temperature and heat transfer are investigated. The results of OHAM are compared with a numerical method and are found to be in good agreement. It is shown that the dimensionless temperature increases with an increase in Biot number at the inner surface and temperature and heat generation parameters, whereas it decreases with an increase in the Biot number at the outer surface and the dimensionless thermal conductivity and radial distance parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 124‐133, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21067     

A new method for heat transfer and fluid flow performance simulation of plate heat exchangers

Successful numerical simulation on heat transfer and fluid flow performances of plate heat exchangers is vital. Their complex structures often make the numerical calculation quite difficult and time-consuming. Conclusions drawn by the present work are promising for greatly simplifying the simulation. Different types of plates consisting of different numbers of periods are analyzed and it is concluded that the Nusselt number remains constant for different periods of different plates under different inlet velocities. The central friction coefficients behave the same as Nusselt number. For the first and last periods, the respective friction coefficient also remains for different plates. A small plate fraction with four periods is enough for performance prediction of any-sized plates.     

Numerical simulation of asymmetrical flow and heat transfer behind a hill in shear flows

Three‐dimensional numerical simulations of asymmetrical flows and heat transfer around a hill in shear flows were performed. When shear velocity distributions are introduced at the inlet, a vortex pair is formed asymmetrically to the spanwise direction behind the hill. Further, an asymmetrical hairpin vortex is periodically generated downstream. The leg of the asymmetrical hairpin vortex on the high‐speed side collapses first. Further downstream, the asymmetrical hairpin vortex breaks down earlier than the symmetrical hairpin vortex, and streamwise vortices appear on the high‐speed side. These streamwise vortices increase the heat transfer downstream. In contrast, no hairpin vortex appears in the case of a strong shear velocity distribution, but instead a streamwise vortex appears. The heat transfer decreases downstream since the turbulence generated by streamwise vortices is weak. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20223     

Direct numerical simulation of convective heat transfer in a zero-pressure- gradient boundary layer with supercritical water

Experimental research has long shown that forced-convective heat transfer in wall-bounded turbulent flows of fluids in the supercritical thermodynamic state is not accurately predicted by correlations that have been developed for single-phase fluids in the subcritical thermodynamic state. In the present computational study, the statistical properties of turbulent flow as well as the development of coherent flow structures in a zero-pressuregradient flat-plate boundary layer are investigated in the absence of body forces, where the working fluid is in the supercritical thermodynamic state. The simulated boundary layers are developed to a friction Reynolds number of 250 for two heat-flux to mass-flux ratios corresponding to cases where normal heat transfer and improved heat transfer are observed. In the case where improved heat transfer is observed, spanwise spacing of the near-wall coherent flow structures is reduced due to a relatively less stable flow environment resulting from the lower magnitudes of the wall-normal viscosity-gradient profile.     

Conjugated heat transfer in unsteady channel flows

The exact analytical solution of the unsteady impulsive Thermo-Fluid Dynamic field arising in a two-dimensional channel with thick solid walls is presented when the thermal field in the fluid is coupled with the thermal field in the solid (conjugated heat transfer). The cases studied in this paper depend on the boundary conditions imposed on the unwetted sides of the channel walls: assigned temperature and adiabatic condition. Moreover the case of a given heat loss at the unwetted wall is also considered in an appendix. The temperature and heat flux at the solid–fluid interface are analyzed as function of time and of the nondimensional parameters governing the problem.     

Conjugate heat transfer analysis of film cooling flows

The objective of this study is to evaluate the potential of various grids to satisfactorily simulate the development of a cooling film, using a coupled computation that takes into account the full geometry. Detailed computations of a single row of 30 degrees round holes on a flat plate are presented for blowing ratios of 0.764,1.01 and 1.54. The simulation results are compared well with experimental data. The two-layer model gave more accurate results but consumed much more computational time than the standard wall functions. The k-e turbulence model with wall functions with appropriate values of y is suitable for practical use. The results show the importance of the conjugate calculation for accurately describing the influence of the heat transfer within the cooling film.     

Coupling conjugate heat transfer with in-cylinder combustion modeling for engine simulation

A conjugate formulation to predict heat conduction in the solid domain and spray combustion in the fluid domain was developed for multidimensional engine simulation. Heat transfer through the wall affects the combustion process in the cylinder and the thermal loading on the combustion chamber surface. To account for the temporal and spatial variations of temperature on the chamber surface, a fully coupled numerical procedure was developed to simulate in-cylinder flow and solid heat conduction simultaneously. Temperature fields in both the fluid and the solid domains were coupled by imposing equal heat flux and equal temperature at the fluid–solid interface. The formulation was first validated against analytical solutions. The formulation was then applied to simulate the in-cylinder combustion process and the solid heat conduction in a diesel engine under different operating conditions. Results show that the present model is able to predict unsteady and non-uniform temperature distributions on the chamber surface, which can fluctuate by nearly 100 K during combustion. The highest temperature on the piston surface occurs at the bowl edge along the spray axis. Predicted global engine parameters agree well with the experimental data. The present approach can be used to improve engine design for optimal combustion and reduced thermal loading.     

Lattice Boltzmann method simulation of backward-facing step on convective heat transfer with field synergy principle

The lattice Boltzmann method (LBM) is applied to simulate the two-dimensional incompressible steady low Reynolds number backward-facing step flows. In order to restrict the approach to the two-dimensional flow, the largest Reynolds number chosen was Re = 200. To increase the uniformity of the radial temperature profile for fluid flow in channel and consequently to enhance the heat transfer, the inserted square blockage is used and investigated numerically. In addition, the field synergy principle is also applied to demonstrate that an interruption within fluid results in decreased intersection angle between the velocity and temperature gradient. The numerical results of velocity and temperature field agree well with the available experimental and numerical results.     

A novel immersed boundary/Fourier pseudospectral method for flows with thermal effects

ABSTRACT

A novel immersed boundary method (IBM) for flows with thermal effects is proposed, combining high accuracy and low computational cost, provided by the Fourier pseudospectral method (FPSM), for the possibility of handling complex and nonperiodical geometries using the IBM. With focus on incompressible flow problems modeled by Navier-Stokes, mass, and energy equations, the method of manufactured solutions is used for the numerical verification of Dirichlet boundary conditions imposed via the IBM. Then, the proposed method is applied on two different 2-D cases: (1) energy transfer due to natural convection in a square cavity, and (2) an annulus between horizontal concentric cylinders nonuniformly heated. Good agreement with available data in the literature has been achieved.     

Adiabatic-isothermal mixed boundary conditions in heat transfer

Mixed boundary conditions of the adiabatic-isothermal type often arise in the mathematical modeling of heat transfer phenomena. Under certain circumstances, the mixed condition gives rise to singular behavior which cannot be adequately treated by numerical means alone. The numerical procedure must be supplemented by an asymptotic analysis for the local behavior near the singularity. In the special case of a mixed boundary condition on a straight boundary, the strength of the singularity is given in terms of a path-independent integral, the value of which can be determined from the numerical solution for the far-field behavior. Implications of overlooking the singular behavior due to the mixed boundary condition are discussed.     

Fast Vortex Method for the Simulation of Flows Inside Channels With and Without Injection

A fast vortex method is presented for the simulation of fluid flows inside two-dimensional channels. The first channel studied is formed by two parallel walls simulating the entrance length of a developing flow. The second channel is similar to the first one but with an injection of a secondary fluid through a slot on one of its walls. In both cases, results are presented for flows at low Reynolds numbers and for flows at a high Reynolds number. The numerical method used is based on the Random Vortex Method and on the Vortex-In-Cell algorithm. Physical analyses of the numerical results are also presented, mostly in application to film cooling.