Turbulent flow and convective heat transfer in a wavy wall channel

This paper reports the numerical modeling of turbulent flow and convective heat transfer over a wavy wall using a two equations eddy viscosity turbulence model. The wall boundary conditions were applied by using a new zonal modeling strategy based on DNS data and combining the standard k– turbulence model in the outer core flow with a one equation model to resolve the near-wall region.It was found that the two-layer model is successful in capturing most of the important physical features of a turbulent flow over a wavy wall with reasonable amount of memory storage and computer time. The predicted results show the shortcomings of the standard law of the wall for predicting such type of flows and consequently suggest that direct integrations to the wall must be used instead. Moreover, Comparison of the predicted results of a wavy wall with that of a straight channel, indicates that the averaged Nusselt number increases until a critical value is reached where the amplitude wave is increased. However, this heat transfer enhancement is accompanied by an increase in the pressure drop.     

Finite element analysis of convective heat transfer in porous media

The finite element method is used to analyse convective heat transfer in a porous medium. Convection past a vertical surface embedded in the medium and convection in a confined porous medium enclosure are analysed using the above method. The results are compared with those available in the literature and the agreement is found to be good. The method is applicable for two-dimensional analysis in a porous body of any arbitrary shape. The restriction of the boundary layer assumption is relaxed.     

Local convective heat transfer past the junction of channels of rectangular cross-section

An experimental study of the local convective heat transfer through the wall is presented in the case of an air flow past the junction of channels of a rectangular cross section. Tests for various flow-rate ratios through the two branches show that these ratios are not adequate to characterize the distribution of local heat transfer through the wall. The flow-rate through the side branch is a particularly significant parameter. Received: 2 June 1998/Accepted: 20 February 1999     

Characterization of convective heat transfer in channels of small cross section using digital interferometry

Forced convection in channels of small cross sectional dimensions has been recommended as an effective heat removal method for electronic components and packages. Many of the experimental results reported in the literature on the heat transfer performance of small-cross section channels are of contradicting nature, even though some generally agreeing results are also found. One of the probable reasons for the deviations, as suggested by investigators, is the intrusive nature of measurement techniques, which interferes with the flow field. Hence a non intrusive measurement technique is preferable for temperature measurement in small channels. The present work is aimed at developing an interferometric method for convective heat transfer measurement in a liquid medium flowing through channels of small cross sectional dimensions, with hydraulic diameters ranging from 12 to 3 mm and characterizing the nature of fluid flow and heat transfer in these channels. Mach–Zehnder interferometric arrangement is used to obtain the temperature distributions in water flowing through the channels, which are further analyzed digitally to obtain the local heat transfer coefficients and Nusselt numbers. The results are compared and contrasted with classical results for channel flow and heat transfer, and attempt has been made to interpret the variations and deviations observed. The experimental study has been performed under different fluid velocities in the laminar flow regime, and under various wall heat fluxes corresponding to the heat dissipation range expected in microelectronic devices. Parametric variations for the heat transfer performance have been obtained and correlated using the experimental results.     

Hydromagnetic convective heat transfer in vertical pipes

In the present analysis, we consider the effect of radial magnetic field on the steady flow produced by the combined free and forced convection in an annulus between two coaxial vertical cylinders. A numerical solution of the problem is obtained by using Runge-Kutta-Merson method. For Rayleigh number Ra<0, that is, when the temperature of the pipes decreases as their height increases, the velocity increases with |Ra|. However, it reduces as the Hartmann number M increases. On the other hand, when Ra>0, there occurs back flow controlled by the effect of the magnetic field. Further, the influence of Rayleigh number and Hartmann number on the temperature is also discussed.Nomenclature c _p specific heat at constant pressure - g acceleration due to gravity - H _r applied magnetic field - H _z induced magnetic field - p pressure - T temperature of the fluid - T ₁, T ₂ temperatures of the inner and outer cylinders at z=0 - U _z velocity - coefficient of volume expansion - density - _w reference density - coefficient of viscosity - _e magnetic permeability - _e electrical conductivity - thermal conductivity - _m magnetic diffusivity     

A generalized variational formulation for convective heat transfer

The Scope of this paper is to develop the basic equations for a variational formulation which can be used to solve problems related to convection and/or diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as the hear displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to a system of equations similar in form to Lagrange's equations of mechanics. These equations can be used for obtaining approximate solutions, though they are of particular interest for application of the finite element method. As an example of the formulation two finite element models are derived for solving convectiondiffusion boundary value problems. The performance of the two models is investigated and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The applications of the developed formulations are not limited to convection-diffusion problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.     

Natural convection heat transfer from sinusoidal wavy surfaces

This paper presents the results of an experimental study of the natural convection heat transfer characteristics of sinusoidal wavy surfaces on vertical plates maintained at a constant temperature. Local heat transfer coefficients were obtained with a Mach-Zehnder interferometer. The heat transfer from the wavy surfaces, compared to a plane plate of equal projected area, increased with increasing amplitude-to-wavelength ratio. The heat transfer was increased by about 15 percent at an amplitude-to-wavelength ratio of 0.3; for this case a flow instability was detected. A quantitative comparison with a previously published numerical investigation is also presented. In general, there is agreement between the two studies.     

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

The combined effects of thermal and mass convection of viscous incompressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part (the zeroth-order) and a perturbed part (the first-order). The first-order quantities are obtained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graphically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.     

二维水平通道内流动沸腾换热的格子Boltzmann模拟

利用格子Boltzmann方法模拟二维水平通道内水的流动沸腾过程,获得不同壁面过热度下流型特点和不同因素对换热过程的影响规律。结果表明,随着壁面过热度升高,流道内流型依次经历从泡状流、弹状流到反环流的转变,平均热流密度和平均换热系数先增大后减小。入口流速降低会使流道内出现受限气泡流,核态沸腾受到抑制。提高入口流速能够有效促进气泡脱离,壁面平均换热系数随入口流速增大而增大,但增长速率有所减小。减小通道宽度有利于汽化现象发生,核态沸腾得到强化,壁面平均换热系数有所提高。     

Formulation of nanofluids for natural convective heat transfer applications

The paper is concerned about formulation of aqueous based nanofluids and its application under natural convective heat transfer conditions. Titanium dioxide nanoparticles are dispersed in distilled water through electrostatic stabilization mechanisms and with the aid of a high shear mixing homogenizer. Nanofluids formulated in such a way are found very stable and are used to investigate their heat transfer behaviour under the natural convection conditions. The preliminary results are presented in this paper. Both transient and steady heat transfer coefficients are measured and the results show a systematic decrease in the natural convective heat transfer coefficient with increasing particle concentration. This is in contradiction to the initial expectation. Possible reasons for the observations are discussed.     

A correlation for free convection heat transfer from vertical wavy surfaces

Free convection heat transfer along an isothermal vertical wavy surface was studied experimentally and numerically. A Mach-Zehnder Interferometer was used in the experiment to determine the local heat transfer coefficients. Experiments were done for three different amplitude–wavelength ratios of α = 0.05, 0.1, 0.2 and the Rayleigh numbers ranging from Ra _l = 2.9 × 10⁵ to 5.8 × 10⁵. A finite-volume based code was developed to verify the experimental study and obtain the results for all the amplitude–wavelength ratios between α = 0 to 0.2. It is found that the numerical results agree well with the experimental data. Results indicate that the frequency of the local heat transfer rate is the same as that of the wavy surface. The average heat transfer coefficient decreases as the amplitude–wavelength ratio increases and there is a significant difference between the average heat transfer coefficients of the surface with α = 0.2 and those surfaces with α = 0.05 and 0.1. The experimental data are correlated with a single equation which gives the local Nusselt number along the wavy surface as a function of the amplitude–wavelength ratio and the Rayleigh number.     

Fluid flow and heat transfer in a two-dimensional wavy channel

A numerical study is presented for the laminar fully developed flow and heat transfer in a two-dimensional wavy channel. The effects of the geometry, Reynolds and Prandtl number on the flow field and heat transfer are investigated. The channel is characterized by a wavy wall, heated at uniform heat flux, and an opposite wall, being plane and adiabatic. The extent of the wall waviness and the distance between the channel walls are found to significantly affect the streamlines contours as well as the heat transfer coefficients. Comparisons with the straight channel, in the same flow rate and heat transfer conditions, have been performed. Pressure drop of the wavy channel is found to be always larger than the value characteristic of a straight channel, while heat transfer performance decreases or increases depending on the values of the parameters (geometry, Reynolds and Prandtl numbers).     

Lattice Boltzmann simulation of the convective heat transfer from a stream-wise oscillating circular cylinder

In this paper, we studied the convective heat transfer from a stream-wise oscillating circular cylinder. Two dimensional numerical simulations are conducted at Re = 100–200, A = 0.1–0.4 and F = f_o/f_s = 0.2–3.0 with the aid of the lattice Boltzmann method. In particular, detailed attentions are paid on the extensive numerical results elucidating the influence of oscillation frequency, oscillation amplitude and Reynolds number on the time-average and RMS value of the Nusselt number. Over the ranges of conditions considered herein, the heat transfer characteristics are observed to be influenced in an intricate manner by the value of the oscillation frequency (F), oscillation amplitude (A) and Reynolds number (Re). Firstly, the heat transfer is enhanced when the cylinder oscillates stream-wise with small amplitude and low frequency, while it will be reduced by large amplitude and high frequency. Secondly, the average Nusselt number (Nu (ave)) decreases against the increasing value of oscillation frequency, while the RMS value of the Nusselt number, Nu (RMS), displays an opposite trend. Third, we obtained a similar frequency effect on the heat transfer over the range of Reynolds numbers investigated in this paper. In addition, detailed analyses on phase portraits, energy spectrum are also made.     

Large-eddy simulation of turbulent flow and heat transfer in plane and rib-roughened channels

Large-eddy simulation results are presented and discussed for turbulent flow and heat transfer in a plane channel with and without transverse square ribs on one of the walls. They were obtained with the finite-difference code Harwell-FLOW3D, Release 2, by using the PISOC pressure-velocity coupling algorithm, central differencing in space, and Crank-Nicolson time stepping. A simple Smagorinsky model, with van Driest damping near the walls, was implemented to model subgrid scale effects. Periodic boundary conditions were imposed in the streamwise and spanwise directions. The Reynolds number based on hydraulic diameter (twice the channel height) ranged from 10 000 to 40 000. Results are compared with experimental data, k-? predictions, and previous large-eddy simulations.     

A note on the heat transfer in convective fins

In this paper a generalized approach to the problem of heat transfer through convective fins is given. The proper dimensionless variables, which specify the general problem are identified, and upper bounds of the values of the dimensionless number N_r defined as “the ratio of the heat transferred by the fin to that of the corresponding bare surface” are derived. It was shwon that these limiting values of the N_r are 1/√B₁ and √2/B₁ for longitudinal fins and spines respectively, where B₁ is the Biot number hb/k, while for annular fins of constant thickness and hyperbolic profile, N_r? K(β)/√B_i, where K(β) is a number determined by the profile of the fin and the ratio β=x₂/x₁ of the outside to the inside radii. It was also shown that for longitudinal fins and spinces the possible adverse insulating effect by the use of the fin is avoided, if one selects the value of √hA/KC < 1, which is a rather stricter criterion than the one reported in the literature, namely that of hA/kC < 1 [2–5]. An example is given to show how one may utilize the appropriate value of N_r and the fin effectiveness e, to obtain the dimensions of the fin.     

Mathematical model of convective heat transfer between flows of finely dispersed media in adjacent channels with permeable walls

The discussion is concerned with a mathematical model for convective heat transfer between the flows of finely dispersed media moving in adjacent channels separated by a permeable wall where portions of the fluid phases are exchanged many times between the flows. Numerical solutions are given for a countercurrent flow of a suspension and a liquid. Equations are derived and curves constructed to show the distribution of the flow velocity and the suspension porosity along the length of the channels as well as the dependence on time of the temperatures of the flows.     

Studies on convective heat transfer through helical coils

An experimental investigation on steady state convection heat transfer from vertical helical coiled tubes in water was performed for laminar flow regime. Three coils with curvature ratios as 0.0757, 0.064, 0.055 and range of Prandtl number from 3.81 to 4.8, Reynolds number from 3,166 to 9,658 were considered in this work. The heat transfer data were generated from 30 experiments conducted at constant water bath temperature (60 °C) for different cold water flow rates in helical coils. For the first time, an innovative approach of correlating Nusselt number with ‘M’ number is proposed which is not available in the literature and the developed correlations are found to be in good agreement with the work of earlier researchers. Thus, dimensionless number ‘M’ was found to be significant to characterize the hydrodynamics of fluid flow and heat transfer correlations in helical coils. Several other correlations based on experimental data are developed. To cover wide range of industrial applications, suitable generalized correlations based on extended parameters beyond the range of present experimental work are also developed. All these correlations are developed by using least-squares power law fit and multiple-regression analysis of MATLAB software. Correlations so developed were compared with published correlations and were found to be in good agreement. Comparison of heat transfer coefficients, friction factor and Nusselt number for different geometrical conditions is presented in this paper.     

Experimental study on axial wall heat conduction for convective heat transfer in stainless steel microtube

Distilled water and nitrogen gas used as the working fluids flow through the stainless steel microtube with inner diameter 168 μm outer diameter 406 μm. Using the Joule heating, the wall temperature field photos of the microtube is acquired by employing an IR camera and the temperature and the volume flow rate of the inlet and the outlet of microtube are measured. A correlation between the axial wall heat conduction and the convective heat transfer is obtained by theoretical analysis based on the experimental results. The investigative results clearly show that the axial heat conduction can reduce the convective heat transfer in the stainless steel microtube and the decrement may reach 2% compared to the convective heat transfer when the working fluid is nitrogen gas, however, the decrement can be neglected for distilled water as the working fluid.