Numerical investigation of heat transfer and fluid flow characteristics inside a wavy channel

The periodically fully developed laminar heat transfer and fluid flow characteristics inside a two-dimensional wavy channel in a compact heat exchanger have been numerically investigated. Calculations were performed for Prandtl number 0.7, and Reynolds number ranging from 100 to 1,100 on non-orthogonal non-staggered grid systems, based on SIMPLER algorithm in the curvilinear body-fitted coordinates. Effects of wavy heights, lengths, wavy pitches and channel widths on fluid flow and heat transfer were studied. The results show that overall Nusselt numbers and friction factors increase with the increase of Reynolds numbers. According to the local Nusselt number distribution along channel wall, the heat transfer may be greatly enhanced due to the wavy characteristics. In the geometries parameters considered, friction factors and overall Nusselt number always increase with the increase of wavy heights or channel widths, and with the decrease of wavy lengths or wavy pitches. Especially the overall Nusselt number significantly increase with the increase of wavy heights or channel widths, where the flow may become into transition regime with a penalty of strongly increasing in pressure drop. An erratum to this article can be found at     

Numerical simulation of forced convection over a periodic series of rectangular cavities at low Prandtl number

Convective heat transfer in laminar conditions is studied numerically for a Prandtl number Pr = 0.025, representative of liquid lead–bismuth eutectic (LBE). The geometry investigated is a channel with a periodic series of shallow cavities. Finite-volume simulations are carried out on structured orthogonal curvilinear grids, for ten values of the Reynolds number based on the hydraulic diameter between Re_m = 24.9 and Re_m = 2260. Flow separation and reattachment are observed also at very low Reynolds numbers and wall friction is found to be remarkably unequal at the two walls. In almost all cases investigated, heat transfer rates are smaller than the corresponding flat channel values. Low-Prandtl number heat transfer rates, investigated by comparison with Pr = 0.71 results, are large only for uniform wall temperature and very low Re. Influence of flow separation on local heat transfer rates is discussed, together with the effect of different thermal boundary conditions. Dependency of heat transfer performance on the cavity geometry is also considered.     

Turbulent forced convection of nanofluid in a wavy channel using two phase model

Two phase mixture model is used to numerically simulate the turbulent forced convection of Al₂O₃-Water nanofluid in a channel with corrugated wall under constant heat flux. Both mixture and single phase models are implemented to study the nanofluid flow in such a geometry and the results have been compared. The effects of the volume fraction of nanoparticles, Reynolds number and amplitude of the wavy wall on the rate of heat transfer are investigated. The results showed that with increasing the volume fraction of nanoparticles, Reynolds number and amplitude of wall waves, the rate of heat transfer increases. Also the results showed that the mixture model yields to higher Nusselt numbers than the single phase model in a similar case.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.     

Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.     

Transient free convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect

A Prandtl transformation method is applied to study the transient free convection of non-Newtonian fluids along a wavy vertical plate in the presence of a magnetic field. A simple transformation is proposed to transform the governing equations into the boundary-layer equations and solved numerically by the cubic spline approximation. A simple coordinate transformation is employed to transform the complex wavy surface to a vertical flat plate for a constant wall temperature by the numerical method. The effects of the magnetic field parameter, the wavy geometry and the non-Newtonian nature of the fluids on the flow characteristics and heat transfer are discussed in detail.     

Entropy generation and natural convection in square cavities with wavy walls

The aim of the present work is to study the entropy generation in the natural convection process in square cavities with hot wavy walls through numerical simulations for different undulations and Rayleigh numbers, while keeping the Prandtl number constant. The results show that the hot wall geometry affects notably the heat transfer rate in the cavity. It has been found in the present numerical study that the mean Nusselt number in the case of heat transfer in a cavity with wavy walls is lower, as compared to heat transfer in a cavity without undulations. Based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction, the local Bejan number, and the local entropy generation are determined and plotted for different undulations and Rayleigh numbers. The study is performed for Rayleigh numbers 10³ < Ra < 10⁵, irreversibility coefficients 10^?4 < φ < 10^?2, and Prandtl numbers Pr = 0.71. The total entropy generation is found to increase with increasing undulation number.     

Experiments on the linear instability of flow in a wavy channel

The effects of wall corrugation on the stability of wall-bounded shear flows have been examined experimentally in plane channel flows. One of the channel walls has been modified by introduction of the wavy wall model with the amplitude of 4% of the channel half height and the wave number of 1.02. The experiment is focused on the two-dimensional travelling wave instability and the results are compared with the theory [J.M. Floryan, Two-dimensional instability of flow in a rough channel, Phys. Fluids 17 (2005) 044101 (also: Rept. ESFD-1/2003, Dept. of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, 2003)]. It is shown that the flow is destabilized by the wall corrugation at subcritical Reynolds numbers below 5772, as predicted by the theory. For the present corrugation geometry, the critical Reynolds number is decreased down to about 4000. The spatial growth rates, the disturbance wave numbers and the distribution of disturbance amplitude measured over such wavy wall also agree well with the theoretical results.     

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.     

Laminar flow and heat transfer in a periodically converging-diverging channel

A finite difference solution for laminar viscous flow through a sinusoidally curved converging-diverging channel is presented. The physical wavy domain is transformed into a rectangular computational domain in order to simplify the application of boundary conditions on the channel walls. The discretized conservation equations for mass, momentum and energy are derived on a control volume basis. The pseudo-diffusive terms that arise from the co-ordinate transformation are treated as source terms, and the resulting system of equations is solved by a semi-implicit procedure based on line relaxation. Results are obtained for both the developing and the fully developed flow for a Prandtl number of 0.72, channel maximum width-to-pitch ratio of 1.0, Reynolds number ranging from 100 to 500 and wall amplitude-to-pitch ratio varying from 0.1 to 0.25. Results are presented here for constant fluid properties and for a prescribed wall enthalpy only.     

Flow and heat/mass transfer in a wavy duct with various corrugation angles in two dimensional flow regimes

In this study, two dimensional heat/mass transfer characteristics and flow features were investigated in a rectangular wavy duct with various corrugation angles. The test duct had a width of 7.3 mm and a large aspect ratio of 7.3 to simulate two dimensional characteristics. The corrugation angles used were 100°, 115°, 130°, and 145°. Numerical analysis using the commercial code FLUENT, was used to analyze the flow features. In addition, the oil-lamp black method was used for flow visualization. Local heat/mass transfer coefficients on the corrugated walls were measured using a naphthalene sublimation technique. The Reynolds number, based on the duct hydraulic diameter, was varied from 700 to 5,000. The experimental results and numerical analysis showed interesting and detailed features in the wavy duct. Main flow impinged on upstream of a pressure wall, and the flow greatly enhanced heat/mass transfer. On a suction wall, however, flow separation and reattachment dominantly affected the heat/mass transfer characteristics on the wall. As the corrugation angle decreased (it means the duct has more sharp turn), the region of flow stagnation at the front part of the pressure wall became wider. Also, the position of flow reattachment on the suction wall moved upstream as the corrugation angle decreased. A high heat transfer rate appeared at the front part of the pressure wall due to main-flow impingement, and at the front part of the suction wall due to flow reattachment. The high heat/mass transfer region by the main-flow impingement and the circulation flow induced at a valley between the pressure and suction walls changed with the corrugation angle and the Reynolds number. As the corrugation angle decreased, the flow in the wavy duct changed to transition to turbulent flow earlier.     

Flow and heat transfer performance of a mini-channel radiator with cylinder disturbed flow

Mini-channel heat sinks have relatively low Nusselt number due to small Reynolds number. For heat transfer enhancement purpose, a mini-channel radiator with cylinder disturbed flow was proposed. The disturbed flow was created by a circular cylinder placed horizontally in front of channels entrance. The performance of heat transfer and pressure drop with/without disturbed flow was studied experimentally. It was found that the friction factor of mini-channel flow was larger than that of the macro-channel flow due to larger surface roughness, and the pressure drop caused by cylinder disturbed flow was less than 5%. It also concluded that the average Nusselt number increases with augment of Reynolds and Prandtl number. The Nusselt number correlations as the function of the Reynolds and Prandtl number were given for evaluation the heat removal performance of similar heat radiators. There is an inflexion point in the empirical formulas when the channel length equals to the thermal entrance length. For the mini-channels heat radiators with disturbed flow, the inflexion Reynolds number is larger than that of without disturbed flow. Due to the flow pulsing caused by circular cylinder placed in front of channels entrance, the thermal entrance length increases. On the other hand, for both mini-channels with or without disturbed flow, the thermal resistance increases with the decrease of pressure drop.     

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger , two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.     

Laminar heat transfer characteristics of internally finned tube with sinusoidal wavy fin

Comparative numerical study of laminar heat transfer characteristics of annular tubes with sinusoidal wavy fins has been conducted both experimentally and numerically with Re = 299–1,475. The uniform heat flux is imposed on the tube outside wall surface. Two tube materials (copper and stainless steel) are considered. It is found that the fluid temperature profile is not linear but convex along the flow direction due to the axial heat conduction in tube wall, and the effects of axial heat conduction on the heat transfer decreases with an increase in Reynolds number or decrease in tube wall thermal conductivity. The axial distributions of local Nusselt number could reach periodically fully developed after 3–5 cycles. The convectional data reduction method based on the traditional method should be improved for tube with high thermal conductivity or low Reynolds numbers, Otherwise, the heat transfer performance of internally finned tube may be underestimated.     

DNS of turbulent heat transfer in a channel flow with a high spatial resolution

Direct numerical simulations of turbulent heat transfer in a channel flow are performed to investigate the effects of Reynolds and Prandtl numbers on higher-order turbulence statistics such as a turbulent Prandtl number and the budget for the dissipation rate of the temperature variance. The Reynolds numbers based on the friction velocity and the channel half width are 180 and 395, and the molecular Prandtl numbers Pr’s 0.71–10.0. Careful attention is paid to ensure accuracy of the higher-order statistics through the use of a high spatial resolution comparable to Batchelor length scale. The wall-asymptotic value of the turbulent Prandtl number is mostly independent of Reynolds number for the current range of Pr’s. The budget for the dissipation rate of the temperature variance has been computed, and the negligible effect of a Reynolds number on the sum of all source and sink terms in near-wall region in the current computational range is found. This result is quite similar to the one in the budget for the dissipation rate of turbulent energy. In addition, a priori test for existing models is also performed to assess the Pr dependence on the individual terms and their summations in the budget.     

Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary conditions

Direct numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.     

Development of a turbulent near-wall temperature model and its application to channel flow

A numerical study of fluid flow and heat transfer in a two-dimensional channel under fully developed turbulent conditions is reported. A computer program which is capable of treating both forced and natural convection problems under turbulent conditions has been developed. The code uses the high-Reynolds-number form of the two equation turbulent model(k-?) in which a turbulent kinetic energy near-wall model is incorporated in order to accurately represent the behavior of the flow near the wall, particularly in the viscous sublayer where the turbulent Reynolds number is small. A near-wall temperature model has been developed and incorporated into the energy equation to allow accurate prediction of the temperature distribution near the wall and, therefore, accurate calculation of heat transfer coefficients. The sensitivity of the prediction of flow and heat transfer to variations in the coefficients used in the turbulence model is investigated. The predictions of the model are compared to available experimental and theoretical results; good agreement is obtained. The inclusion of the near-wall temperature model has further improved the predictions of the temperature profile and heat transfer coefficient. The results indicate that the turbulent kinetic energy Prandtl number should be a function of Reynolds number.     

Heat transfer in turbulent pipe flow based on a new mixing length model

A new model for the heat transfer in turbulent pipe flow is presented based on a modified form of the mixing length theory developed by Cebeci [1] for boundary layer flow problems. The model predicts the velocity and temperature distributions and the Nusselt number for fluids with low, medium and high Prandtl numbers (Pr=.02 to 15) and fits the available experimental data very accurately for values of Reynolds number exceeding 10⁴. Expressions for the eddy conductivity and for the turbulent Prandtl number are presented and shown to be dependent upon the Reynolds number, the Prandtl number, and the distance from the tube wall.     

Instationärer Wärmeübergang bei turbulenter Ringspaltströmung

An analysis is made of unsteady convective heat transfer in a hydrodynamically stabilized steady turbulent flow of a viscous incompressible fluid in concentric annuli. The wall heat flux varies with time according to an arbitrary law. The formulation permits the heat transfer coefficient to vary also with time and position. The energy equation is solved using the method of superposition and separating variables by finite integral transform. Use of the generalized results is detailed illustrated by application to the case where the wall heat flux varies exponentially with time. Results are discussed subject to different Reynolds and Prandtl numbers.     

Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls

Interest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo-spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant-property, turbulent fluid in a two-dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions. Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half-height of 180 or 2800 based on channel half-height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two-point velocity correlations are given. Deficiencies are that the calculation requires many hours on a fast computer with a large high-speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.