Study of conjugate natural convection between vertical coaxial rectangular cylinders

Laminar natural convection between two coaxial vertical rectangular cylinders is numerically studied in this work. The outer cylinder is connected with vertical rectangular inlet and outlet pipes. The inner cylinder dissipates volumetric heat. The fluid flow and heat transfer characteristics between the cylinders are analyzed in detail for various Grashof numbers. The heat transfer rates on the individual faces of the inner cylinder are reported. The bottom face of the inner cylinder is found to associate with much higher heat rates than those of the other faces. The average Nusselt number on bottom face is more than 2.5 times of the Nusselt number averaged on all the faces. At a given elevation, local Nusselt number on the inner cylinder faces increases towards cylinder edges. The effect of thermal condition of the walls of outer cylinder, inlet and outlet on the natural convection is analyzed. The thermal condition shows strong qualitative and quantitative impact on the fluid flow and heat transfer. The variation of induced flow rate, dimensionless maximum temperature and average Nusselt numbers with Grashof number is studied. Correlations for dimensionless buoyancy-induced mass flow rate and temperature maximum are presented.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Numerical analysis of heat transfer and flow field around cross-flow heat exchanger tube with fouling

Fouling is one of the main problems of heat transfer which can be described as the accumulation on the heat exchanger tubes, i.e.; ash deposits on the heat exchanger unit of the boiler. A decrease in heat transfer rate by this deposition causes loss in system efficiency and leads to increasing in operating and maintenance costs. This problem concerns with the coupling among conduction heat transfer mode between solid of different types, conjugate heat transfer at the interface of solid and fluid, and the conduction/convection heat transfer mode in the fluid which can not be solved analytically. In this paper, fouling effect on heat transfer around a cylinder in cross flow has been studied numerically by using conjugate heat transfer approach. Unlike other numerical techniques in existing literatures, an unstructured control volume finite element method (CVFEM) has been developed in this present work. The study deals with laminar flow where the Reynolds number is limited in the range that the flow field over the cylinder is laminar and steady. We concern the fouling shape as an eccentric annulus with constant thermal properties. The local heat transfer coefficient, temperature distribution and mean heat transfer coefficient along the fouling surface are given for concentric and eccentric cases. From the results, we have found that the heat transfer rate of cross-flow heat exchanger depends on the eccentricity and thermal conductivity ratio between the fouling material and fluid. The effect of eccentric is dominant in the region near the front stagnation point due to high temperature and velocity gradients. The mean Nusselt number varies in asymptotic fashion with the thermal conductivity ratio. Fluid Prandtl number has a prominent effect on the distribution of local Nusselt number and the temperature along the fouling surface.     

Nanofluid multi-phase convective heat transfer in closed domain: Simulation with lattice Boltzmann method

The lattice Boltzmann method is applied to simulate the thermal field and flow field of nanofluid natural convection in a square cavity. The heat transfer characteristics of nanofluid are compared with that of water to explore nanofluid heat transfer mechanism. The flow field shows different characters at different Rayleigh number and the average Nusselt number is obtained changing with Rayleigh number.     

Effect of fluid thermal properties on the heat transfer characteristics in a double-pipe helical heat exchanger

Heat transfer characteristics of a double-pipe helical heat exchanger were numerically studied to determine the effect of fluid thermal properties on the heat transfer. Two studies were performed; the first with three different Prandtl numbers (7.0, 12.8, and 70.3) and the second with thermally dependent thermal conductivities. Thermal conductivities of the fluid were based on a linear relationship with the fluid temperature. Six different fluid dependencies were modeled. Both parallel flow and counterflow configurations were used for the second study.Results from the first study showed that the inner Nusselt number was dependent on the Prandtl number, with a greater dependency at lower Dean numbers; this was attributed to changing hydrodynamic and thermal entry lengths. Nusselt number correlations based on the Prandtl number and a modified Dean number are presented for the heat transfer in the annulus. Results from the second part of the study showed that the Nusselt number correlated better using a modified Dean number. The counterflow configuration had higher heat transfer rates than the parallel flow, but the ratio of these differences was not different when comparing thermally dependent properties and thermally independent properties.     

NATURAL CONVECTION IN VERTICAL PARALLEL PLATES WITH AN UNHEATED ENTRY OR UN HEATED EXIT

This study aims to investigate the effects of the unhealed entry or unheated exit section on the free convection heat transfer in airflow in vertical parallel plate channels resulting from the thermal boundary conditions of uniform heat flux (VHF) and uniform wall temperature (UWT). Results of average Nusselt number and dimensionless volume flow rate are presented in terms of the ratio of the length of heated section to the full channel length and a Rayleigh number, ranging from the limit for the fully developed flow to that for single-plate behavior. Analytical equations for dimensionless volume flow rate and average Nusselt number for both unheated restrictions and both thermal boundary conditions have been developed for the fully developed flow limit. The numerical solutions are shown to approach asymptotically the approximate solution for fully developed flow as the Rayleigh number approaches 1 or less. An important finding of the study is that an unheated exit characterizes greater total heat transfer and volume flow rate than an unheated entry does. The presence of the unheated entry or unheated exit severely affects the convection process, especially at low Rayleigh number. A notable effect of an unheated exit on convection characteristics was found for the case of UHF at high Rayleigh number.     

Effect of laminar separation flow and nanofluids on heat transfer augmentation with passive techniques: A review

Heat transfer in flow channels can be improved by using passive techniques such as ribs on wall and change cross section area where these modifications have practical engineering application for thermal power plant, refrigerators, and radiators. Effects of separation flow and nanofluids on thermal performance for laminar range presented experimentally and numerically in this review. The augmentations of heat transfer with fluid and nanofluid flow through sudden expansion, over backward and forward facing step, and rib channels have been concerned. The experimental results showed good agreement with numerical results and indicated the effects of separation flow and nanoparticles on augmentation of heat transfer rate. The results showed increase in Nusselt number with increase of Reynolds number, step height, and number of ribs. It was detected that by increasing the nanoparticle volume concentrations of nanofluids, improves the heat transfer coefficient. Also different nanoparticles used in the literature investigations are based on thermal conductivity where enhancement of heat transfer rate was obtained significantly.     

Artificial neural network modeling of nanofluid flow in a microchannel heat sink using experimental data

The present paper deals with the artificial neural network modeling (ANN) of heat transfer coefficient and Nusselt number in TiO₂/water nanofluid flow in a microchannel heat sink. The microchannel comprises of 40 channels; each channel has a length of 4 cm, a width of 500 μm, and a height of 800 μm. In the ANN modeling of heat transfer coefficient and Nusselt number 23 and 72 datasets have been used, respectively. The experimental Nusselt number has been calculated based on three different thermal conductivity models, four volume fractions of 0, 0.5, 1, and 2%, two values of Reynolds number i.e. 400 and 1200 and three different heating rates including 50.6, 60.7, and 69.1 W. Therefore, the inputs that are introduced to the neural network are volume fraction of nanoparticles, Reynolds number, heating rate, and model number while the output of network is the Nusselt number. It is elucidated that an appropriately trained network can act as a good alternative for costly and time-consuming experiments on the nanofluid flow in microchannels. The average relative errors in the prediction of Nusselt number and heat transfer coefficients were 0.3% and 0.2%, respectively.     

矩形微通道中流体流动阻力和换热特性实验研究

以去离子水为流体工质,对其在矩形微尺度通道中的流动阻力和传热特性进行了实验研究。通过测量流量、进出口压力和温度等参数,获得了流体流过微通道时的摩擦阻力系数、对流换热过程中的热流通量和N u等。微尺度通道中流体流动的摩擦阻力系数较常规尺度通道中的摩擦阻力系数小,仅是常规尺度通道中摩擦阻力系数的20%~30%;且流动状态由层流向湍流转捩的临界R e也远小于常规尺度通道的。微尺度通道中对流换热的N u与常规尺度通道的显著不同。流量较小时,N u较常规尺度通道中充分发展段的小;随着水流量的增加,微通道的N u迅速增加,并很快超过常规尺度通道的N u,表现出微尺度效应。热流通量对微尺度通道中对流换热N u存在影响,其影响规律在不同流速条件下呈不同趋势,流速较小时,N u基本保持不变;而在流速较大时,N u随热流通量增加而呈增加趋势。     

A Review on Thermophysical Properties and Nusselt Number Behavior of Al_2O_3 Nanofluids in Heat Exchangers

During the last several years, the increase in cooling power requirements for heat exchangers have led to an escalation in heat transfer studies being performed on the use of nanofluids as heat transfer fluids. However, limited effort has been attempted to relate and interpret these findings or the anomalies associated with them. The paper compiles test data from several studies conducted on different types of heat exchangers. In this review, a concentrated effort is spent to clarify the ambiguities regarding the effect of nanoparticle size on the nanofluid thermal conductivity and Nusselt number. Results show that the nanofluid thermal conductivity is not influenced by the nanoparticle size, but by the clustering of the particles themselves. The less compact the structure of the nanoparticle clustering is, the greater the enhancement in the nanofluid thermal conductivity is. Data were also compiled to interpret the relation between the nanofluid flow pattern, nanoparticles volume fraction in the base fluid, and the convective heat transfer. The results from the majority of the heat exchanger studies show an increase in the heat transfer coefficient with the increase in nanoparticle volume fraction. However, studies conducted on plate heat exchanges display some inconsistencies. In the majority of the heat exchanger studies with the exception of few, the decrease in the nanoparticle size is shown to result in an enhancement of the bulk fluid Nusselt number. Compiled test data also reveal that the effectiveness of the alumina nanoparticles is dependent on the flow pattern. The increase in the nanoparticles concentration is shown to result in an increase in the nanofluid heat transfer enhancement as the fluid is transitioning from laminar to turbulent flow. In general, the smaller the nanoparticle size is, the greater the enhancement in the fluid Nusselt number is.     

Generation of entropy during forced convection of heat in nanofluid stagnation-point flows over a cylinder embedded in porous media

Thermodynamics and heat transfer of an impinging nanofluid flow upon a cylinder with constant surface temperature and embedded in porous media are investigated. Numerical solutions reveal the flow velocity and temperature fields as well as the Nusselt number. These are then used to calculate the rate of entropy generation within the system by viscous and heat transfer irreversibilities. It is demonstrated that changes in the concentration of nanoparticles modify the thermal and hydrodynamic boundary layers and hence can alter the Nusselt number and entropy generation considerably. However, the shear stress on the surface of the cylinder is observed to be less affected by the variations in the concentration of nanoparticles. Further, the Reynolds number and non-uniform transpiration are shown to affect the Nusselt number and entropy generation. It is argued that the influences of Reynolds number on the boundary layer thickness can majorly modify the irreversibility and Bejan number.     

Thermal performance of finned aluminum heat sink filled with ERG aluminum foam: Experimental and numerical approach

The rapid improvements in electronic devices have led to a high demand for effective cooling techniques. The purpose of this study was to investigate the heat transfer characteristics and performance of different aluminum heat sinks filled with aluminum foam for an Intel core i7 processor. The aluminum foam heat sinks were subjected to water flow covering the non-Darcy flow regime (300-600 Reynolds numbers). The bottom side of the heat sinks was heated with a heat flux between 8.5 and 13.8 W/cm². Three different heat sinks were examined in this study. Models A, B, and C contained two, three and four channels, respectively. Each channel gap was filled with ERG aluminum foam. The distributions of the local surface temperature and the local Nusselt number were measured for each heat sink design. The experimental data were compared with the numerical results. The average Nusselt number was obtained for the range of Reynolds numbers, and an empirical correlation of the average Nusselt number as a function of the Reynolds number was derived for each heat sink. The pressure drop across the characteristics of each heat sink design was measured. The thermal performance of each aluminum foam heat sink was evaluated based on the average Nusselt number and the required pumping power. The experimental results revealed that model B achieved the highest average Nusselt number compared with models A and C. However, model C had the highest surface to volume ratio; the thermal boundary layers, which are formed on adjacent fin surfaces inside the aluminum foam, interface with each other causing a reduction in the overall heat transfer. The numerical results were in good agreement with experimental data of local Nusselt number and local temperature with maximum relative errors of 2% and 1%, respectively.     

Fluid flow and heat transfer characteristics in rectangular microchannels

Experiments were conducted to investigate flow and heat transfer characteristics of water in rectangular microchannels. All tests were performed with deionized water. The flow rate, the pressures, and temperatures at the inlet and outlet were measured. The friction factor, heat flux, and Nusselt number were obtained. The friction factor in the microchannel is lower than the conventional value. That is only 20% to 30% of the convectional value. The critical Reynolds number below which the flow remains laminar in the microchannel is also lower than the conventional value. The Nusselt number in the microchannel is quite different from the conventional value. The Nusselt number for the microchannel is lower than the conventional value when the flow rate is small. As the flow rate through the microchannel is increased, the Nusselt number significantly increases and exceeds the value of Nusselt number for the fully developed flow in the conventional channel. The micro‐scale effect was exhibited. The Nusselt number is also affected by the heat flux. The Nusselt number remains the constant value when the flow rate is small. The Nusselt number increases with the increase in the heat flux when the flow rate is large. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(4): 197–207, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20206     

Heat transfer enhancement by recirculating flow within liquid plugs in microchannels

Plug flow can significantly enhance heat transfer in microchannels as compared to single phase flow. Using an analytical model of flow field, heat transfer in plug flow is investigated. The constant-surface-temperature boundary condition is considered. Three stages of the heat transfer in plugs are identified: (i) development of thermal boundary layer; (ii) advection of heated/fresh fluid in the plug; and (iii) thermally fully developed flow. Due to the transport of heated fluid and fresh fluid within the plug by the recirculating flow, oscillations of the Nusselt number at high Peclet numbers are observed and explained. The effects of the Peclet number and the plug length on the heat transfer process are evaluated. The results show that short plugs are preferable to long plugs since short plugs result in high Nusselt numbers and high heat transfer indices.     

Heat transfer enhancement through control of thermal dispersion effects

Heat transfer enhancements are investigated inside channels by controlling thermal dispersion effects inside the fluid. Different distributions for the dispersive elements such as nanoparticles or flexible hairy fins extending from the channel plates are considered. Energy equations for different fluid regions are dimensionalized and solved analytically and numerically. The boundary arrangement and the exponential distribution for the dispersive elements are found to produce enhancements in heat transfer compared to the case with a uniform distribution for the dispersive elements. The presence of the dispersive elements in the core region does not affect the heat transfer rate. Moreover, the maximum Nusselt number for analyzed distributions of the dispersive elements are found to be 21% higher than that with uniformly distributed dispersive elements for a uniform flow. On the other hand, the parabolic velocity profile is found to produce a maximum Nusselt number that is 12% higher than that with uniformly distributed dispersive elements for the boundary arrangement. The distribution of the dispersive elements that maximizes the heat transfer is governed by the flow and thermal conditions plus the properties of the dispersive elements. Results in this work point towards preparation of super nanofluids or super dispersive media with enhanced cooling characteristics.     

Effect of Thermal Buoyancy on Fluid Flow and Heat Transfer Across a Semicircular Cylinder in Cross-Flow at Low Reynolds Numbers

The influence of superimposed thermal buoyancy on hydrodynamic and thermal transport across a semicircular cylinder is investigated through numerical simulation. The cylinder is fixed in an unconfined medium and interacted with an incompressible and uniform incoming flow. Two different orientations of the cylinder are considered: one when the curved surface is exposed to the incoming flow and the other when the flat surface is facing the flow. The flow Reynolds number is varied from 50 to 150, keeping the Prandtl number fixed (Pr = 0.71). The effect of superimposed thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ Ri ≤ 2. The unsteady two-dimensional governing equations are solved by deploying a finite volume method based on the PISO (Pressure Implicit with Splitting of Operator) algorithm. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds and Richardson numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag, lift and pressure coefficients, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. Additionally, intriguing effects of thermal buoyancy can be witnessed. It is established that heat transfer rate differs significantly under the superimposed thermal buoyancy condition for the two different orientations of the obstacle.     

Conjugate natural convection in a fluid-saturated porous enclosure with two solid vertical partitions

Conjugate natural convection in a fluid-saturated square porous enclosure with two solid vertical partitions of finite and equal thickness equispaced from center of enclosure is investigated in this paper. The primary objective is to attenuate the Nusselt number (Nu) and hence the heat transfer rate across a differentially heated enclosure. Darcy's model is considered. Numerical computation is performed using successive accelerated replacement and explicit scheme. Partition ratio, partition length, thermal conductivity ratio, and modified Rayleigh number are the parameters under study. Fluid flow is analyzed by observing transient changes of streamlines and isotherms for partition length 0.3-1, thermal conductivity ratio 0.5-2, partition ratio 0.1-0.3 and modified Rayleigh number 100 and 1000 where partition ratio is the ratio of distance between center of enclosure and either of the partition center to the total length of the enclosure; while Nusselt number is calculated to estimate the heat transfer rate for each configuration. It is found that, employing a solid partition within the enclosure most definitely reduces the Nusselt number. The drop in Nusselt number is more for partition length 0-0.6 after which it does show a drop in Nu but only very subtle. Further, Nu is the least for partition ratio 0.2. Also, Nusselt number is proportional to thermal conductivity ratio which is the ratio of thermal conductivity of solid to porous medium.     

Effects of Magnetic Field and Inclination on Natural Convection in a Cavity Filled with Nanofluids by a Double Multiple-Relaxation-Time Thermal Lattice Boltzmann Method

Abstract

The present study numerically investigates the magneto-hydrodynamic flow and heat transfer of copper (Cu)-water nanofluids in an inclined cavity with one heat and one cold source. Simulations have been done via double multiple-relaxation-time thermal lattice Boltzmann method. Impacts of Hartmann number, Rayleigh number, inclination angle and the volume fraction of nanoparticles on the fluid flow and heat transfer performance are illustrated in terms of streamlines, isotherms, local, and average Nusselt numbers. Outputs demonstrate that the average Nusselt number decreases remarkably first as the inclination angle increases and then the average Nusselt number increases continuously and approaches a maximum value at a certain inclination angle for high Rayleigh numbers. In addition, the position where the average Nusselt number is maximized moves toward the lower inclination angle with increasing the Hartmann number for high Rayleigh numbers.     

APPLICATION OF GROOVED FINS TO ENHANCE FORCED CONVECTION TO TRANSVERSE FLOW

A numerical study is performed to investigate the heat transfer characteristics of a two-dimensional forced convection over a plate with protruded transverse groove fins. The study is made for four geometries, five different Reynolds numbers, and for more groove fins with smaller size. Numerical analysis is carried out to investigate the flow patterns, isotherms, heat transfer rates, and the effectiveness of the increased grooves. Local Nusselt number and total heat transfer rate are calculated and the average Nusselt number is correlated as a function of Reynolds and Prandtl numbers. Protruded grooves yield a much larger heat transfer rate than a flat plate owing to flow penetration into the groove. Grooved fins with protruded mounting are suitable for heat transfer enhancement, and the total length is recommended not to exceed the reattachment length significantly. The derived correlations and physical considerations may be used when designing grooved plates to enhance heat transfer.     

Heat transfer augmentation in a circular tube with perforated double counter twisted tape inserts

The present study explored the effects of perforated double counter twisted tapes on heat transfer and fluid friction characteristics in a heat exchanger tube. The twisted tapes with four different porosities of R_p = 1.2, 4.6, 10.4 and 18.6% were used as counter-swirl flow generators in the test section. The experiments were conducted in a circular tube in turbulent flow regime with Reynolds number ranging from 7200 to 50,000 using air as the working fluid under uniform wall heat flux boundary condition. The experimental results demonstrated that the Nusselt number, friction factor and thermal enhancement efficiency were increased with decreasing porosity except porosity of 1.2%. The results also revealed that the heat transfer rate of the tube fitted with tapes were significantly increased with corresponding increase in friction factor. In the range of the present investigation, heat transfer rate and friction factor were obtained to be around 80 to 290% and 111 to 335% higher than those of the plain tube values, respectively. Based on constant blower power, the highest thermal enhancement efficiency of 1.44 was achieved. In addition, the empirical correlations of Nusselt number, friction factor and thermal enhancement efficiency were developed based on the experimental data.