Numerical solution of power law fluids flow and heat transfer with a magnetic field in a rectangular duct

The steady laminar flow and heat transfer of an incompressible, electrically conducting, power law non-Newtonian fluids in a rectangular duct are studied in the presence of an external uniform magnetic field. The momentum and energy equations are solved iteratively using a finite difference method. Two cases of the thermal boundary conditions are considered; (1) T thermal boundary condition “constant temperature at the wall” and (2) H2 thermal boundary condition “constant heat flux at the wall”. The viscous and Joule dissipations are taken into consideration in the energy equation. A numerical solution for the governing partial differential equations is developed and the influence of the magnetic field on the velocity distribution, the friction factor and the average Nusselt number are discussed.     

矩形肋片导流角度对内冷通道流动与换热特性的影响

利用数值模拟方法分析了矩形仿螺旋肋片内冷通道中肋片导流角度对内冷通道三维流场特性、换热特性以及流动阻力特性的影响。数值计算结果表明,肋片导流角度对内冷通道的流动与换热特性具有较大的影响。流场中冷却介质螺旋流动的强度随着肋片导流角增大而增强,肋片导流角度越大则内冷通道的换热强度越强,同时通道中流动阻力也明显增大。从内冷通道的综合换热效果来看,当肋片导流角度为7。时,矩形仿螺旋肋片内冷通道的综合换热效果最好。     

Numerical simulation of buoyancy-assisting,backward-facing step flow and heat transfer in a rectangular duct

Two- and three-dimensional numerical simulations have been performed for mixed convective upward flows over a backward-facing step in a duct. The Reynolds number, expansion ratio, and aspect ratio (in 3-D simulations) were kept constant at Re = 125, ER = 2, and AR = 16, respectively. The heat flux at the wall downstream of the step was uniform. The straight wall, the step, and the side walls (in 3-D simulations) were assumed to be adiabatic. The effect of the buoyancy level, Ri^*, was the major interest in this study. It was found that the reattachment point and the peak Nusselt number point moved upstream as Ri^* was increased. The secondary recirculation region, which developed at the corner of the step, became larger. A secondary flow was also found in a cross section immediately downstream of the step. Flow directed toward the center of the duct became more intensive as Ri^* increased, which possibly resulted from an increase in the level of three-dimensionality of the flow and thermal fields. © 1999 Scripta Technica, Heat Trans Asian Res, 28(1): 58–76, 1999     

MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity and hall effect

In the present paper the laminar fully developed MHD flow and heat transfer through a rectangular duct of a viscous incompressible electrically conducting fluid is studied. A constant pressure gradient and an external uniform magnetic field are applied and the Hall effect is taken into consideration. The fluid viscosity is assumed to be temperature dependent with the assumption of constant wall heat flux axially and constant wall temperature peripherally. A numerical solution for the governing non-linear partial differential equations is obtained. The effect of the Hall term and the variable viscosity on the velocity and temperature fields is examined.     

Experimental investigation on heat transfer and fluid flow characteristics of air flow in a rectangular duct with Multi v-shaped rib with gap roughness on the heated plate

In this work, results of an experimental investigation of the effect of geometrical parameters of Multi v-shaped ribs with gap on heat transfer and fluid flow characteristics of rectangular duct with heated plate having rib roughness on its underside have been reported. The range of parameters for this study has been decided on the basis of practical considerations of the system and operating conditions of solar air heaters. The experimental investigation encompassed the Reynolds number (Re) range from 2000 to 20,000, relative width ratio (W/w) of 6, relative gap distance (Gd/Lv) of 0.24–0.80, relative gap width (g/e) of 0.5–1.5, relative roughness height (e/D) of 0.043,relative roughness pitch (P/e) of 10, angle of attack (α) of 60°. The maximum enhancement in Nusselt number and friction factor is observed to be 6.32–6.12 times of that of the smooth duct, respectively. The thermo-hydraulic performance parameter is found to be the best for the relative gap distance of 0.69 and the relative gap width of 1.0.     

Numerical investigation of fluid flow and heat transfer under high heat flux using rectangular micro-channels

A 3D-conjugate numerical investigation was conducted to predict heat transfer characteristics in a rectangular cross-sectional micro-channel employing simultaneously developing single-phase flows. The numerical code was validated by comparison with previous experimental and numerical results for the same micro-channel dimensions and classical correlations based on conventional sized channels. High heat fluxes up to 130 W/cm² were applied to investigate micro-channel thermal characteristics. The entire computational domain was discretized using a 120 × 160 × 100 grid for the micro-channel with an aspect ratio of (α = 4.56) and examined for Reynolds numbers in the laminar range (Re 500–2000) using FLUENT. De-ionized water served as the cooling fluid while the micro-channel substrate used was made of copper. Validation results were found to be in good agreement with previous experimental and numerical data [1] with an average deviation of less than 4.2%. As the applied heat flux increased, an increase in heat transfer coefficient values was observed. Also, the Reynolds number required for transition from single-phase fluid to two-phase was found to increase. A correlation is proposed for the results of average Nusselt numbers for the heat transfer characteristics in micro-channels with simultaneously developing, single-phase flows.     

Laminar heat transfer in an asymmetrically heated rectangular duct

This paper presents a numerical study concerning the effects of non-uniform heating on the heat transfer of a thermally undeveloped gas flow in a horizontal rectangular duct; a vertical side wall is uniformly heated, and the other walls are insulated. As an initial step of the study, the duct flow is assumed to be laminar, and buoyancy effects are considered. The heat transfer rate and drag increase with the secondary flow due to buoyancy; the effects of the buoyancy force on the heat transfer and friction coefficient of the thermally undeveloped region are found to depend only upon modified Grashof numbers of the duct entrance.     

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     

Three dimensional laminar non-Newtonian fluid flow and heat transfer in the entrance region of a cross-shaped duct

The Galerkin finite element is used to solve the three dimensional momentum and energy equations for laminar non-Newtonian flow in cross-shaped straight duct. Both flow and heat transfer develop simultaneously from the entrance of the channel. Uniform wall temperature (T) and also constant wall heat flux both axially and peripherally (H2) are used as thermal boundary conditions. The power-law model is chosen to characterize the non-Newtonian behaviour of the fluid. The effect of power-law index and geometric parameter on the apparent friction factor as well as Nusselt number are presented and discussed.     

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。     

Direct numerical simulation of fluid flow and heat transfer in periodic wavy channels with rectangular cross-sections

Fully-developed flow and heat transfer in periodic wavy channels with rectangular cross sections are studied using direct numerical simulation, for increasing Reynolds numbers spanning from the steady laminar to transitional flow regimes. The results show that steady flow is characterized by the formation of symmetric secondary flow or Dean vortices when liquid flows past the bends. It is found that the patterns of Dean vortices may evolve along the flow direction, thus leading to chaotic advection, which can greatly enhance the convective fluid mixing and heat transfer. With increasing Reynolds numbers, the flow undergoes transition from a steady state to a periodic one with a single frequency, and subsequently to a quasiperiodic flow with two incommensurate fundamental frequencies. Within these unsteady regimes, the flow is characterized by very complex Dean vortices patterns which evolve temporally and spatially along the flow direction, and the flow symmetry may even be lost. Further increase in Reynolds number leads to chaotic flow, where the Fourier spectrum of the velocity evolution becomes broadband. The bifurcation scenario in wavy channels may thus share some common features with the well-known Ruelle–Takens–Newhouse scenario. Heat transfer simulation in all flow regimes is carried out with constant wall temperature condition and liquid water as the coolant. It is found that due to the efficient mixing in wavy channels, the heat transfer performance is always significantly more superior to that of straight channels with the same cross sections; at the same time the pressure drop penalty of wavy channels can be much smaller than the heat transfer enhancement. The present study shows that these wavy channels may have advantages over straight channels and thus serve as promising candidates for incorporation into efficient heat transfer devices.     

Forced convection heat transfer to water with air injection in a rectangular duct

A study was made of forced convection heat-transfer to water and air-water mixtures in a horizontal rectangular duct with air injection through one porous heated wall. The main independent variables are the rate of air injection through the porous wall, the superficial liquid velocity in the duct, and the amount of air mixed with the water upstream of the heated test section; the method of mixing the upstream air and water is also varied. The dependent variables reported are the heat-transfer coefficient, over a range of approximately 60:1, and the flow pattern, extending from bubble flow through to annular flow.     

An Investigation of the Swirling Flow and Heat Transfer in a Duct

This paper presents the results of experiments and numerical simulation of the turbulent swirling flow and heattransfer in a duct.The calculated results are in good agreement with data obtained by measurements.It isfound that the swirling flow promotes heat transfer to the wall of the duct;the swirl numbers are dependentupon the vane exit angles of the swirler,distance from the swirler and the duct Reynolds number.But the decayof swirling flow in streamwise direction is related to local Reynolds numbers and is independent of the swirlerexit angle.The swirl flow characteristics presented in this paper may be used for engineering purposes.     

Experiments on laminar flow and heat transfer in an elliptical duct

Experiments were performed to study the laminar developing and fully developed flow and heat transfer inside an elliptical duct having an aspect ratio of 0.5. The working fluid was air and two thermal situations were investigated, the first with the duct at a uniform temperature and the second when the wall temperature distribution is linear in the axial direction and does not vary transversely. The hydrodynamic results are presented in the form of a sequence of velocity profiles on the major and minor axes, measured at axial locations extending from the duct entrance to the fully developed regime. The axial drop in the static pressure due to the combined effect of the flow development and wall friction is also reported. The extended length necessary for static pressure development, expressed as x/Re D_h, was found to be 0.0345. The thermal information depicts the temperature development in the duct entrance by a series of temperature profiles on the major and minor axes. The thermal results encompass as well the Nusselt number and the thermal entrance length in each of the above two thermal situations. To the author's knowledge, theoretical solutions for the hydrodynamic flow development in the entrance of elliptical ducts do not exist. The present experimental fully developed dimensionless velocity and friction factor were compared to the analytic value of L. N. Toa [On some laminar-forced-convection problems, ASME J. Heat Trans. 83, 466–472 (1961)]. The percentage difference in the friction factor is 0.78%. The thermal development of the flow in the elliptical duct was studied analytically by N. T. Dunwoody [Thermal results for forced heat convection through elliptical ducts, J. appl. Meal. 29, 165–170 (1962)] and V. Javeri [Analysis of laminar thermal entrance region of elliptical and rectangular channels with the Kantorowich method, Wärme Stoffubert. 9, 85–98 (1976)] for the uniform and linear wall temperature ducts respectively. Both analyses assume either uniform or fully developed velocity profiles in the developing regime.     

矩形通道内冲孔矩形小翼涡流发生器的流动换热特性

雷诺数Re=214～10 703时,通过数值模拟方法对布置有冲孔和无孔的两种矩形小翼涡流发生器的矩形通道进行了传热和流阻特性的研究。计算结果表明:在低雷诺数下,冲孔矩形小翼涡流发生器的传热因子j值与无孔矩形小翼涡流发生器相差不大,而在高雷诺数下,冲孔涡流发生器的传热因子j值略低于无孔涡流发生器,大约低1.03%～3.05%。在相同的雷诺数下,无孔矩形小翼涡流发生器的阻力因子f大于冲孔涡流发生器,而且随着雷诺数的增大二者的差距也越来越大。通过对比综合性能指标可知,两种通道的综合性能指标均随着雷诺数的增加而减小,而且冲孔矩形小翼涡流发生器的综合性能要优于无孔矩形小翼涡流发生器。     

哥氏力对旋转方通道内流动与换热的影响

在雷诺数亿为6000,旋转数助为0～0．26内,数值模拟了旋转光滑径向出流通道的内流动与换热分布,分析了哥氏力对旋转管流的作用机理。计算结果表明,切向哥氏力推动了通道截面内的双涡二次流,径向哥氏力则使得近侧壁流体加速和中心流体减速。换热计算结果从定性趋势上吻合公开文献中的实验现象。反映了旋转附加力的基本影响规律。     

Laminar forced convection heat transfer of a non-newtonian fluid in a square duct

Numerical solutions for laminar heat transfer of a non-Newtonian fluid in the thermal entrance region of a square duct are presented for three thermal boundary conditions. The power-law model characterises the non-Newtonian behavior. The numerical results show that for each flow behavior index the Nusselt number decreases from a maximum value at the entry plane to a limiting value when both velocity and temperature profiles are fully developed. The results are compared with the available solutions for Newtonian fluid and excellent agreement is found.     

Non-Newtonian laminar pulsating heat and fluid flow in plane duct

In the present study, laminar pulsating power-law momentum and heat transfer in a uniformly heated plane duct is studied analytically. Assuming that fully developed conditions exist both hydrodynamically and thermally, a perturbation series method is utilized to derive analytical solutions for the momentum and energy balance equations, and the amplitude is prescribed as the perturbation parameter. For varying values of the power-law index ( $n$), representing pseudoplastic, Newtonian, and dilatant fluids, effects of dimensionless amplitude ( $ϵ$) and frequency ( $F$) on periodic and period-averaged friction factor and Nusselt number are obtained. The results obtained for Newtonian fluid are shown to be in good harmony with the corresponding findings in the open literature.