Adverse and favorable mixed convection heat transfer in a two-side heated square channel

Experimental heat transfer measurements and analysis for mixed convection in a vertical square channel are presented. Water flow directions are selected such that buoyancy assists or opposes the bulk flow pressure gradient. Unlike most previous experiments with symmetrically heated circular tubes, the present configuration uses an asymmetric heating condition (two sides heated and two sides insulated) and shows significant increase in the Nusselt number for both assisted and opposed flow conditions. Observed heat transfer coefficient distributions are different from the symmetrically heated channels; and this difference in heat transfer coefficient is attributed to the formation of buoyancy driven large-scale flow structures. In general, opposed flow shows higher heat transfer coefficients, and the Nusselt number ratio is observed to increase as Gr/Re or Gr/Re² ratios increase for both assisted and opposed flow conditions. A correlation based on the buoyancy parameter predicts the heat transfer pattern well in both assisted and opposed mixed convection. The range of Reynolds numbers discussed (Re=400–10,000) is of importance for direct numerical simulations and the details provided here can serve as the benchmark data required for complicated buoyancy affected turbulence simulations.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

Three-dimensional numerical study and field synergy principle analysis of wavy fin heat exchangers with elliptic tubes

Three dimensional numerical studies were performed for laminar heat transfer and fluid flow characteristics of wavy fin heat exchangers with elliptic/circular tubes by body-fitted coordinates system. The simulation results of circular tube were compared with the experiment data, then circular and elliptic (e = b/a = 0.6) arrangements with the same minimum flow cross-sectional area were compared. A max relative heat transfer gain of up to 30% is observed in the elliptic arrangement, and corresponding friction factor only increased by about 10%. The effects of five factors on wavy fin and elliptic tube heat exchangers were examined: Reynolds number (based on the smaller ellipse axis, 500  4000), eccentricity (b/a, 0.6  1.0), fin pitch (F_p/2b, 0.05  0.4), fin thickness (F_t/2b, 0.006  0.04) and tube spanwise pitch (S₁/2b, 1.0  2.0). The results show that with the increasing of Reynolds number and fin thickness, decreasing of the eccentricity and spanwise tube pitch, the heat transfer of the finned tube bank are enhanced with some penalty in pressure drop. There is an optimum fin pitch (F_p/2b = 0.1) for heat transfer, but friction factor always decreases with increase of fin pitch. And when F_p/2b is larger than 0.25, it has little effects on heat transfer and pressure drop. The results were also analyzed from the view point of field synergy principle. It was found that the effects of the five factors on the heat transfer performance can be well described by the field synergy principle.     

Conjugate natural convection from an array of discrete heat sources: part 1 — two- and three-dimensional model validation

Two- and three-dimensional (2- and 3-D) numerical models have been developed for conjugate natural convection in a discretely heated cavity. Experimental results obtained for the same geometry, using water and FC-77 as the coolants, were in excellent agreement with the 3-D numerical predictions. In contrast, because of the inability to account for thermal spreading in the lateral direction, the 2-D model overpredicted measured average surface temperatures of the discrete heat sources. However, the 2-D model still predicted general trends and flow patterns that were experimentally obtained. The nature and extent of 3-D effects on the flow and heat transfer have been delineated.     

Mathematical simulation of conjugate mixed convection in a rectangular region with a heat source

Conjugate convective-conductive heat transfer in a rectangular region with forced flow and a heat source is simulated numerically. Distributions of the thermal and hydrodynamic characteristics of the flow regimes studied are obtained. The evolution of the process analyzed is shown. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 69–81, November–December, 2008     

Numerical simulation of natural and mixed convection flows by Galerkin‐characteristic method

A numerical investigation is performed to study the solution of natural and mixed convection flows by Galerkin‐characteristic method. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization in primitive variables. It can be interpreted as a fractional step technique where convective part and Stokes/Boussinesq part are treated separately. The main feature of the proposed method is that, due to the Lagrangian treatment of convection, the Courant–Friedrichs–Lewy (CFL) restriction is relaxed and the time truncation errors are reduced in the Stokes/Boussinesq part. Numerical simulations are carried out for a natural convection in squared cavity and for a mixed convection flow past a circular cylinder. The computed results are compared with those obtained using other Eulerian‐based Galerkin finite element solvers, which are used for solving many convective flow models. The Galerkin‐characteristic method has been found to be feasible and satisfactory. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers

A numerical investigation of the mixed convection heat transfer from vertical helically coiled tubes in a cylindrical shell at various Reynolds and Rayleigh numbers, various coil‐to‐tube diameter ratios and non‐dimensional coil pitches was carried out. The particular difference in this study compared with other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid‐to‐fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell‐side mass flow rate on shell‐side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell‐side of the heat exchanger reasonably demonstrates the desired relation. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical study of turbulent flow over two‐dimensional surface‐mounted ribs in a channel

This study accurately predicts the cases of turbulent flow around a surface‐mounted two‐dimensional rib with varying lengths. The numerical method employs a differencing scheme for integrating the elliptic Reynolds‐averaged Navier–Stokes equations and the continuity equation. A two‐equation k–ε turbulence model is employed to simulate the turbulent transport quantities and close the solving problem. The near‐wall regions of the separated sides of the rib are resolved by a near‐wall model of a two‐layer approach instead of the wall function approximation. Computations for flow over a surface‐mounted rectangular rib are conducted for the variations in the rib lengths. Results indicate that upstream of the obstacle, the length of the recirculating region remains unchanged with varying rib lengths; while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly for the varying lengths of B/H=0.1 to B/H=4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development. Copyright © 1999 John Wiley & Sons, Ltd.     

Three dimensional simulations of penetrative convection in a porous medium with internal heat sources

The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.     

On the Reynolds-number independence of mixed convection in a vertical channel subjected to asymmetric wall temperatures with and without flow reversal

The problem of mixed convection in a vertical channel with asymmetric wall temperatures including situations of flow reversal is studied numerically. The SIMPLER algorithm with a staggered grid system is employed to solve the corresponding numerical equations formulated by the finite-volume method. A second-order upwind scheme is used to model the convective term, and a suitable grid distribution is introduced. The ranges of the parameters studied are 0 r_t 1, 1 Re 1000, and 0 Gr/Re 500.

The numerical results, with the streamwise coordinate scaled by the Reynolds number (Re), show that solutions for the velocity and temperature fields are independent of the Reynolds number when Re 50, even in the presence of flow reversal. These solutions, however, are dependent on r_t and Gr/Re. Subsequently, correlations are proposed for the bulk temperature distribution and the local Nusselt numbers along the hot wall and the cold wall.     

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.     

液封液桥内热毛细对流的数值模拟

建立了液封液桥(不相溶混的双层同轴液柱)内热毛细对流的物理数学模型,采用涡量-流 函数法、利用有限差分格式对微重力条件下液封液桥内热毛细对流进行了数值模拟,得到了 双层液柱主流区的温度场和流场,证实了液封技术能削弱液桥主流区的热毛细对流,从而提 高浮区晶体生长质量,找出了液封厚度以及内、外层流体物性参数比对液桥内热毛细对流的 影响规律.     

Flow and heat transfer analysis in porous wick of CPL evaporator based on field synergy principle

In order to optimize the structure of a CPL evaporator and enhance heat transfer, a mathematical and physical model is developed to analyze the flow and heat transfer in the porous wick of the evaporator, whose calculation domain is divided into two parts: vapor-saturated region and liquid-saturated region. The characteristics of flow and heat transfer in the porous wick of a CPL evaporator have been numerically studied according to the field synergy principle. The influences of geometrical structures and heat flux on heat transfer enhancement are analyzed and illustrated by the figures in the present paper.     

Numerical solution of the three‐dimensional fluid flow in a rotating heterogeneous porous channel

A numerical solution to the problem of the three‐dimensional fluid flow in a long rotating heterogeneous porous channel is presented. A co‐ordinate transformation technique is employed to obtain accurate solutions over a wide range of porous media Ekman number values and consequent boundary layer thicknesses. Comparisons with an approximate asymptotic solution (for large values of Ekman number) and with theoretical predictions on the validity of Taylor–Proudman theorem in porous media for small values of Ekman number show good qualitative agreement. An evaluation of the boundary layer thickness is presented and a power‐law correlation to Ekman number is shown to well‐represent the results for small values of Ekman number. The different three‐dimensional fluid flow regimes are presented graphically, demonstrating the distinct variation of the flow field over the wide range of Ekman numbers used. Copyright © 1999 John Wiley & Sons, Ltd.     

Effect of nanoparticles mean diameter on mixed convection heat transfer of a nanofluid in a horizontal tube

Fully developed mixed convection of a nanofluid (water/Al₂O₃) has been studied numerically. Two-phase mixture model has been used to investigate the effects of nanoparticles mean diameter on the flow parameters. The calculated results demonstrate that the convection heat transfer coefficient significantly increases with decreasing the nanoparticles means diameter. However it does not significantly change the hydrodynamics parameters. Nanoparticles distribution at the tube cross section shows that the non-uniformity of the particles distribution augments when using larger nanoparticles and/or considering relatively high value of the Grashof numbers.     

正弦波温度边界下多孔介质方腔内非热平衡对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化、右侧壁面温度均一的边界条件下,通过SIM-PLER算法数值研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:正弦波温度边界使得方腔内的流场出现了复杂的变化,流体及固体区域左侧壁面附近出现了周期性的正负变化的温度场分布,左侧壁面局部Nusselt数出现了周期性的震荡现象;存在一个最佳温度波动参数N=1,此时多孔介质方腔内的整体散热量达到最大值;增加方腔高宽比会显著地削弱方腔内的自然对流传热过程,小高宽比也会在一定的程度上削弱多孔介质方腔内的对流传热。     

Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated.The plate exchanges heat with an external fluid.Both conditions of equal and different reference temperatures of the external fluid are considered.First,the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically.Then,the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter.To relax the conditions on the perturbation parameter,the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique.The velocity,temperature,skin friction,and Nusselt numbers at the plates are discussed numerically and presented through graphs.