Parametric studies and correlations for combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate

The present paper reports the parametric studies and correlations for the problem of combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate. Three discrete heat sources of non-identical heights but with identical volumetric rate of heat generation are assumed to be flush-mounted in a thin vertical plate. The longest and the shortest heaters are provided at the leading and trailing edges of the plate, while the remaining heater is located centrally. The governing fluid flow and heat transfer equations are considered in their full strength without the boundary layer approximations and are solved using the finite volume method. A computer code is written to solve the problem and various parametric studies have been performed. The relative roles of free convection, forced convection and radiation in various fluid flow and heat transfer results have been elucidated. In conclusion, based on a large set of data generated from the code, correlations for maximum non-dimensional plate temperature, average non-dimensional plate temperature and mean friction coefficient have been evolved.     

ISPH modeling of natural convection heat transfer with an analytical kernel renormalization factor

The objective of this study is to extend the attention of the incompressible smoothed particle hydrodynamics method (ISPH) in the heat transfer field. The ISPH method for the natural convection heat transfer under the Boussinesq approximation in various environments: pure-fluid, nanofluid, and non-Darcy porous medium is introduced. We adopted the improved analytical method for calculating the kernel renormalization factor and its gradient based on a quintic kernel function for the wall boundary treatment in the ISPH method. The proposed method requires no dummy particle layer to meet the impermeability condition and makes the heat flux over the wall boundary easy to implement. We performed four different numerical simulations of natural convection in cavities with increasing complexity in modeling and implementation: the natural convection in a square cavity with constant differentially heated wall temperature, natural convection with the heat flux from the bottom wall for a wide range of Rayleigh numbers, natural convection in a non-Darcy porous cavity fully filled with nanofluid in different flow regimes, and natural convection in a partially layered porous cavity. The results showed excellent agreement with results from literatures and the in-house P1–P1 finite element method code.     

Interaction of surface radiation with combined conduction and convection from a discretely heated L-corner

Prominent results pertaining to the problem of multi-mode heat transfer from an L-corner equipped with three identical flush-mounted discrete heat sources in its left leg are given here. The heat generated in the heat sources is conducted along the two legs of the device before being dissipated by combined convection and radiation into air that is considered to be the cooling agent. The governing equations for temperature distribution along the L-corner are obtained by making appropriate energy balance between the heat generated, conducted, convected and radiated. The non-linear partial differential equations thus obtained are converted into algebraic form using a finite-difference formulation. The resulting equations are solved simultaneously by Gauss–Seidel iterative solver. A computer code is specifically written to solve the problem. The computational domain is discretised using 101 grids along the left leg, with 15 grids taken per heat source, and 21 grids along the bottom leg. The effects of surface emissivity, convection heat transfer coefficient, thermal conductivity and aspect ratio on local temperature distribution, peak device temperature and relative contributions of convection and radiation to heat dissipation from the L-corner are studied in detail. The point that one cannot overlook radiation in problems of this class has been clearly elucidated.     

Volumetric methods for evaluating energy loss and heat transfer in cavity flows

Methods have been developed for calculating irreversible energy losses and rates of heat transfer from computational fluid dynamics solutions using volume integrations of energy dissipation or entropy production functions. These methods contrast with the more usual approach of performing first law energy balances over the boundaries of a flow domain. Advantages of the volumetric approach are that the estimates involve the whole flow domain and are hence based on more information than would otherwise be used, and that the energy dissipation or entropy production functions allow for detailed assessment of the mechanisms and regions of energy loss or entropy production. Volume integrations are applied to the calculation of viscous losses in a lid‐driven cavity flow, and to the viscous losses and heat transfer due to natural convection in a side‐heated cavity. In the convection problem comparison with the entropy increase across a stationary heat conducting layer leads to a novel volume integral expression for the Nusselt number. The predictions using this method compare well with traditional surface integrals and benchmark results. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical simulation of three-dimensional natural convection inside a heat generating anisotropic porous medium

Natural convection in anisotropic heat generating porous medium enclosed inside a rectangular cavity has been studied. A 3D finite volume based code is developed using the Darcy approximation and validated using experimental results of natural convection around an enclosed rod bundle. Subsequently, detailed simulation is carried out for a cavity, filled with orthotropic porous medium. The effects of heat generation, geometry and anisotropy are studied. Anisotropy is found to be of significant importance for both maximum value and distribution of temperature.     

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 analysis of mixed convection in three‐dimensional rectangular channel with flush‐mounted heat sources based on field synergy principle

In this paper the fluid flow and heat transfer characteristics of mixed convection in three‐dimensional rectangular channel with four heat sources are investigated numerically. The SIMPLEC algorithm is applied to deal with the coupling between pressure and velocity, and a new high‐order stability‐guaranteed second‐order difference (SGSD) scheme is adopted to discretize the convection term. The influence of four parameters is studied: Richardson number, heat source distribution, channel height and inclination angle. The numerical results are analysed from the viewpoint of the field synergy principle, which says that the enhanced convective heat transfer is related not only to the velocity field and temperature field, but also to the synergy between them. It is found that the effects of the four parameters on the thermal performance can all be explained with the field synergy principle. To obtain better electronic cooling, the synergy between the velocity and temperature gradient should be increased when other conditions are unchanged. Copyright © 2006 John Wiley & Sons, Ltd.     

Experimental and numerical study on unsteady natural convection heat transfer in helically coiled tube heat exchangers

Both of experimental and numerical investigations were performed to understand unsteady natural convection from outer surface of helical coils. Four helical coils with two different curvature ratios were used. Each coil was mounted in the shell both vertically and horizontally. The cold water was entered the coil and the hot water in the shell was cooling by unsteady natural convection. A CFD code was developed to simulate natural convection heat transfer. Equations of tube and shell are solved simultaneously. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It was revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, specific heat of fluids and geometrical parameters including length, inner diameter of the tube and the volume of the shell, and time.     

Development of numerical techniques for near‐field aeroacoustic computations

This work is concerned with the development of a numerical scheme capable of producing accurate simulations of sound propagation in the presence of a mean flow field. The method is based on the concept of variable decomposition, which leads to two separate sets of equations. These equations are the linearised Euler equations and the Reynolds‐averaged Navier–Stokes equations. This paper concentrates on the development of numerical schemes for the linearised Euler equations that leads to a computational aeroacoustics (CAA) code. The resulting CAA code is a non‐diffusive, time‐ and space‐staggered finite volume code for the acoustic perturbation, and it is validated against analytic results for pure 1D sound propagation and 2D benchmark problems involving sound scattering from a cylindrical obstacle. Predictions are also given for the case of prescribed source sound propagation in a laminar boundary layer as an illustration of the effects of mean convection. Copyright © 1999 John Wiley & Sons, Ltd.     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

Large eddy simulation of natural convection along a vertical isothermal surface

Large eddy simulations of natural convection along a vertical isothermal surface have been carried out using a parallel CFD code SMAFS (Smoke Movement And Flame Spread) developed by the first author to study the dynamics of the natural convection flow and the associated convective heat transfer, with sub-grid scale turbulence modeled using the Smagorinsky model. In the computation, the filtered governing equations are discretized using finite volume method, with the variables at the cell faces in the finite volume discrete equations approximated by a second order bounded QUICK scheme and the diffusion term computed based on central difference scheme. The computation was time marched explicitly, with momentum equations solved based on a second order fractional-step Adams–Bashford scheme and enthalpy computed using a second order Runge–Kutta scheme. The Poisson equation for pressure from the continuity equation was solved using a multi-grid solver. The results including the temperature and velocity profiles of the boundary layer and the local heat transfer rate are analyzed. Comparison is made with experimental data and good agreement is found.     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999     

3D Numerical study of the effect of aspect ratio on mixed convection air flow in upward solar air heater

A 3D Numerical study of mixed convection air flow in upward solar air heater with large spanwise aspect ratio (A = 10 to 40) was performed using CFD commercial code Fluent 14.5 (ANSYS). The main objective of this study is to investigate the channel height's effect (aspect ratio) on flow pattern and heat transfer in upward solar air heater in the particular case of low Re and high aspect ratio. The bottom plate (absorber) was submitted to Constant Heat Flux (CHF) in the range of 200 to 1000 W/m² and Reynolds number was varied from 50 to 1000. Our results are in concordance with most of authors conclusions about Poiseuille–Rayleigh–Benard flows. In mixed convection, increasing heat flux enhances heat transfer unlike forced convection flows. Simulation results of flow visualizations and Nusselt number calculations have shown that depending on Ri*, the velocity and temperature distributions in SAH vary greatly with the channel's height. The obtained results were different from previous studies. Indeed, our investigation of channel's height was achieved for the same heat flux but different Grashof numbers. For low channel's heights (high aspect ratio), increasing heat flux has not a significant effect but for higher channel's heights, an augmentation of heat flux enhances buoyancy effects in the flow and causes high turbulence. Also, increasing Reynolds number in low channel's heights (high A), can enhance substantially heat transfer. For higher channel's heights (low A), increasing Reynolds number decreases Ri* and thus buoyancy forces. Heat transfer is reduced and so Nusselt number. The obtained results may be very useful for engineers in designing and testing solar collectors.     

Level‐set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavity

In the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo‐solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi‐component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two‐dimensional code is extended to treat axis‐symmetric geometries. The code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level‐set related tools of redistancing and off‐interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd.     

A combined level set/ghost cell immersed boundary representation for floating body simulations

A six degrees of freedom (6DOF) algorithm is implemented in the open‐source CFD code REEF3D. The model solves the incompressible Navier–Stokes equations. Complex free surface dynamics are modeled with the level set method based on a two‐phase flow approach. The convection terms of the velocities and the level set method are treated with a high‐order weighted essentially non‐oscillatory discretization scheme. Together with the level set method for the free surface capturing, this algorithm can model the movement of rigid floating bodies and their interaction with the fluid. The 6DOF algorithm is implemented on a fixed grid. The solid‐fluid interface is represented with a combination of the level set method and ghost cell immersed boundary method. As a result, re‐meshing or overset grids are not necessary. The capability, accuracy, and numerical stability of the new algorithm is shown through benchmark applications for the fluid‐body interaction problem. Copyright © 2016 John Wiley & Sons, Ltd.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Similarity conditions for heat transfer in incompressible two-dimensional laminar boundary layer flow

Summary Similarity conditions are presented for the solution of some problems of heat transfer in incompressible two-dimensional boundary layer flow. The treatment holds for forced convection as well as for free convection. For free convection no a priori restriction is made with respect to geometry or temperature distribution of the solid surface. For forced convection the treatment is restricted to uniform bulk flow parallel to a flat surface of non-uniform temperature or heat flux. The results are summarized in some tables that facilitate comparison with older work.     

Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity

In this study, a transient heat transfer process of freezing water inside a two-dimensional square cavity has been investigated numerically. Water was used as a phase-change medium, and the numerical model has been created with control volume approach by using C++ programming language. To be able to accelerate the numerical calculations, CUT (Consistent-Update-Technique) algorithm has been implemented in the numerical code. Span-wise variations of the vertical component of the velocity have been represented in comparison with the experimental measurements from the literature at various vertical positions to examine the accuracy of the numerical scheme. The influence of natural convection has been considered by comparing the conduction and convection dominated solidification under same boundary conditions. Comparative results have been obtained regarding time-wise variations of the cold wall temperature and the dimensionless effectiveness. Moreover, the streamlines and isotherms have been represented to understand the differences between the conduction and convection driven phase change processes.Results indicate that natural convection becomes remarkable and has different forms at the initial periods of the phase change process. Increasing the effect of natural convection in the cavity increases the cooling rate of water. Near the density inversion temperature of water (4°C), temperature variations fluctuate and counter currents observed in the domain.     

Mixed convection from an isothermal vertical flat plate moving in parallel or reversely to a free stream

Mixed convection heat transfer from a vertically moving plate to a flowing free stream is investigated. The plate moves either in parallel or reversely to the free stream; and the buoyancy force accelerates or retards the flow. An universal formulation can be obtained from which similarity and nonsimilarity equations for six limiting cases of forced, natural, and mixed convection can be readily reduced. Accurate finite-difference solutions and comprehensive correlations of heat transfer rate for 0.01≤Pr≤10000 are presented over the entire domains of mixed convection and relative velocity.     

Magnetic and Gravitational Convection of Air in a Porous Cubic Enclosure with a Coil Inclined Around the Y Axis

The natural convection heat transfer of air in a porous media can be controlled by gradient magnetic field. Thermomagnetic convection of air in a porous cubic enclosure with an electric coil inclined around the $Y$ axis was numerically investigated. The Biot–Savart law was used to calculate the magnetic field. The governing equations in primitive variables were discretized by the finite-volume method and solved by the SIMPLE algorithm. The flow and temperature fields for the air natural convection were presented and the mean Nusselt number on the hot wall was calculated and compared. The results show that both the magnetic force and coil inclination have significant effect on the flow field and heat transfer in a porous cubic enclosure, the natural convection heat transfer of air can be enhanced or controlled by applying gradient magnetic field.