Finite Element Solution of Navier-Stokes Equations for Steam Flow and Heat Transfer

Computational simulation of steam flow and heat transfer in power plant condensers on the basis of the threedimensional mathematical model for the flow through porous media is presented. In order to solve the mathematical model of steam flow and heat transfer in power plant condensers, the Streamline Upwind Petrov-Galerkin finite element method is applied. By comparison of the results of simulation with experimental results about an experimental condenser, it is confirmed that SUPG finite element method can be successfully applied for solving the three-dimensional mathematical model of steam flow and heat transfer in power plant condensers.

Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder

Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Analysis on Influence of Gravity on Convection Heat Transfer in Manned Spacecraft during Terrestrial Test

How to simulate experimentally the air flow and heat transfer under microgravity on the ground is important, which has not been completely solved so far. Influence of gravity on air natural convection results in convection heat transfer on ground difference from that on orbit. In order to obtain air temperature and velocity deviations of manned spacecraft during terrestrial thermal test, dimensionless number analysis and numerical simulation analysis are performed. The calculated temperature distribution and velocity distribution of the horizontal test cases are compared to the vertical cases. The results show that the influence of gravity is neglected for facility drawer racks and more obvious for vertical cabins.

Two Dimensional Simulation of Fluid Flow and Heat Transfer in the Transition Flow Regime using a Lattice Boltzmann Approach

The significant effects of the interactions between the system boundaries and the near wall molecules in miniaturized gaseous devices lead to the formation of the Knudsen layer in which the Navier-Stokes-Fourier (NSF) equations fail to predict the correct associated phenomena. In this paper, the well-known lattice Boltzmann method (LBM) is employed to simulate the fluid flow and heat transfer processes in rarefied gaseous micro media. Persuaded by the problematic deficiency of the LBM in capturing the Knudsen layer phenomena, present study tends to concentrate on the effective molecular mean free path concept the main essence of which is to compensate the incapability of this mesoscopic method in dealing with the momentum and energy transport within the above mentioned kinetic boundary layer. The results show qualitative and quantitative accuracy comparable to the solutions of the linearized Boltzmann equation or the DSMC data for the Knudsen numbers of O (1) .

Two-dimensional Heat Conduction of Direct Cooling in the Rotor of an Electrical Generator(Numerical Analysis)

Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Role of Oxide Scale Thickness Measurements in Boiler Conditions Assessment

Oxide scale thickness measurements are used in assessing the life of different components operating at high temperature environment. Such measurements provide an approximation for the temperature inside components such as reheater and superheater tubes. A number of failures were encountered in one of the boilers in one of Kuwaiti power plants. These failure were mainly in the first row of the primary super heater tubes, therefore, the specialized engineer decide to replace them during the annual shutdown. As a tool for failure analysis, oxide scale thickness measurement were used to investigate the temperature distribution in these tubes. In this paper, the oxide scale thickness of these tubes were measured and used for analysis. The measurements provide an illustration of the distribution of heat transfer of the primary superheater tubes in the boiler system. Remarks and analysis about the design of the boiler are also provided.

Effects of Thermal Radiation and Magnetic Field on Unsteady Stretching Permeable Sheet in Presence of Free Stream Velocity

The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.

Improvement of Energy Efficiency using Porous Fins in Heat Exchangers

The forced convection heat transfer in high porosity metal-foam filled tube heat exchangers are studied in this paper. The Brinkman Darcy momentum model and two energy equations for both solid and fluid phases in porous media are employed .The study shows that using metal-foams can significantly improve the heat transfer in heat exchangers.

Numerical Simulation of Convective Heat Transfer and Fluid Flow through Porous Media with Different Moving and Heated Walls

The present study is concerned with the free convective two dimensional flow and heat transfer, within the framework of Boussinesq approximation, in anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Lattice Boltzmann method fornon-Darcy flow model. Effects of the moving lid direction (top, bottom, left, and right wall moving in the negative and positive x&ydirections), number of moving walls (one or two opposite walls), the sliding wall velocity, and four different constant temperatures opposite walls cases (two surfaces are being insulated and the twoother surfaces areimposed to be at constant hot and cold temperature)have been conducted. The results obtained are discussed in terms of the Nusselt number, vectors, contours, and isotherms.

Analysis of a Fluid Behavior in a Rectangular Enclosure under the Effect of Magnetic Field

In this research, a 2-D computational analysis of steady state free convection in a rectangular enclosure filled with an electrically conducting fluid under Effect of Magnetic Field has been performed. The governing equations (mass, momentum, and energy) are formulated and solved by a finite volume method (FVM) subjected to different boundary conditions. A parametric study has been conducted to consider the influence of Grashof number (Gr), Prantdl number (Pr) and the orientation of magnetic field on the flow and heat transfer characteristics. It is observed that Nusselt number (Nu) and heat flux will increase with increasing Grashof and Prandtl numbers and decreasing the slope of the orientation of magnetic field.

Tuning of Thermal FEA Using Krylov Parametric MOR for Subsea Application

A dead leg is a typical subsea production system component. CFD is required to model heat transfer within the dead leg. Unfortunately its solution is time demanding and thus not suitable for fast prediction or repeated simulations. Therefore there is a need to create a thermal FEA model, mimicking the heat flows and temperatures seen in CFD cool down simulations. This paper describes the conventional way of tuning and a new automated way using parametric model order reduction (PMOR) together with an optimization algorithm. The tuned FE analyses replicate the steady state CFD parameters within a maximum error in heat flow of 6 % and 3 % using manual and PMOR method respectively. During cool down, the relative error of the tuned FEA models with respect to temperature is below 5% comparing to the CFD. In addition, the PMOR method obtained the correct FEA setup five times faster than the manually tuned FEA.

Effects of the Wavy Surface on Free Convection-Radiation along an Inclined Plate

A numerical analysis used to simulate the effects of wavy surfaces and thermal radiation on natural convection heat transfer boundary layer flow over an inclined wavy plate has been investigated. A simple coordinate transformation is employed to transform the complex wavy surface into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm with relaxation coefficient. Effects of the wavy geometry, the inclination angle of the wavy plate and the thermal radiation on the velocity profiles, temperature profiles and the local Nusselt number are presented and discussed in detail.

Effect of Prandtl Number on Natural Convection Heat Transfer from a Heated Semi-Circular Cylinder

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number. The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number, . The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. The resulting flow and temperature fields are visualized in terms of the streamline and isotherm patterns in the proximity of the cylinder. The flow remains attached to the cylinder surface over the range of conditions spanned here except that for and ; at these conditions, a separated flow region is observed when the condition of the constant wall temperature is prescribed on the surface of the cylinder. The heat transfer characteristics are analyzed in terms of the local and average Nusselt numbers. The maximum value of the local Nusselt number always occurs at the corner points whereas it is found to be minimum at the rear stagnation point on the flat surface. Overall, the average Nusselt number increases with Grashof number and/ or Prandtl number in accordance with the scaling considerations. The numerical results are used to develop simple correlations as functions of Grashof and Prandtl number thereby enabling the interpolation of the present numerical results for the intermediate values of the Prandtl or Grashof numbers for both thermal boundary conditions.

Convective Heat Transfer of Viscoelastic Flow in a Curved Duct

In this paper, fully developed flow and heat transfer of viscoelastic materials in curved ducts with square cross section under constant heat flux have been investigated. Here, staggered mesh is used as computational grids and flow and heat transfer parameters have been allocated in this mesh with marker and cell method. Numerical solution of governing equations has being performed with FTCS finite difference method. Furthermore, Criminale-Eriksen- Filbey (CEF) constitutive equation has being used as viscoelastic model. CEF constitutive equation is a suitable model for studying steady shear flow of viscoelastic materials which is able to model both effects of the first and second normal stress differences. Here, it is shown that the first and second normal stresses differences have noticeable and inverse effect on secondary flows intensity and mean Nusselt number which is the main novelty of current research.

Numerical Analysis of Air Flow and Conjugated Heat Transfer in Internally Grooved Parallel- Plate Channels

A numerical investigation of surface heat transfer characteristics of turbulent air flows in different parallel plate grooved channels is performed using CFD code. The results are obtained for Reynolds number ranging from 10,000 to 30,000 and for arc-shaped and rectangular grooved channels. The influence of different geometric parameters of dimples as well as the number of them and the geometric and thermophysical properties of channel walls are studied. It is found that there exists an optimum value for depth of dimples in which the largest wall heat flux can be achieved. Also, the results show a critical value for the ratio of wall thermal conductivity to the one of fluid in which the dependence of wall heat flux to this ratio almost vanishes. In most cases examined, heat transfer enhancement is larger for arc-shaped grooved channels than rectangular ones.

Analysis of Combustion, Performance and Emission Characteristics of Turbocharged LHR Extended Expansion DI Diesel Engine

The fundamental aim of extended expansion concept is to achieve higher work done which in turn leads to higher thermal efficiency. This concept is compatible with the application of turbocharger and LHR engine. The Low Heat Rejection engine was developed by coating the piston crown, cylinder head inside with valves and cylinder liner with partially stabilized zirconia coating of 0.5 mm thickness. Extended expansion in diesel engines is termed as Miller cycle in which the expansion ratio is increased by reducing the compression ratio by modifying the inlet cam for late inlet valve closing. The specific fuel consumption reduces to an appreciable level and the thermal efficiency of the extended expansion turbocharged LHR engine is improved. In this work, a thermodynamic model was formulated and developed to simulate the LHR based extended expansion turbocharged direct injection diesel engine. It includes a gas flow model, a heat transfer model, and a two zone combustion model. Gas exchange model is modified by incorporating the Miller cycle, by delaying inlet valve closing timing which had resulted in considerable improvement in thermal efficiency of turbocharged LHR engines. The heat transfer model, calculates the convective and radiative heat transfer between the gas and wall by taking into account of the combustion chamber surface temperature swings. Using the two-zone combustion model, the combustion parameters and the chemical equilibrium compositions were determined. The chemical equilibrium compositions were used to calculate the Nitric oxide formation rate by assuming a modified Zeldovich mechanism. The accuracy of this model is scrutinized against actual test results from the engine. The factors which affect thermal efficiency and exhaust emissions were deduced and their influences were discussed. In the final analysis it is seen that there is an excellent agreement in all of these evaluations.

Natural Convection of Water-Based CuO Nanofluids in a Cylindrical Enclosure

Buoyancy driven heat transfer of nanofluids in a cylindrical enclosure used as a control unit in the subsea hydrocarbon injection wells is investigated in this study. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. The base fluid is water and CuO is used as nanoparticles. Solution is obtained for nanoparticle solid volume fraction of 8% and for Rayleigh number in the range of 105-107. The results show that nanoparticle usage in the cylindrical electronic control unit has a significant effect on the flow and heat transfer.

An Improved Model for Prediction of the Effective Thermal Conductivity of Nanofluids

Thermal conductivity is an important characteristic of a nanofluid in laminar flow heat transfer. This paper presents an improved model for the prediction of the effective thermal conductivity of nanofluids based on dimensionless groups. The model expresses the thermal conductivity of a nanofluid as a function of the thermal conductivity of the solid and liquid, their volume fractions and particle size. The proposed model includes a parameter which accounts for the interfacial shell, brownian motion, and aggregation of particle. The validation of the model is verified by applying the results obtained by the experiments of Tio2-water and Al2o3-water nanofluids.

Numerical Investigation of Non Fourier Heat Conduction in a Semi-infinite Body due to a Moving Concentrated Heat Source Composed with Radiational Boundary Condition

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Measurement of Convective Heat Transfer from a Vertical Flat Plate Using Mach-Zehnder Interferometer with Wedge Fringe Setting

Laser interferometric methods have been utilized for the measurement of natural convection heat transfer from a heated vertical flat plate, in the investigation presented here. The study mainly aims at comparing two different fringe orientations in the wedge fringe setting of Mach-Zehnder interferometer (MZI), used for the measurements. The interference fringes are set in horizontal and vertical orientations with respect to the heated surface, and two different fringe analysis methods, namely the stepping method and the method proposed by Naylor and Duarte, are used to obtain the heat transfer coefficients. The experimental system is benchmarked with theoretical results, thus validating its reliability in heat transfer measurements. The interference fringe patterns are analyzed digitally using MATLAB 7 and MOTIC Plus softwares, which ensure improved efficiency in fringe analysis, hence reducing the errors associated with conventional fringe tracing. The work also discuss the relative merits and limitations of the two methods used.