Gauss-Seidel Iterative Technique Research Articles

A New Non-Linear Hyperbolic-Parabolic Coupled PDE Model for Image Despeckling.

In this work, we propose a non-linear hyperbolic-parabolic coupled Partial Differential Equation (PDE) based model for image despeckling. Here, a separate equation is used to calculate the edge variable, which improves the quality of edge information in the despeckled images. The existence of the weak solution of the present system is achieved via Schauder fixed point theorem. We used a generalized weighted average finite-difference scheme and the Gauss-Seidel iterative technique to solve the coupled system. Numerical studies are reported to show the effectiveness of the proposed approach with respect to standard PDE-based and nonlocal methods available in the literature. Numerical experiments are performed over gray-level images degraded by artificial speckle noise. Additionally, we investigate the noise removal efficiency of the proposed algorithm when applied to real synthetic aperture radar (SAR) and Ultrasound images. Overall, our study confirms that in most cases, the present model performs better than the other PDE-based models and shows competitive performance with the nonlocal technique. To the best of our knowledge, the proposed despeckling approach is the first work that utilizes the advantage of the non-linear coupled hyperbolic-parabolic PDEs for image despeckling.

Effect of humidity on the performance of rooftop solar chimney

A mathematical model of a solar chimney was developed considering moist air as a participatory media. This model coheres to the steady-state heat transfer equations derived for glass cover, moist-air between the glass cover and the absorber wall, and for the absorber wall separately. An in-house developed MATLAB code solves the equations via matrix method, utilizing the Gauss–Seidel iteration technique. A study was done on dry as well as moist air that flows between the glass and absorber plate of the solar chimney. Air absorbing heat by mode of convection, radiation, and both was considered. Performance of the system is characterized in terms of the mass flow rate of air. Variation of mass flow rate of air with the gap between the glass and the absorber plate is studied as a function of relative humidity. The effect of ambient temperature and radiation on solar chimney’s performance was reported. The result shows an improvement of 10% in the performance of solar chimney driven by moist air as compared to dry air at 45°inclination of chimney. Chimney inclination of 45°was found to be optimum for Bhubaneswar (India), as it has higher mass flow rate compared to other inclination for most duration. It is also concluded that the mass-flow rate through the solar chimney directly depends on the gap between absorber plate and glass cover. Compared to 0.1 m air gap, there is about 62% and 114% increase in mass flow for the gap of 0.2 m and 0.3 m, respectively.

Heat transfer enhancement with nanofluid in an open enclosure due to discrete heaters mounted on sidewalls and a heated inner block

Purpose The purpose of this study is to explore the heat transfer enhancement in copper–water nanofluid flowing in a diagonally vented rectangular enclosure with four discrete heaters mounted centrally on the sidewalls and a square-shaped embedded heated block in the influence of a static magnetic field. Design/methodology/approach Four discrete heaters are mounted centrally on each sidewall of the rectangular enclosure that embraces a heated square block. A static transverse magnetic field is acting on the vertical walls. The Navier–Stokes equations of motion and the energy equation are modified by incorporating Lorentz force and basic physical properties of nanofluid. The derived momentum and energy equations are tackled numerically using the successive over-relaxation technique associating with the Gauss–Seidel iteration technique. The effects of physical parameters connected to dynamics of flow and heat convection are explored from streamlines and isotherms graphs and discussed numerically in terms of Nusselt number. Findings The effect of the embedded heated square block size and its location in the enclosure, nanoparticles volume fraction and the intensity of the magnetic field on flow and heat transfer are computed. Compared with the case when no heated block is embedded in the enclosure, in free convection at Ra = 106, the average local Nusselt number on the wall-mounted heaters is attenuated by 8.25%, 11.24% and 12.75% when the enclosure embraced a heated square block of side length 10% of H, 20% of H and 30% of H, respectively. An increase in Hartmann number suppresses the heat convection. Research limitations/implications The enhancement in the convective heat is greater when the buoyancy effect dominates the viscous effects. Placing the embedded heated block near the inlet vent, the lower temperature zone has reduced while the embedded heated block is at the central location of the enclosure, the high-temperature zone has expanded. The external magnetic field can be used as a non-invasive controlling device. Practical implications The numerically simulated results for heat convection of water-based copper nanofluid agreed qualitatively with the existing experimental results. Social implications The models could be used in designing a target-oriented heat exchanger. Originality/value The paper includes a comparative study for three locations of the embedded heated square. The optimal results for the centrally located heated block are also performed for three different sizes of the embedded block. The numerically simulated results are compared with the published numerical and experimental studies.

NATURAL CONVECTION IN A MICROPOLAR NANOFLUID FILLED OPEN RECTANGULAR ENCLOSURE EMBEDDED WITH A HEATED OBJECT OF DIFFERENT GEOMETRIES

A numerical investigation has been performed to analyze heat convection through a micropolar nanofluid in an open rectangular enclosure. It embedded the inner heated object of different geometries and finite heat source length on the bottom wall with uniform heat flux. The remaining portion of the wall containing heat source and all the remaining walls are assumed as adiabatic except the top wall. Successive over-relaxation (SOR) method coupled with Gauss-Seidel iteration technique are employed in order to numerically tackled the nonlinear model momentum and energy equations. The effect of the calibrated parameters such as Rayleigh number, length of the wall heat source, the geometry of the inner block, vortex viscosity parameter, the type of nanoparticles, and the concentration of nanoparticles on the flow and thermal performance is studied. The computed results show that increasing in the Rayleigh number and the concentration of nanoparticles have a positive effect on Nusselt number whereas increasing in wall heat source length and vortex viscosity attenuates the Nusselt number. Also, the geometry of the inner block has effect in the flow pattern and the temperature distribution.

Heat convection in micropolar nanofluid through porous medium-filled rectangular open enclosure: effect of an embedded heated object with different geometries

A numerical investigation has been performed to analyze heat convection through a micropolar nanofluid in an open rectangular enclosure filled with a porous medium. The enclosure is embedded with a heated object and having a heated non-planar bottom wall. Three different shapes of the embedded heated object, diamond-shaped, L-shaped, and triangular-shaped, are considered, and their effects are compared numerically. Successive over-relaxation method coupled with Gauss–Seidel iteration technique are employed in order to numerically tackle the nonlinear model momentum and energy equations. The outcomes are discussed in terms of streamlines, isotherms, and isolines of microrotation, averaged Nusselt number on the heated wall for different values of intricated parameters. The calibrated parameters Darcy number, vortex viscosity, Rayleigh number, and volume fraction of nanoparticles, respectively, are taken in the range 0.0001 ≤ Da ≤ 0.1, 0.5 ≤ K ≤ 5.0, 104 ≤ Ra ≤ 106, and 0 ≤ φ ≤ 0.04. It reveals that in the absence of heated object, the non-planarity of the wall lessens the heat transfer rate by 12.95% (when compared to the planar wall). The impact of the shape of the embedded heated object on the heat transfer rate is estimated and found an enhancement of 15.34%, 11.63%, 13.51% for diamond-shaped, L-shaped, and triangular-shaped objects, respectively. Increasing the Darcy number boosts the heat transfer rate while an upsurge in the vortex viscosity parameter lessens the heat transfer rate. The Nusselt number in the enclosure with and without a heated object (depending on the volume fraction of nanoparticles) is also computed numerically.

A Novel Simulation Framework for Predicting the Formation Parameters Variation in Unconsolidated Sandstone Reservoir

After long-term waterflooding in unconsolidated sandstone reservoir, the high-permeability channels are easy to evolve, which leads to a significant reduction in water flooding efficiency and a poor oilfield development effect. The current researches on the formation parameters variation are mainly based on the experiment analysis or field statistics, while lacking quantitative research of combining microcosmic and macroscopic mechanism. A network model was built after taking the detachment and entrapment mechanisms of particles in unconsolidated sandstone reservoir into consideration. Then a coupled mathematical model for the formation parameters variation was established based on the network modeling and the model of fluids flowing in porous media. The model was solved by a finite-difference method and the Gauss-Seidel iterative technique. A novel field-scale reservoir numerical simulator was written in Fortran 90 and it can be used to predict 1) the evolvement of high-permeability channels caused by particles release and migration in the long-term water flooding process, and 2) well production performances and remaining oil distribution. In addition, a series of oil field examples with inverted nine-spot pattern was made on the new numerical simulator. The results show that the high-permeability channels are more likely to develop along the main streamlines between the injection and production wells, and the formation parameters variation has an obvious influence on the remaining oil distribution.

Effects of pressure work, viscous dissipation, shear work and axial conduction on convective heat transfer in a microtube

This paper investigates the effects of viscous dissipation, pressure work, shear work, rarefaction and axial heat diffusion on convective heat transfer in a microtube gaseous flow. The problem is investigated numerically for the whole flow region using a finite difference scheme and the line Gauss-Seidel iterative technique. Exact solutions of the problem in terms of temperature distribution and Nusselt number variations are also derived under fully developed flow conditions. The microtube is assumed to be sufficiently long, so that fully developed conditions are established. The analysis presented demonstrate that the effect of the boundary shear work is significant and its contribution to heat transfer can be as high as that due to heat conduction close to the upper limit of the slip flow regime. As the shear work is a result of the combined effects of viscous dissipation and pressure work at the boundary, including these effects in the analysis leads to better predictions of heat transfer phenomena. Axial heat diffusion effect on Nusselt number and the thermal entrance length are also quantified.

Simulation Studies on Buoyancy-Aided Conjugate Mixed Convection With Radiation From a Vertical Plate With Multiple Nonidentical Heat Sources

ABSTRACTThis paper documents certain salient results of the simulation studies performed on conjugate mixed convection with surface radiation from a vertical electronic board equipped with multiple nonidentical flush-mounted discrete heat sources. Air that is assumed to be radiatively transparent with constant thermophysical properties subjected to the Boussinesq approximation is considered to be the cooling agent. The governing fluid flow and heat transfer equations without the boundary-layer approximations are initially transformed into vorticity-stream function form and are later appropriately normalized. The resulting equations, along with pertinent boundary conditions, are subsequently solved using a finite-volume-based finite-difference method coupled with Gauss–Seidel iterative technique. An extended computational domain has been used to capture the fluid flow and heat transfer adequately employing optimum combination of finer and coarser grids. A computer code is specifically written for the job. Effects of modified Richardson number, surface emissivity, and thermal conductivity on local temperature distribution, peak board temperature, and contributions of mixed convection and radiation in heat dissipation have been clearly elucidated. Two correlations that help in calculation of maximum and average nondimensional plate temperatures have also been developed.

Linear stability analysis of finite hydrodynamic journal bearing under turbulent lubrication with coupled-stress fluid

Purpose Several researchers have observed that to satisfy modern day’s need, it is essential to enhance the characteristics of journal bearing, which is used in numerous applications. Moreover, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of Non-Newtonian fluids is coming more into picture. Furthermore, if turbo-machinery applications are taken into account, then it can be seen that journal bearings are used for high speed applications as well. Thus, neglecting turbulent conditions may lead to erroneous results. Hence, this paper aims to present focuses on studying the stability characteristics of finite hydrodynamic journal bearing under turbulent coupled-stress lubrication. Design/methodology/approach First, the governing equation relevant to the problem is generated. Then, the dynamic analysis is carried out by linear perturbation technique, leading to three perturbed equations, which are again discretized by finite difference method. Finally, these discretized equations are solved with the help of Gauss-Seidel Iteration technique with successive over relaxation scheme. Consequently, the film response coefficients and the stability parameters are evaluated at different parametric conditions. Findings It has been concluded from the study that with increase in value of the coupled-stress parameter, the stability of the journal may increase. Whereas, with increase in Reynolds number, the stability of the journal decreases. On the other hand, stability increases with increasing values of slenderness ratio. Originality/value Researches have been performed to study the dynamic characteristics of journal bearing with non-Newtonian fluid as the lubricant. But in the class of non-Newtonian lubricants, the use of coupled-stress fluid has not yet been properly investigated. So, an attempt has been made to perform the stability analysis of bearings with coupled-stress fluid as the advanced lubricant.

Numerical Analysis of the Effects of Selected Geometrical Parameters and Fluid Properties on MHD Natural Convection Flow in an Inclined Elliptic Porous Enclosure with Localized Heating

Magnetohydrodynamic (MHD) natural convection flow and associated heat convection in an oriented elliptic enclosure has been investigated with numerical simulations. A magnetic field was applied to the cylindrical wall of the configuration, the top and bottom walls of the enclosure were circumferentially cooled and heated, respectively, while the extreme ends along the cross‐section of the elliptic duct were considered adiabatic. The full governing equations in terms of continuity, momentum, and energy transport were transformed into nondimensional form and solved numerically using finite difference method adopting Gauss–Seidel iteration technique. The selected geometrical parameters and flow properties considered for the study were eccentricity (0, 0.2, 0.4, 0.6, and 0.8), angle of inclination (0°, 30°, 60°, and 90°), Hartmann number (0, 25, and 50), Grashof number (104, 105, and 106), and Darcy number (10−3, 10−4, and 10−5). The Prandtl number was held constant at 0.7. Numerical results were presented by velocity distributions as well as heat transfer characteristics in terms of local and average Nusselt numbers (i.e., rate of heat transfer). The optimum heat transfer rate was attained at e value of 0.8. Also, the heat transfer rate increased significantly between the angles of inclination 58° and 90°. In addition, Hartmann number increased with decreased heat transfer rate and flow circulation. A strong flow circulation (in terms of velocity distribution) was observed with increased Grashof and Darcy numbers. The combination of the geometric and fluid properties therefore can be used to regulate the circulation and heat transfer characteristics of the flow in the enclosure.

A Numerical Investigation of the Temperature Uniformity of a Billet due to Thermal Radiation in a Reheating Furnace

In Thailand, the iron and steel industry is one of the major industries to provide raw materials to other ones. In order to heat a billet to a proper temperature, it is fed into a reheating furnace, which generates heat by the combustion of fuel from direct-fired burners. After the temperature uniformity of the billet is achieved, it will be sent to the rolling process. The major mechanism of heat transfer in the reheating furnace is the thermal radiation because of the high combustion gas temperature. The temperature distribution of a billet subjected to the thermal radiation of the enclosure surfaces in a reheating furnace is presented in this study. The 2-D steady-state heat conduction equation is numerically solved by the finite volume method together with the Gauss-seidel iterative technique. A qualitative agreement between the numerical result and the data from filed measurement is presented. The variations of the temperature uniformity of the billet with different insulation thicknesses, flame temperatures and furnace floor temperatures are investigated. The result indicates the hot spot at the middle of billet originated from the position of combustion flame. When the wall insulation thickness is decreased, the thermal radiation of combustion flame is decreased, leading to the higher degree of the temperature uniformity of the billet. In case of the lower flame temperature or the higher the floor temperature, the degree of the temperature uniformity of the billet also increases.

Gauss–Seidel Iterative Solution of Electromagnetic Pulse Coupling to Three-Conductor Transmission Lines

This paper proposes a distributed analytical representation and Gauss-Seidel iterative technique (Seidel-DARIT-field), which has a faster convergence rate than the Jacobi-DARIT-field method in the simulation of electromagnetic pulse (EMP) radiated field coupling to multiconductor transmission lines (MTLs) and is more valid and accurate. The process of the first iteration in this method is similar to that in the Jacobi-DARIT-field method. At the second iteration and after, every line will be updated based on the present iteration state of other lines.

Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

Numerical studies on the performance enhancement of an encapsulated thermal storage unit

This paper investigates numerically the performance of an encapsulated latent heat thermal storage (LHTS) unit containing a phase change material (PCM) dispersed with high conductivity particles. A temperature based numerical model that incorporates the effect of particles via an effective thermal conductivity model has been developed considering the energy discharging (solidification) process. The system of governing equations has been solved using finite difference scheme employing Gauss–Seidel iteration technique. The results have shown a significant reduction in the time taken for complete solidification of the PCM due to the addition of high conductivity particles. It has been found that the time taken for complete solidification of the PCM decreased by about 26% with a particle fraction of about 30%. Compared to thermal conductivity of particles, the influence of particle fraction (ζ) on the performance enhancement of the unit has been found to be significant. For a given particle fraction, the performance enhancement obtained was almost the same for particle–PCM thermal conductivity ratio (kc/kpl) between 10 and 100 for the Pe, St and Ste studied in this work. The enhancement in energy discharge rate was found to be remarkable due to the addition of high conductivity particles to the PCM.

Transient behavior of co-current parallel flow three-fluid heat exchanger

Transient behavior of co-current parallel flow three-fluid compact heat exchangers with the effect of two-dimensional longitudinal heat conduction through the separating sheet and axial dispersion in fluids has been investigated numerically by using the Gauss–Seidel iterative technique for step excitation provided to hot fluid inlet temperature. The results reveal that the performance of the heat exchanger is affected when two-dimensional longitudinal conduction in separating sheets and axial dispersion in fluids are considered.

Mixed Convection with Conduction and Surface Radiation from a Vertical Channel with Discrete Heating

A numerical investigation into fluid flow and heat transfer for the geometry of a vertical parallel plate channel subjected to conjugate mixed convection with radiation is attempted here. The channel considered has three identical flush-mounted discrete heat sources in its left wall, while the right wall that does not contain any heat source acts as a sink. Air, assumed to be a radiatively non-participating and having constant thermophysical properties subject to the Boussinesq approximation, is the cooling agent. The heat generated in the left wall gets conducted along it and is later dissipated by mixed convection and radiation. The governing equations, considered in their full strength sans the boundary layer approximations, are converted into vorticity-stream function form and are then normalized. These equations along with pertinent boundary conditions are solved through finite volume method coupled with Gauss-Seidel iterative technique. The effects of modified Richardson number, surface emissivity, thermal conductivity and aspect ratio on local temperature distribution along the channel, maximum channel temperature and relative contributions of mixed convection and radiation have been thoroughly studied. The prominence of radiation in the present problem has been highlighted.

Conjugate Convection with Surface Radiation from a Square-Shaped Electronic Device with Multiple Identical Discrete Heat Sources

Numerical simulation studies on combined conduction–convection–radiation from a square-shaped electronic device with multiple identical flush-mounted discrete heat sources have been performed and the prominent results are reported here. The problem geometry comprises a square shaped slab with four symmetrically located flush mounted identical discrete heat sources. The heat generated in the heat sources gets conducted through the slab and subsequently gets dissipated from its boundaries by the combined modes of convection and radiation. Air, a radiatively transparent medium is considered to be the cooling agent. The governing equations for temperature distribution in the entire computational domain are obtained by appropriate energy balance between the heat generated, conducted, convected and radiated. The resulting partial differential equations are solved using finite difference method in conjunction with Gauss–Seidel iterative technique. A computer code is prepared for the purpose. Exhaustive numerical studies are performed to elucidate the effects of parameters like volumetric heat generation, thermal conductivity, surface emissivity and convection heat transfer coefficient on local temperature distribution, peak device temperature and relative contributions of convection and radiation in heat dissipation.

Flexural response of footing on reinforced granular beds of variable subgrade modulus

The paper pertains to the study of the flexural response of a shallow footing resting on a compacted granular bed overlying a deposit of poor granular soil, with reinforcement (e.g. geogrid and geocells) placed at the interface of the two media. The footing and reinforcement are considered as free ended beams. The granular soil media are represented by a series of Winkler springs. Taking into account the effect of confining pressure along the footing and reinforcement at the beam-soil interface, various distribution of subgrade modulus along the length of footing and reinforcement (uniform, linear and quadratic) are considered. Governing equations for the above problem are derived and subsequently normalized, which is then solved by using Finite Difference Method (FDM) in conjunction with Gauss-Seidel Iterative Technique (GSIT). Comparison of the obtained solutions with those available in literature for the case of uniform subgrade modulus exhibited a deviation of 24%-40% in the settlement characteristics of the reinforced foundation bed. Parametric studies were performed to study the effect of various parameters, such as, relative flexural rigidity of beams (<i>R</i>), relative length of beams (<i>l_n</i>), relative stiffness of soils (<i>k_r</i>), relative depth of placement of reinforcement (H'), effect of interface friction and effect of variation in subgrade modulus. The developed method has been found to be realistic in predicting the behavior of reinforced foundation beds.

A Software Tool for Determining Steady-State Temperature Distributions in a Square Domain by the Finite-Difference Method

This paper presents the development of an interactive program (called SSTDD) to solve two-dimensional conduction heat transfer equations in a square domain using the finite-difference method. The development of the tool (based on a computer-aided design package), on a Visual BASIC 6.0 platform, involved the application of the heat transfer equations and the appropriate boundary conditions to a square domain. The finite-difference method was used to express the elliptic differential equation in a form suitable for numerical solution. The system of linear equations generated was solved by the Gauss–Seidel iterative technique. The SSTDD model was tested by using problems solved by conventional analytical techniques. The results generated by the model and the analytical method were in good agreement. Hence the model can be used to solve practical engineering problems, with good accuracy, and also as a demonstration tool to students in the area of design and heat transfer of mechanical engineering.

Interaction of Surface Radiation with Conduction and Convection from a Vertical Channel with Multiple Discrete Heat Sources in the Left Wall

This article reports the results of a numerical study of the problem of interaction of surface radiation with conduction and convection from a vertical channel equipped with three flush-mounted discrete heat sources in the left wall. The governing equations for temperature distribution along each of the two channel walls have been deduced based on appropriate energy balance between various energy interactions in which the channel is involved. Radiosity-irradiation formulation is employed to tackle radiation-related calculations, with the view factors involved therein obtained using Hottel's crossed-string method. The governing nonlinear partial differential equations are converted into algebraic form through a finite-volume-based finite-difference method, and are subsequently solved using Gauss-Seidel iterative technique. An optimum grid system, with 26 grids along each of the three discrete heat sources and 11 grids along each of the two non-heat source portions of the board, is used for discretization of the computational domain. The effects of various pertinent parameters, viz., aspect ratio, volumetric heat generation, thermal conductivity, surface emissivity, and convection heat transfer coefficient, on temperature distribution along the left board, maximum temperature in the channel, and relative contributions of convection and surface radiation to heat dissipation from the channel are probed.