Papers by Keyword: Finite Volume Method

Abstract: A numerical study investigates the flow behavior inside a three-sided lid-driven cavity. The physical problem is represented by a square cavity with two opposite horizontal walls moving translationally and independently to the right. The left vertical sidewall moves upward while the right vertical sidewall remains stationary. This study applies different Reynolds numbers to the moving walls to define three different configurations. In each configuration, two moving walls operate at the same Reynolds number (Re=100), while the Reynolds number of the remaining wall varies (Re=200, 400, 800, 1600, 3200, and 6400). We explore the flow patterns for each case, including the generated primary and secondary vortices, vorticity, velocity profiles, and fluid properties. Special attention is given to the formation and evolution of primary and secondary vortices to provide insights into the complex flow mechanisms governing this type of flow. The study reveals that varying the Reynolds number of one of the moving walls significantly impacts the flow structure within the three-sided lid-driven cavity. The asymmetry in wall motion is a powerful trigger for vortex genesis and evolution. The findings also lead to a better understanding of the flow mechanisms of driven cavity flows bounded by three walls with asymmetric boundary conditions.

Abstract: This study investigated the influence of nanoparticle material type and weight percentage on the flow behaviour of underfill encapsulation in Ball Grid Array (BGA) assemblies. As BGA packages are increasingly used in high-density and high-performance electronic devices, ensuring reliable solder joint encapsulation becomes critical. While nanoparticle-reinforced underfills enhance thermal and mechanical performance, they also introduce complexities in flow behaviour due to changes in viscosity and particle–fluid interactions. To address this, a multiphase numerical model was developed using the Finite Volume Method (FVM) and the Discrete Phase Model (DPM) in ANSYS Fluent to simulate the transient flow of underfill resin reinforced with Al₂O₃, SiO₂, and TiO₂ nanoparticles at varying weight percentages (5%, 10%, 15%, and 20%). The simulation captured the progression of fluid fill at intervals (25%, 50%, 75%, 95%) and measured total flow time. Results revealed Al₂O₃-based underfill consistently achieved faster flow, with the shortest 95% fill time recorded at 69.84 seconds for a 17.16% weight load concentration, while SiO₂-based underfill had the slowest flow, with times exceeding 74 seconds at 20% loading. These differences were attributed to variations in nanoparticle density and dispersion behaviour. A Random Forest regression model trained on simulation data further confirmed that nanoparticle type and concentration were the most significant predictors of flow time. These findings demonstrate that optimal nanoparticle selection can balance mechanical reinforcement with manufacturability. The results offer practical insights for electronics manufacturers aiming to improve process throughput and reliability in advanced packaging by selecting suitable nanoparticle-enhanced underfill formulations.Keywords: Underfill encapsulation, Nanoparticle reinforcement, Finite Volume Method, Discrete Phase Model, Artificial Neural Network.

Abstract: This paper investigates the thermal performance of a longitudinal trapezoidal fin using the Finite Volume Method, considering temperature-dependent thermal conductivity and heat transfer coefficient. The governing energy equation is developed by incorporating nonlinear thermal parameters and transforming these to dimensionless forms. The domain is discretized into control volumes and the energy balance is applied to each node to develop a system of algebraic equations. The effect of parameters like effectiveness factor, fin steepness, thermal conductivity and scale factor on temperature distribution is then studied. The results provide insights into optimizing fin geometry and thermal properties for efficient heat dissipation in engineering applications, while the temperature gradients along the fin length offers useful information for design. The Finite Volume Method ((FVM) proves advantageous in handling irregular geometries and conserving local balances. Overall, this comprehensive numerical approach enables accurate prediction of the intricate thermal response of longitudinal trapezoidal fins.

Abstract: This work presents a computational analysis of the heat-exchange characteristics in a double-cylinder (also known as a double-pipe) geometrical arrangement. The heat-exchange is from a hotter viscoelastic fluid flowing in the core (inner) cylinder to a cooler Newtonian fluid flowing in the shell (outer) annulus. For optimal heat-exchange characteristics, the core and shell fluid flow in opposite directions, the so-called counter-flow arrangement.The mathematical modelling of the given problem reduces to a system of nonlinear coupled Partial Differential Equations (PDEs). Specifically, the rheological behaviour of the core fluid is governed by the Giesekus viscoelastic constitutive model. The governing system of coupled nonlinear PDEs is intractable to analytic treatment and hence is solved numerically using Finite Volume Methods (FVM). The FVM numerical methodology is implemented via the open-source software package OpenFOAM. The numerical methods are stabilized, specifically to address numerical instabilities arising from the High Weissenberg Number Problem (HWNP), via a combination of the Discrete Elastic Viscous Stress Splitting (DEVSS) technique and the Log-Conformation Reformulation (LCR) methodology. The DEVSS and LCR stabilization techniques are integrated into the relevant viscoelastic fluid solvers. The novelties of the study center around the simulation and analysis of the optimal heat-exchange characteristics between the heated Giesekus fluid and the coolant Newtonian fluid within a double-pipe counter-flow arrangement. Existing studies in the literature have either focused exclusively on Newtonian fluids and/or on rectangular geometries. The existing OpenFOAM solvers have also largely focused on non-isothermal viscoelastic flows. The relevant OpenFOAM solvers are modified for the present purposes by incorporating the energy equation for viscoelastic fluid flow. The flow characteristics are presented qualitatively (graphically) via the fluid pressure, temperature, velocity, and the polymer-stress components as well as the related normal stress differences. The results illustrate the required decrease in the core fluid temperature in the longitudinal direction due to the cooling effects of the shell fluid, whose temperature predictably increases in the counter-flow direction.

Abstract: The present study investigates the combined free convection and surface radiation in a conical annular cylinder filled with air (Pr=0.71). The steady-state continuity, Navier–Stokes and energy equations were carried out by the finite volume method, and the Discrete Ordinates Method (DOM) was used to solve the radiative heat transfer equation (RTE). The boundary conditions are such that the inner and the outer radius of cone are maintained at hot (T_h) and cold (T_c) isothermal temperature. The horizontal upper and lower walls are assumed to be isolated. Concerning the radiation exchange, we consider that the fluid (air) is transparent, so only the solid surfaces contribute to the radiation exchange and assumed to be diffuse-gray. The computations are performed for Rayleigh number (Ra) in the range 10³≤Ra≤10⁶ , the surface emissivity (ε) 0≤ε≤1 and the cone angle () 63o, 76o, 80o and 84o. The key parameters for this analysis are considered as Rayleigh number (Ra), surface emissivity (ε) and the cone angle (). Results are presented in terms of isotherms, streamlines and the average Nusselt numbers.

Abstract: The present work is a contribution to the development of a calculation code that determines the temperature field on fins having rectangular geometry for any bi-dimensional or three-dimensional simulation conditions. Different cases of simulations are presented. An implicit finite volume method, unconditionally stable, is extended in this study for the discretization of the governing equations. The representative results, validated by the Ansys code, show that the fin temperature increases with the increase of the temperature values selected as the boundary conditions, with the addition of a heat flow or any additional heat source. The numerical results are very consistent with the theory and the results obtained from commercialized codes. By increasing the diffusivity one converge more quickly towards the stationary solution. Upon reducing the fin size a very drastic shift occurs from the transient regime to a permanent one. In the case of a refinement of the mesh, the use of a very small epsilon ensures the convergence. Therefore, the results obtained in this study serve as basis of comparison with any other study on heat transfer on rectangular fins.

Abstract: Interfacial thermal resistance of Al-AlN composites was evaluated by comparing the measured thermal conductivity and the simulated thermal conductivity. Al-10vol.%AlN and Al-20vol.%AlN composites were fabricated by spark plasma sintering. Effective thermal conductivity was measured with the steady state thermal conductivity measuring device. Effective thermal conductivity was also simulated by using FE-SEM image and the measured relative density. Comparing the measured thermal conductivity and the simulated thermal conductivity, interfacial thermal resistance in Al-AlN composites was evaluated as about 1.27-6.2510^-9 m²K/W.

Abstract: In Thailand, the sheet metal products that were produced by rolling process have high demand and the consumption trend to grow in the future. Many new products, which made from rolling steel sheet, had been developed with various design. Thus the manufacturers have to improve the productivity through the investigation and analysis of different process parameters, which affect to the quality during the production. In this paper, finite volume method FVM had been applied to analyze different effects of processes parameters such as temperature, roller speed, friction, size and capacity of rolling machine. The commercial software MSC.SuperForge was used in the modeling and simulation of metal deformation under the flat rolling process. Considering the predicted results compared with the experimental data, the different in dimension error data were within an acceptable range of quality specification. The error in width of finished steel sheet was 1.17%, the length was error of 1.50%, and the thickness was error of 2.32%. By using this technique, different factors affected during rolling process can be investigated and controlled such as the metal flow, the distribution of stress and strain, and the deformation zone.

Abstract: The mathematical modeling of wildland fires impact on buildings have been carried out to study the effects of fires at different conditions of buildings ignition. The forest is modeling as a porous reactive medium. The formulation of this problem was developed using standard nonstationary three-dimensional Reynolds equations for flow in a multiphase reactive medium. These equations are solved numerically using finite volume method. The influence of meteorological conditions, properties of the forest and its state on the possibility of ignition of buildings located near forests is studied.

Abstract: The shape memory alloys have been used in the most different sectors such as aerospace, automotive and biomedical due to their ability to return to their original shape when subjected to high temperatures. Modeling and numerical simulation have become great allies in engineering due to the possibility of solving complex problems, especially in cases where experimental research is limited. In the present study, a two-dimensional mathematical model was developed to describe the solidification process of a Ni-Ti alloy in stainless steel metal mold sand confined. It was considered the flow of a refrigerant fluid (air) in the top of the mold. The energy conservation equation, including the phase change term, was discretized using finite volume method (FVM) and a fully implicit formulation. Results of the Ni-Ti alloy and mold temperature distributions over time are presented and analyzed. It was verified that results are independent of the mesh size and time step. The last point to be solidified is located at the top left corner of the study domain and the temperature distribution over time proved to be satisfactory for the absence of internal defects, such as voids, cracks, residual stresses and macro segregation.