Gien-Huang Wu

Non-isothermal flow of a polymeric fluid past a submerged circular cylinder

Abstract In this paper, non-isothermal flow of a polymeric liquid past a circular cylinder in an infinite domain is investigated numerically. A non-Newtonian fluid, known as a differential-type White–Metzner model, is used in the flow simulation. The computer code developed is based on the elastic-viscous split-stress finite element method incorporating the streamline-upwind Petrov–Galerkin scheme. Numerical solutions for several cases are obtained. Global flow characteristics, such as drag coefficient and heat transfer coefficient, are derived. The effects of fluid elasticity, inertia, and shear-thinning on drag and heat transfer are also investigated.

Creeping flow of a polymeric liquid passing over a transverse slot with viscous dissipation

Abstract Numerical simulations for the non-isothermal flow of a nylon-6 fluid passing over a transverse slot with heat dissipation are considered with a differential-type non-isothermal White–Metzner model describing the non-Newtonian behavior of the melt. The results obtained in the study are computed by using the elastic–viscous split-stress finite element method incorporating the non-consistent streamline-upwind scheme. As a verification of the numerical scheme, the algorithm is first applied to compute the corresponding isothermal flow of the upper-convected Maxwell fluid, a special case of the melt, characterized by constant viscosity and relaxation time. Hole pressure was evaluated for various Deborah numbers ( De ), and compared with that derived from the Higashitani–Pritchard (HP) theory. The agreement between the two is found to be satisfactory for creeping flow in the De range for which the HP theory is valid. Subsequently, hole pressure and other flow characteristics were predicted. Furthermore, the effects of heat-transfer, shear-thinning, and slot geometry on hole pressure were also investigated.

Non-isothermal flow of a polymeric liquid passing an asymmetrically confined cylinder

Abstract Non-isothermal polymeric flow past an asymmetrically confined cylinder has been analyzed using a finite-element based numerical technique. The fluid model in this numerical simulation is a differential-type non-isothermal Bird–Carreau model describing the non-Newtonian behavior of the melt. The generated thermal field is entirely due to viscous heating. Drag, lift force and heat transfer on the cylinder and other flow characteristics are predicted. The influences of cylinder lateral position and Reynolds number are also investigated.

Numerical prediction of non-isothermal flow of nylon-6 past a cylinder between plates

Numerical simulations were undertaken for the non-isothermal creeping flow of a nylon-6 melt past a circular cylinder between plates. The fluid model used for this flow simulation is a non-isothermal White-Metzner constitutive equation, which describes the non-Newtonian behavior of nylon-6. The results were computed by an elastic-viscous split stress finite element method (EVSS-FEM), a mixed finite element method, incorpor-ating the streamline upwind Petrov-Galerkin (SUPG) scheme. To verify the numerical algorithm, it was first applied to compute the corresponding isothermal flow of a shearthinning solution of 5 wt% polyisobutylene in tetradecane (PIB/C14), modeled by the Phan-Thien Tanner model. The resulting velocity and stress fields were compared with known experimental data. Subsequently, both the isothermal and non-isothermal drag forces on the cylinder and the local heat transfer coefficients along the cylinder wall and channel wall were predicted. The effects of fluid elasticity, shear-thinning, temperature-thinning, and heat transfer were investigated.

Three-dimensional Finite Element Analysis of Thermomechanical Behavior in Flip-chip Packages under Temperature Cycling Conditions:

Flip-chip packaging provides a high-performance low-cost approach for the development of electronic packages. A three-dimensional viscoelastic-plastic finite element analysis using the commercial software ANSYS has been performed to study the thermomechanical behavior in flip-chip assemblies, i.e., the four components, chip, solder ball, underfill, and substrate. The viscoelastic behavior of the underfill is modeled on the Maxwell constitutive equation while the viscoplastic behavior of the solder balls is modeled by the Anand model. Both the chip and the substrate are assumed to be elastic materials modeled by the Hookes law. As in standard industry practice, temperature cycling from 125 to 55°C is used. Simulated thermomechanical behavior is presented for the solder balls. Subsequently, the effects of underfill-material properties, such as elasticity and coefficient of thermal expansion are also investigated.

On the flow of a polymer melt passing over a transverse slot

Abstract The phenomenon of hole pressure occurs whenever a polymeric or viscoelastic liquid flows over a depression in a conduit wall. Numerical simulations undertaken for the flow of an aqueous polyacrylamide melt passing over a transverse slot arc considered here. The fluid model used for this study is a White-Metzner constitutive equation describing the non-Newtonian behavior of the melt. The results were computed by an elastic-viscous split-stress finite clement method (EVSS-FEM). a mixed finite clement method incorporating the non-consistent streamline upwind scheme. For verification, the numerical algorithm was first applied to compute the corresponding flow of the upper-convected Maxwell fluid model, a special case of the Whitc-Metzner model characterized by constant viscosity and relation time. The resulting hole pressure (Ph) was evaluated for various Deborah numbers (De) and compared with the analytical prediction derived from the Higashitani-Pritchard (HP) theory. The agreement was found to be satisfactory for creeping flow in the low De range, for which the HP theory is valid. Subsequently, the hole pressure of this flow problem was predicted. The streamlines and pressure distribution along the channel walls arc also presented. Furthermore, the effects of fluid elasticity, shear thinning, the exponent in the viscosity function and the relaxation-time function, and slot geometry on the hole pressure were investigated.

Thermal Study of Enhanced Plastic Ball Grid Array Package with Flat Heat Spreader

Three-dimensional finite element simulations are performed to study the thermal performance of a thermally enhanced plastic ball grid array (EPBGA) package with a flat heat spreader adhered to the top surface of the package. Variables available for modification during simulation include heat spreader thickness, heat spreader conductivity and airflow. Specific study is made of the relative effects on thermal resistance of variation of heat spreader conductivity (from 0 to 350 W/m.K), heat spreader thickness (from 0 to 5.5 mm) and airflow speed (from 0 to 3 m/s). Improved thermal performance by use of a heat spreader is confirmed and dangerous package hot spots are minimized. Increasing the thermal conductivity of the heat spreader is found significant at levels up to around 100 W/m.K, but beyond this value the thermal performance improvement is negligible. Increasing heat spreader thickness is found to have a positive effect on thermal performance, but over the range (thickness >0.2 mm) the improvement is small. Increasing the airflow has a positive effect on thermal performance, but again the level of improvement decreases as the airflow increases.

Numerical study of thermal performance of FC-PBGA assembly with extruded-fin heatsink

The trend in microelectronics is toward increasingly higher input/output, higher component density and higher electrical performance, which makes thermal enhancement of package performance an increasingly important issue. In both natural and forced convection environments, three-dimensional finite element simulation is used to study thermal performance of a flip-chip plastic ball grid array (FCPBGA) assembly with an extruded-fin heatsink on top of the assembly. The finite element model is complete enough to include key elements such as bumps, solder balls, substrate, printed circuit board, vias and ground planes for both signal and power. Temperature fields are simulated and presented for several FC-PBGA assembly configurations. Thermal resistance is calculated to characterize and compare the thermal performance by considering alternative design parameters of the extruded-fin heatsink and the lid.

Non-isothermal flow of a polymeric liquid through rounded L-channels

Abstract The non-isothermal creeping flow of nylon-6 in L-channels with rounded corner has been studied numerically. A differential-type, non-isothermal White-Metzner constitutive equation is used for this flow simulation. Computational results were obtained by the elastic-viscous split-stress (EVSS) finite element method, incorporating the streamline-upwind Petrov-Galerkin (SUPG) scheme. The generated thermal field is entirely due to viscous heating. Essential flow characteristics, including temperature distribution in the flow field, are predicted. The resulting local Nusselt numbers along the walls and dimensionless bulk temperature along the channel are predicted. Furthermore, the effects of flow-rate, temperature-thinning, and geometry are investigated. In the curved elbow, the local heat transfer coefficient is higher along the outer wall than along the inner, and the difference is more significant for higher flow-rate. The local Nusselt number and bulk temperature distributions increase with flow-rate, but decrease with fluid temperature-thinning. The effect of elbow radius on these two values is only significant in the curved elbow.