Design of a novel chip on glass package solution for CMOS image sensor device

This paper presents a chip-on-glass (COG) package solution for CMOS image sensors based on highly precise and reliable bumping and flip-chip bonding techniques. The package is fabricated using three core techniques, namely the damage-free image sensor bumping technique, the wafer form glass substrate patterned technique, and the damage-free flip-chip bonding technique. Since the proposed package concept is new, the effects of the package geometry and material properties on the package reliability are uncertain in the initial design stage. A three-dimensional nonlinear finite element model of the proposed CMOS image sensor package is created. In the simulations, the applied thermal load is cooled from 200 °C to ambient temperature (25 °C) to model the thermal deformation and warpage of the package during the practical ACF assembly cooling process. The design parameters influencing the reliability of the package, i.e. the material properties of the ACF, the thickness of the image chip and the thickness of the optical glass are investigated. Two control levels are specified for the chip, glass, and ACF factors and a 2³ factorial design is created to determine the appropriate combination of material properties and geometric size. It is found that the glass thickness and the ACF properties significantly affect the thermal deformation of the package, while the chip and glass factors, and the interaction between them, significantly affect the warpage. Regression models are developed to perform a series of surface response simulations. Using the developed statistical tests and regression models, suitable material selection criteria and geometric sizes can be specified to satisfy various reliability considerations in the initial design stage.     

FORCED CONVECTION IN MICROPOLAR FLUID FLOW OVER A WAVY SURFACE

Forced convection in the boundary layer flow of a micropolar fluid over a wavy surface is studied by the coordinate transformation and the spline alternating direction implicit method. Effects of the vortex viscosity parameter and the wavy geometry on the velocity, the local skin friction coefficient, and the local Nusselt number (Nu) are studied. Results show that the harmonic curves for the local skin friction coefficient and the local Nu have the same frequency as the frequency of the wavy surface. Moreover, the vortex viscosity parameter tends to decrease the heat transfer rate and to increase the skin friction coefficient.     

MAGNETIC FIELD EFFECTS ON LAMINAR FILM CONDENSATION ON A FINITE-SIZE HORIZONTAL WAVY DISK

This work aims to study the laminar film condensation heat transfer with magnetic field effects on a finite-size horizontal wavy disk. Mathematical analysis is used to obtain the dimensionless governing equations and boundary conditions, and the cubic spline collocation method is then used to calculate the flow and heat transfer characteristics along the wavy disk. The effects of the important parameters, such as Hartmann number, condensation parameter, wave number, amplitude-wavelength ratio, and Pr/Ja on the heat transfer characteristics have been successfully examined. The magnetic field effect increases the critical condensate thickness and thus decreases the condensation heat transfer. Odd wave number effects decrease the critical condensate thickness and thus enhance the condensation heat transfer.     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Soret and Dufour effects on free convection boundary layers of non-Newtonian power law fluids with yield stress in porous media over a vertical plate with variable wall heat and mass fluxes

This work studies the Soret and Dufour effects on the free convection boundary layers over a vertical plate with variable wall heat and mass fluxes in a porous medium saturated with a non-Newtonian power law fluid with yield stress. The governing equations are transformed into a dimensionless form by the similarity transformation and then solved by a cubic spline collocation method. Results are presented for the local surface temperature and concentration for various parameters of the power law fluid with yield stress in porous media. An increase in the power law exponent decreases the local surface temperature and concentration, thus increasing the local Nusselt and Sherwood numbers. An increase in the Soret parameter tends to increase the local surface concentration, thus decreasing the local Sherwood number. Moreover, increasing the Dufour number increases the surface temperature and thus decreases the local Nusselt number.     

Soret and Dufour effects on free convection heat and mass transfer from an arbitrarily inclined plate in a porous medium with constant wall temperature and concentration

The free convection boundary layer flow over an arbitrarily inclined heated plate in a porous medium with Soret and Dufour effects is studied by transforming the governing equations into a universal form. The generalized equations can be used to derive the similarity solutions for limiting cases of horizontal and vertical plates and to calculate the heat and mass transfer characteristics between these two limiting cases. The heat and mass transfer characteristics are presented as functions of Soret parameter, Dufour parameter, inclination variable, Lewis number, and buoyancy ratio. Results show that an increase in the Dufour parameter tends to decrease the local heat transfer rate, and an increase in the Soret parameter tends to decrease the local mass transfer rate. As the inclination variable increases, the local Nusselt number and the local Sherwood number decrease from their respective values for horizontal plates, reach their respective minima, and then increase to their respective values for vertical plates. The minima are where the tangential and normal components of buoyancy force are comparable.     

Double diffusive natural convection along an inclined wavy surface in a porous medium

This paper studies the double diffusive natural convection near an inclined wavy surface in a fluid saturated porous medium with constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are solved by the cubic spline collocation method. Effects of angle of inclination, Lewis number, buoyancy ratio, and wavy geometry on the heat and mass transfer characteristics are studied. Results show that a decrease in the angle of inclination leads to a greater fluctuation of the local Nusselt and Sherwood numbers. Moreover, increasing the angle of inclination tends to increase the total heat and mass transfer rates.     

Modeling of Moisture Diffusion in Heterogeneous Epoxy Resin Containing Multiple Randomly Distributed Particles Using Hybrid Moisture Element Method

This paper employs a novel numerical technique, designated as the hybrid moisture element method (HMEM), to model and analyze moisture diffusion in a heterogeneous epoxy resin containing multiple randomly distributed particles. The HMEM scheme is based on a hybrid moisture element (HME), whose properties are determined by equivalent moisture capacitance and conductance matrixes calculated using the conventional finite element formulation. A coupled HME-FE scheme is developed and implemented using the commercial FEM software ABAQUS. The HME-FE scheme is then employed to analyze the moisture diffusion characteristics of a heterogeneous epoxy resin layer containing particle inclusions. The analysis commences by comparing the performance of the proposed scheme with that of the conventional FEM in modeling the moisture diffusion process. Having validated its performance, the scheme is then employed to investigate the relationship between the volume fraction of the particles in the resin composite and the rate of moisture diffusion. It is found that moisture diffusion is retarded significantly as the volume fraction of particles increases.
The HMEM approach proposed in this study provides a straightforward and efficient means of modeling moisture diffusion in a heterogeneous epoxy resin containing multiple randomly distributed particles since only one HME moisture characteristic matrixes needs to be calculated for all HMEs sharing the same characteristics. Furthermore, different volume fractions can be modeled without modifying the original model simply by controlling the size of the inter-phase region within the HME domain.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a downward-pointing vertical cone in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local Nusselt number tends to decrease as the Dufour parameter is increased. The effect of the Dufour parameter on the local Nusselt number becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number.