Experimental study on enhancement characteristics of steam/nitrogen condensation inside horizontal multi-start helical channels

The aim of this study was to reveal the internal mechanism of enhanced condensation heat transfer, by experimentally performing steam condensation with higher inlet velocity in the horizontal multi-start helical channels (HMSHCs), and investigating the influences of pressure of steam, mass flowrate of cooling water, and mass fraction of noncondensable (NC) gas on steam condensation performance. Taking steam condensation in horizontal circular condensation channel (HCCC) as a reference, the condensation heat transfer coefficients (CHTCs), the outlet condensate mass flowrates (CMFRs), and the total steam condensation pressure drops (SCPDs) were compared and discussed, respectively. The results indicated that NC gas had a strong inhibitory effect on steam condensation, and average condensation characteristics decreased with the increase in NC gas fraction for lower Rem. But for higher Rem, the gas–liquid interfacial shearing stress can likely weaken the negative effect of NC gas. In addition, increasing the cooling water flowrate can entirety promote steam condensation. The comparison results indicated that steam condensation performance of HMSHC is better than that of HCCC under same experimental conditions. For the specific experimental scope, the average CHTCs and the outlet CMFRs in HMSHC are approximately 2.35 and 1.25 times of that inside HCCC, respectively, while the overall SCPDs in HMSHC are about 1.16 times of that inside HCCC. After introducing the performance evaluation factor, the calculation results revealed that the performance evaluation factor h PEC {h}_{\text{PEC}} of the average CHTCs in HMSHC is approximately 2.02, and the performance evaluation factor m PEC {{m}}_{\text{PEC}} of the outlet CMFRs in HMSHC is approximately 1.08. The two evaluating values are reasonable.

Lattice-Misfit Stresses in a Circular Bi-Material Gallium-Nitride Assembly

A simple and physically meaningful analytical (“mathematical”) predictive model is developed using two-dimensional (plane-stress) theory-of-elasticity approach (TEA) for the evaluation of the effect of the circular configuration of the substrate (wafer) on the elastic lattice-misfit (mismatch) stresses (LMS) in a semiconductor and particularly in a gallium nitride (GaN) film grown on such a substrate. The addressed stresses include (1) the interfacial shearing stress supposedly responsible for the occurrence and growth of dislocations, for possible delaminations, and for the cohesive strength of the intermediate strain buffering material, if any, as well as (2) normal radial and circumferential (tangential) stresses acting in the film cross-sections and responsible for the short- and long-term strength (fracture toughness) of the film. The TEA results are compared with the formulas obtained using strength-of-materials approach (SMA). This approach considers, instead of the actual circular substrate, an elongated bi-material rectangular strip of unit width and of finite length equal to the wafer diameter. The numerical example is carried out, as an illustration, for a GaN film grown on a silicon carbide (SiC) substrate. It is concluded that the SMA model is acceptable for understanding the physics of the state of stress and for the prediction of the normal stresses in the major midportion of the assembly. The SMA model underestimates, however, the maximum interfacial shearing stress at the assembly periphery and, because of the very nature of the SMA, is unable to address the circumferential stress. The developed TEA model can be used, along with the author's earlier publications and the (traditional and routine) finite-element analyses (FEA), to assess the merits and shortcomings of a particular semiconductor crystal growth (SCG) technology, as far as the level of the expected LMS are concerned, before the actual experimentation and/or fabrication is decided upon and conducted.

Assembly Bonded at the Ends: Could Thinner and Longer Legs Result in a Lower Thermal Stress in a Thermoelectric Module Design?

An analytical (mathematical) thermal stress model has been developed for an electronic assembly comprised of identical components bonded at their end portions and subjected to different temperatures. The model is used to assess the effect of the size (dimension in the x-direction) and compliance of the bonded regions (legs) on the maximum interfacial shearing stress that is supposedly responsible for the mechanical robustness of the assembly. The numerical example is carried out for a simplified two-legged Bismuth-Telluride-Alloy (BTA)-based thermoelectric module (TEM) design. It has been determined that thinner (dimension in the horizontal, x-direction) and longer (dimension in the vertical, y-direction) bonds (legs) could result in a considerable relief in the interfacial stress. In the numerical example carried out for a 10 mm long (dimension in the x-direction) TEM assembly with two peripheral 1 mm thick (dimension in the x-direction) legs, the predicted maximum interfacial shearing stress is only about 40% of the maximum stress in the corresponding homogeneously bonded assembly, when the bond occupies the entire interface between the assembly components. It has been determined also that if thick-and-short legs are employed, the maximum interfacial shearing stress might not be very much different from the stress in a homogeneously bonded assembly, so that there is no need, as far as physical design and robustness of the assembly is concerned, to use a homogeneous bond or a multileg system. The application of such a system might be needed, however, for the satisfactory functional (thermo-electrical) performance of the device. In any event, it is imperative that sufficient bonding strength is assured in the assembly. If very thin legs are considered for lower stresses, the minimum acceptable size (real estate) of the interfaces (in the horizontal plane) should be experimentally determined (say, by shear-off testing) so that this strength is not compromised. On the other hand, owing to a lower stress level in an assembly with thin-and-long legs, assurance of its interfacial strength is less of a challenge than for an assembly with a homogeneous bond or with stiff thick-and-short legs. The obtained results could be used particularly for considering, based on the suggested predictive model, an alternative to the existing TEM designs, which are characterized by multiple big (thick-and-long) legs. In our novel design, fewer small (thin-and-short) legs could be employed, so that the size and thickness of the TEM is reduced for the acceptable stress level.

Underfill Filler Settling Effect on the Die Backside Interfacial Stresses of Flip Chip Packages

Underfill is usually modeled as an isotropic medium containing uniformly distributed filler particles. However, filler particles tend to settle (or segregate) and thus alter the mechanical response of the flip chip die attachment package. The integrity of such flip chip attachment is different from that with an ideal, isotropic underfill with very uniform distribution of filler. We analyzed the thermomechanical implications of filler settling to the stresses along the die/underfill interface by considering different profiles for the local concentration of filler and calculating their effective material properties by employing the Mori–Tanaka method. As the worst-case scenario, direct silicon die attach with solder bumps was assumed to analyze the interfacial stresses, which were predicted in trend by a simplified multilayered stack model and calculated in detail by finite element simulation. The filler settling has a localized but strong influence on the interfacial peeling stress near the edge of the die. The extent of this influence is determined by the profile of filler settling: (1) if the filler is assumed to settle in the form of a bilayer, then the peeling stress near the die’s edge increases and it is directly proportional to the average volume fraction of the filler; (2) if the filler is assumed to settle gradually, then the magnitude of the peeling stress near the edge of the die becomes smaller as the local filler volume fraction near the die interface increases. The filler settling has no significant effect on the other components of the interfacial stresses. The edge fillet of underfill in pure resin can locally reverse the direction of the interfacial peeling stress and increase the interfacial shearing stress near the die’s edge.

Bonding strength of a carbon nanofiber array to its substrate

The bonding strength of a carbon nanofiber array (CNFA) grown on a copper substrate is evaluated based on the measured shearing force-at-failure and the developed analytical stress model that enables one to determine the magnitude and the distribution of the interfacial shearing stress causing the measured (given) shearing force. The experiment is conducted using specially designed test specimens. A table version of the Instron tester is used to measure the applied force and the corresponding displacement in shear. The maximum predicted shear-off stress is about 300 psi (0.211 kgf/m2), and was determined, based on the developed stress model, as a product of the measured 5 kgf/m force at the interface failure and the computed parameter k = 0.0422 m–1 of the interfacial shearing stress.