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The purpose of this study is to investigate the dynamics of capillary underfill flow (CUF) in flip-chip packaging, particularly in a multi-chip configuration. The study aims to understand how various parameters, such as chip-to-chip spacing (S12), chip thickness (tc) and others, affect the underfill flow process. By using computational fluid dynamics (CFD) simulations and experimental studies, the goal is to provide insights into understanding the dynamics of CUF in heterogeneous electronic packaging.

The paper introduces a CFD analysis and experimental study on CUF in a multi-chip configuration, aiming to understand underfill flow dynamics. A 3D geometry models of multi-chip arrangement are created using computer-aided design (CAD) software. After that, the CAD models are meshed and simulated in Ansys Fluent using incompressible and non-Newtonian fluid properties. The study maintains S12 of 2.86 and tc of 22.29 between experimental and simulation data for results validation. Next, a various of S12 values (1.14, 2.86, 5.71, 8.57, 14.29 and 20) which focus on tc of 22.29 have been investigated. Further studies have been conduct using S12 of 5.71 and tc of 8.00, 14.29 and 22.29.

Results show a strong correlation between simulation and experiment which validate the correctness and robustness of simulation. Further parameter’s studies using simulation for various of S12 indicated that higher S12 values lead to faster flow. This effect is due to large underfill weight from reservoir able to flow into S12 region which contributed to higher mass momentum movement. Furthermore, the effect of various of tc shows that the thicker the chip the faster the underfill to flow in S12 region.

The intentional exclusion of solder bump pattern arrangements from the experiment and simulation may limit the study's ability to fully understand the impact of solder bump patterns on underfill flow. Therefore, more parameters can be investigated such as solder bump pattern, underfill weight and dispense pattern in the future using CFD.

The manuscript provides a comprehensive examination of the contributions of CFD to the advancement of knowledge regarding CUF phenomena in heterogeneous electronic packaging assemblies. Moreover, it delineates the utilization of CFD methodologies to assess the influence of chip-to-chip spacing (S12) and the thickness of the chip (tc) on the underfill flow characteristics.

This paper fulfills an identified need of computational fluid dynamics method to study capillary underfill flow dynamics in heterogenous electronic packaging.

This paper aims to view the tradition of the Prophet in zakat payment, especially the attributed measurements, and adapt these measures to current zakat measurement practices.

This study is designed with an exploratory sequential mixed method where qualitative data were collected from historical archives and also from the measurement of available ṣāʿ صاع and mud_ مد. These standard measures were collected from Malaysia and other Muslim countries and calibrated at the National Measurement Standards Laboratory (currently carried out by the National Metrology Institute of Malaysia). The volume of the ṣāʿ were tabulated, charted, analyzed and determined.

Prophet Muḥammad ordered for zakat al-fiṭr زكاة الفطر to measure the crops using ṣāʿ (gallon: volume measure), not raṭl رطل (pound: standard weight). This paper recommends a reference volume for the ṣāʿ, and from this value, the volume for the smaller measure mud and much larger measure wasq وسق were calculated. The agricultural niṣāb (5 wasq) is one of the key parameters in ṣāʿ volume analysis.

This study covers standard measures acquired from Malaysia, Saudi Arabia and the United Kingdom (traceable to India). Several empirical data are attained from previous studies from Saudi Arabia and North Africa. Also, some theoretical data are obtained from kitab tafsir, hadith and kitab turath (books and records written by early scholars). A concern in this study is the ratio of de-husked grains currently approximated at half of un-hulled grains. This might not necessarily be accurate and may differ by different types of grains.

After the introduction of the modern measurement system known as the International System of Units (SI) in 1971, ṣāʿ became obsolete, leaving each state in Malaysia to define and convert ṣāʿ to SI units variously. This paper contributes to standardizing the conversion to one value with an appropriate SI unit, that has traceability to the Prophet’s ṣāʿ. This national reference standard ṣāʿ is essential for zakat al-fiṭr measurement, important for zakat centers and impacting every Muslim in Malaysia. Often overlooked, ṣāʿ is more crucial as a basis in determining and standardizing the seasonal crops niṣāb, unfolding the reasons why the poor are paying the paddy zakat in Malaysia.

The Prophet’s tradition for ablution is to use water not more than one mud, this is aligned with the 12th Sustainable Development Goals by the United Nations which promoted the responsible consumption of water. Considering half (adults) of the 1.9 billion Muslims in the world, multiplied by 5 times of prayer, the Muslims will at least use 4.75 billion muds of water for ablution alone in 1 day. This is approximately 3.5 billion liters of water daily, and if they limit their water usage to 1 mud for each ablution, they collectively will save at least four times more water (about 14 billion liters) daily than performing ablution from a running tap. Though for ablution, accuracy is not an issue, the mud impact on all Muslims is vital on a daily basis, literally by volume.

Ṣāʿ is essential in measuring food for the annually obligated zakat al-fiṭr and more crucial as a basis in determining the seasonal crops niṣāb. This paper contributes to the development of a national reference standard ṣāʿ for Malaysia that has traceability to the Prophet’s ṣāʿ.