غریبوں کی معاشی کفالت میں صحابیات رضی اﷲ عنھن کا کردار

Islamic cardinal precepts include seeking benefaction and patronage of other Muslims. Generally, Islamic history is replete with such munificent and generous personages as were ever geared up to serving humanity, yet the golden era of Islamic history excelled in profusion of such noble persons. When we review the aspect of serving mankind in the life history of the reverend Sahaba (the holy prophet’s disciples), we come to know that they had highly remarkable passions for helping, beneficing, supporting and sustaining their relatives, friends as well as the common run. The level of their charity was so great that they felt felicity and prostrated to Allah in gratitude even after giving away their all possessions and belongings for Allah’s sake only. In fact, the motivation behind this generosity was the attainment of pleasing Allah and the obedience and submission to the holy prophet. They had no iota of worldly voracity or avarice. Therefore, they were ever elated over giving away their assets.

Nanofluid Flows in Different Geometries

Many conventional fluids, such as water, sodium alginate, organic liquids (e.g., propylene and ethylene glycols, etc.) and some others, are quite often used in various engineering and industrial processes as coolants. The use of water in car radiators is a very basic example. Nowadays, scientists are keenly looking for ways to enhance the performance of engines and such equipment where these coolants are being used. Conventionally, the heat transfer capability of these liquids is not up to the mark. Therefore several attempts have been made to enhance their thermo-physical capabilities. The use of nanofluids is one of such efforts. Scientists, over the past few decades, have been working on the idea of mono-nanofluids (nanofluids with single nanomaterials), to enhance the thermal efficiency of these traditional fluids. However, to improve the number of desirable features of mononanofluids, a novel subject of hybrid nanofluids (nanofluids with two or more nanomaterials) has come into existence. It exhibits superior thermo-mechanical properties when compared to mono nanofluids. In this manuscript, a number of thermal conductivity models, for both mono and hybrid nanofluids, have been employed to see the working of these models in different geometries. In the case of hybrid nanofluids, the modified versions of the models (such as Renovated Hamilton and Crosser’s model, Bruggeman’s model, Hamilton and Crosser’s model, Maxwell’s model, and Xue’s model) for thermal conductivity have been considered. The flow of mono as well as hybrid nanofluids inside an expanding\contracting domains, rectangular conduit with the lower stretchable wall, curved stretching surface, and curved channels, have been studied in details. A novel analysis of hybrid nanofluid flow between two Riga plates is also a part of this manuscript. Moreover, the squeezing flow of a hybrid nanofluid inside a rotating rectangular conduit, with lower stretchable walls, has also been investigated. The impact of the externally applied magnetic field, along with the internal heat generation phenomena, on the flows and heat transport mechanism of some mono and hybrid nanofluids have thoroughly been examined. Heat and mass transfer under the influence of nonlinear thermal radiation and chemical reaction effects in several geometries have been studied in this manuscript. xi In our analysis, we have used certain similarity transformations and scaling parameters to reduce the governing partial differential equations to the corresponding systems of nonlinear ordinary differential equations (dimensionless). This process reduces the number of variables, and parameters, which leads to a relatively more straightforward mathematical treatment. However, the resulting systems are still complicated enough to have an exact solution. For their treatment, we have discussed the implementation of several approximation techniques based on the method of weighted residuals and wavelet methods. We have also proposed some modifications in wavelet methods for a better and more flexible implementation. The plots for velocity, together with temperature, and concentration profiles (wherever applicable) are presented to capture the effects of involved parameters on the respective profiles. It has been found that the addition of nanomaterials significantly boosts the thermal and heat transport properties of the host fluid and that these phenomena are more prominent for the hybrid nanofluids.