علم الروایہ و الدرايۃ٬ مفہوم اور تاریخی پس منظر

Hadith and Science of Hadith are the terms used by specialists of Hadith known as Mohaditeen. A hadith is a recorded statement, action or approval of the Prophet Muhammad (S.A.W). It is considered as the second primary source of Islamic law after Quran. It is also a part of revelation. Prophet Muhammad (S.A.W) described it through his words. The science of hadith examplifies the principles with which a specialist in the field of Hadith evaluates the authenticity and accuracy of narrations. In the past there were two specific and developmental stages for the Books of Hadith terminology. In its 1st stage, the Scholars focused on the compilation of the statements of earlier scholars, quoting the expressions they had used without evaluating those terms or suggesting terms applicable to those expressions. This methodology was adopted by the earlier scholars such as Yaḥyā ibn Ma`īn, `Alī ibn al-Madīnī, Muslim ibn al-Ḥajjāj, and Al – Tirmidi. In the second period the Authors cited the quoted statements of the earlier works and began the collection and codification of relevant terms. In this period, the specific Principles were established. Examples of books authored in this manner are: Ma`rifah `Ulūm al-Ḥadīth by al-Ḥākim, Al-Kifāyah by al-Khaṭīb alBaghdādī and the Introduction of Ibn al-Ṣalāḥ. In this article the two major types of science of Hadith have been mentioned, Rewayat-ul-Hadith and Derayat-ulHadith. Its definition and historical background has been described.

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.