ﷺ
اُن کی سوچوں کا سفر شہرِ مدینہ کی طرف
جن کے خوابوں کا نگر شہرِ مدینہ کی طرف
آنے والوں کے دل و جان وہیں رہ جائیں
جانے والوں کی نظر شہرِ مدینہ کی طرف
قبلۂ دنیا و دیںؐ ، شمعِ حرم گاہِ مبیںؐ
رہبرِ جنّ و بشرؐ ، شہرِ مدینہ کی طرف
ایسی تسکین کسی گوشۂ دنیا میں کہاں
خُلد کا کُھلتا ہے در شہرِ مدینہ کی طرف
ذرّے ذرّے میں وہاں طور نظر آتا ہے
قطرہ قطرہ ہے گُہر شہرِ مدینہ کی طرف
سوز جامیؔ کی جھلک لفظوں میں آئے تو کہوں
’’سطرِ مدحت کا سفر شہرِ مدینہ کی طرف‘‘
کام آتا ہے فقط جذبۂ صادق عرفانؔ
لے کے جاتا نہیں زر ؛ شہرِ مدینہ کی طرف
This paper establishes a novel breakthrough in my world pioneering academic theory of unfolding the miracles ofIslam in Mathematical Sciences. Ofparticular significance is the humble step on the way of computing the First Minimum Newtonian Approximation (FMNA) of the distance between the lobe of the ear and the shoulder ofone of the bearer angels of the Divine Throne of Allah the Almighty according to the approved correct speech ofProphet Muhammad(p). The paper makes an effort to illustrate that at the top level of human intelligence, even numbers, dimensions, spaces and all other forms of human knowledge would definitely prostrate in full submission to the greatness ofAllah, the most exalted.
A Numerical Study of Flow Past Bluff Bodies in Tandem and Side-By-Side Arrangements Using the Lattice Boltzmann Methods Flow around bluff bodies is an area of interest for scientist from several years. A flow over bluff bodies is commonly seen in engineering, for example, wind over a group of tall buildings and fluid flow over heat exchanger tube arrays. A flow past bluff bodies in tandem and side-by-side arrangements are investigated numerically using lattice Boltzmann methods in this thesis. The numerical methods are validated for flow past a single square cylinder, and the numerical results show a good agreement with the available reference data. In the first problem of this thesis a numerical simulation is carried out for flow past a square cylinder with a detached flat plate using the lattice Boltzmann method for gap spacing (g) ranging from 0 to 11 and Reynolds number (Re) ranging from 75 to 200. Numerical results reveal that as gap spacing increases, there exist a critical gap spacing at g = 2 - 2.25, where the mean drag coefficient, Strouhal number, root-mean-square values of the drag and lift coefficients reach either maxima or minima. The shed vortices behind the detached flat plate and flow regimes are affected by gap spacing and Reynolds number. The observed results further indicates that the critical gap spacing and flow regimes are strongly dependent on g and Re. Flow control aims to reduce the wake dynamics and the fluctuating force. Second problem focuses on the effect of equal and unequal gap spacing and Reynolds number ranging from 75 to 175 on flow characteristics by identifying wake patterns, force statistics as well as wake oscillation frequencies. Different kinds of wake patterns are observed for the flow past three side-by-side square cylinders for equal and unequal gap spacing. It is found that the characteristics of the flow significantly depend on both the Reynolds number and gap spacing and the latter is much stronger than the former. In the third problem of this thesis, lattice Boltzmann simulations are carried out for flow past a row of rectangular cylinders at aspect ratios (AR) 0.5 and 2 for different gap spacings at Re = 150. The numerical results reveal that wake patterns are strongly dependent on g and Re. There exist secondary cylinder interaction frequencies along with primary vortex shedding frequency due to jet flow between the gaps. More interesting variation in fluid forces are observed for the case of AR = 2, as vortices generated on the surface of cylinder because the width of the cylinder is 2d. This study shows that lattice Boltzmann method is a good tool to capture the important features of flow past bluff bodies and suppression of fluid forces.