Mathematical Journal of Interdisciplinary Sciences

Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary Layer

Manisha Patel, Hema Surati, M G Timol — Tue, 08 Jun 2021 00:00:00 +0530

Blasius equation is very well known and it aries in many boundary layer problems of fluid dynamics. In this present article, the Blasius boundary layer is extended by transforming the stress strain term from Newtonian to non-Newtonian. The extension of Blasius boundary layer is discussed using some non-newtonian fluid models like, Power-law model, Sisko model and Prandtl model. The Generalised governing partial differential equations for Blasius boundary layer for all above three models are transformed into the non-linear ordinary differewntial equations using the one parameter deductive group theory technique. The obtained similarity solutions are then solved numerically. The graphical presentation is also explained for the same. It concludes that velocity increases more rapidly when fluid index is moving from shear thickninhg to shear thininhg fluid.
MSC 2020 No.: 76A05, 76D10, 76M99

Some Identities Involving the Generalized Lucas Numbers

Mansi S. Shah, Devbhadra V. Shah — Thu, 22 Oct 2020 00:00:00 +0530

Determination of Exponential Congestion Factor of Road Traffic Flow Caused By Irregular Occurrences

DK Gangeshwer, Thaneshwar Lal Verma — Thu, 22 Oct 2020 00:00:00 +0530

The present paper deals exponential congestion model of road traffic flow caused by irregular occurrences. Congestion that is happened by unpredictable events, for example, auto collisions, handicapped vehicles, climate conditions, over burdens and unsafe materials of vehicles. On account of these sorts of sudden occasions, the travel times taken on the roadways are questionable. We established the steady state conditions based on number of vehicles on road links. The large c values of those links, M/M/1 queues model under the batch service interruptions may be used. The formulation and assumptions of the proposed models have been developed. The exponential congestion factor (ECF) models based on M/MSP/C queuing have been presented. Finally, the numerical examples have also been discussed.

Infinite Nested Radicals - A Way to Express All Quantities Rational, Irrational Transcendental By a Single Integer Two

Narinder Kumar Wadhawan, Priyanka Wadhawan — Fri, 09 Oct 2020 00:00:00 +0530

This paper proves that all mathematical quantities including fractions, roots or roots of root, transcendental quantities can be expressed by continued nested radicals using one and only one integer 2. A radical is denoted by a square root sign and nested radicals are progressive roots of radicals. Number of terms in the nested radicals can be finite or infinite. Real mathematical quantity or its reciprocal is first written as cosine of an angle which is expanded using cosine angle doubling identity into nested radicals finite or infinite depending upon the magnitude of quantity. The finite nested radicals has a fixed sequence of positive and negative terms whereas infinite nested radicals also has a sequenceof positive and negative terms but the sequence continues infinitely. How a single integer 2 can express all real quantities, depends upon its recursive relation which is unique for a quantity. Admittedly, there are innumerable mathematical quantities and in the same way, there are innumerable recursive relations distinguished by combination of positive and negative signs under the radicals. This representation of mathematical quantities is not same as representation by binary system where integer two has powers 0, 1, 2, 3…so on but in nested radicals, powers are roots of roots.