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

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

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

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

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.

Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

A New Proof of the Lester’s Perimeter Theorem in Euclidean Space

An injection defined from Euclidean space n-space E^n to itself which preserves the triangles of perimeter 1 is an Eucldean motion. J. Lester gave two different proofs for this theorem in Euclidean plane [1] and Euclidean space [2]. In this study a new technique is developed for the proof of this theorem which is valid in both Euclidean plane and Euclidean space.

On The Numerical Solutions of Boundary Layer Equations of Williamson Fluid Past a Moving Plate

Laminar boundary layer flow of Williamson fluid over a moving plate is discussed in this paper. The governing equations of the flow problem are transformed into similarity equations using similarity technique. The reduced equations are numerically solved by finite difference method. The graphical presentation is discussed.

Scientific Numerical Pattern in Stringed-Fretted Musical Instrument

Music, a creative art has a strong foundation on science and mathematics. Source of music can vary from vocal chord to various types of musical instruments. One of the popular stringed and fretted musical instrument, the guitar has been discussed here. The structure of the guitar is based on mathematical and scientific concepts. Harmonics and frequency play pivotal role in generation of music from a guitar. In this paper, the authors have investigated various factors related to the structure of a guitar. Aspects related to the musical notes of a guitar have been analyzed to gain a better insight into the mathematical pattern involved in the music of a guitar.

Stability Analysis of the Corruption Free Equilibrium of the Mathematical Model of Corruption in Nigeria

In this paper, a mathematical model of the transmission dynamics of corruption among populace is analyzed. The corruption free equilibrium state, characteristic equation and Eigen values of the corruption model were obtained. The basic reproductive number of the corruption model was also determined using the next generation operator technique at the corruption free equilibrium points. The condition for the stability of the corruption free equilibrium state was determined. The local stability analysis of the mathematical model of corruption was done and the results were presented and discussed accordingly. Recommendations were made from the results on measures to reduce the rate of corrupt practices among the populace.

Effect of Nonthermal Ions on Dust Acoustic Waves in Magnetized Plasma

A fluid model is considered to study the nonlinear dust- acoustic waves (DAW) in magnetized dusty plasma. The model consists of dust articles having negative charge, nonthermal ions, and Boltzmann electrons. Sagdeev Potential equation is derived in the form of an energy integral by applying nonperturbative approach. The pseudopotential (Sagdeev potential) profile is analyzed to study the characteristic of the solitary waves. The study has been made related to the transition of the DAW and the corresponding characters by observing the variation of amplitudes and width of the solitons with Mach number, temperature ratio, density ratio, concentration of nonthermal ions, and the direction cosine. The parametric ranges are estimated numerically to confirm the existence of solitary waves of arbitrary amplitude.