iosr-Jm   Volume-18 ~ Issue-1 ~ Jan. – Feb. 2022

Abstract:An analytical study to determine the effect of certain material parameters on the rate of heat transfer and rate of mass transfer was made. The hydrodynamical equations of continuity, momentum, energy and concentration were non dimensionalized and solution obtained by perturbation method. Using numerical values, it was observed that increase in Prandtl number, radiation and heat absorption, depreciated the Nusselt number and skin friction of the nanofluid. Enhancement of the magnetic Hartmann number also enhanced the skin friction but increase in the frequency of oscillation depreciates skin friction and enhanced the rate of mass transfer. The Schmidt number depreciates both the skin friction and the Sherwood number as it is enhanced.......

Keywords: Rate of Heat transfer; Rate of mass transfer; Pertubation method, Nanofluids, Skin friction.

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[4]. Ngiangia, Alalibo.T and Orukari M.A. (2021); Heat Transfer Coefficient and Skin Friction Determination of Thermal Radiation Effects on MHD Convective Flow of Alumina Nanofluid Through a Non-Darcian Porous Plate. International Journal of Scientific and Engineering Research 12(5): 355-378
[5]. Ngiangia, Alalibo.T, Orukari M.A. Amadi, O and Nwabuzor, P. (2021); Onset of Transition to Non-Newtonian MHD Chemically Reacting Couette Copper Nanofluid Flow in a Radiative Porous Medium. International Journal of Mathematics Trends and Technology 67(5): 126 – 149 Doi: 10.14445/22315373/IJMTT-V6715P515

Abstract:Graph theory is one of the most important and basic topics of discrete mathematics in Mathematics. In all sectors of science graph theory has a great impact. The most common use of graphs occurs in Physics and Chemistry except Mathematics. It is also used in the modeling of Biology, Finance, and Computer science. Basic concepts of graphs are discussed here with classification with figures.
In this paper Historical background of graphs, classification, matrix representation of graphs, different types of graph operations, isomorphism, and some important theorems and problems are briefly reviewed. We will get a clear and visual concept on graph theory of discrete mathematics in this paper.

Key Word: Graphs, Matrix Representation, Incidence matrix, Adjacency Matrix, Cut-Set Matrix, Circuit Matrix, Graph operations.

[1]. Discrete Mathematics and its applications - Kenneth H. Rosen (7th edition)
[2]. Discrete Mathematics - Prof. Dr. Md. Ayub Ali and Prof. Dr. M.F Rahman
[3]. Graph theory - Harary
[4]. Graph Theory with Applications - J.A. Bondy and U.S.R. Murty
[5]. Graph Theory- Reinhard Diestel

Abstract: The mathematical modeling of cigarette smoking has an important role in understanding the transmission dynamics and developing effective prevention methods. In this study, a non-linear mathematical model is used to examine the extent of smoking from person to person and in a group of large social networks, as well as the social influence on temporary quit smokers. Firstly, the positivity and boundedness of the model solution are determined by the complete differential process, followed by the computation of the infection-free and endemic equilibrium of the system. The basic reproductive number is calculated by the next-generation matrix method. The local and global stability of the system is also presented.......

Keywords: Smoking model, social factor, smoking generation number, stability analysis, sensitivity analysis, numerical simulation.

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