~76~ International Journal of Statistics and Applied Mathematics 2021; 6(3): 76-82 ISSN: 2456-1452 Maths 2021; 6(3): 76-82 © 2021 Stats & Maths www.mathsjournal.com Received: 01-02-2021 Accepted: 03-03-2021 Felix Kibet Rotich MSc Applied Mathematics, Department of Mathematics and Computer Science, School of Science, University of Eldoret, Kenya Julius Shichikha Maremwa MSc Applied Mathematics, Department of Mathematics and Computer Science, School of Science, University of Eldoret, Kenya Joseph Kipchirchir Kandie MSc Applied Mathematics, Department of Mathematics and Computer Science, School of Science, University of Eldoret, Kenya Corresponding Author: Felix Kibet Rotich MSc Applied Mathematics, Department of Mathematics and Computer Science, School of Science, University of Eldoret, Kenya Mathematical modeling of flow of fluids in an open channel of parabolic cross-section Felix Kibet Rotich, Julius Shichikha Maremwa and Joseph Kipchirchir Kandie Abstract This study finds turbulent, non-uniform and Newtonian fluid flows with a parabolic cross-section in the open channel. On parabolic channels, we examine the effects of top width, channel slope and energy coefficient on flow velocity. Because of its stability, convergence and precision, the governing equations are solved by finite difference approximation approach. Using MATLAB software, the result is presented graphically. The findings are that; an increase in the channel slope, top width and energy coefficient has been shown to lead to increased velocity of flow. This study helps in floods control, construction of channels such as canals and crop irrigation. Keywords: rate of metabolism, blood mass stream rate, warm conductivity, warm era, limited component method, Pennes Bio - heat model 1. Introduction 1.1 Background information Heavy Rainfall in Kenya has been experienced in most parts of the country in several years. Areas most affected by the Heavy rainfall includes; Baringo, Budalangi, TanaRiver, West Pokot, Makueni and Machakos. This amount of water from heavy rainfall causes flooding in the affected areas. Flooding leads to the destruction of houses, bridges and other land structures. It also leads to the death of people and animals. The soil, crops and plantations have been destroyed. In addition, roads made impassable and transport paralyzed. Moreover, flooding water is a breeding ground for mosquitoes that causes malaria. The handling of such unexpected amounts of water is a challenge for open channel designers in Kenya and around the world. The solution to such disasters is the design of channels of different cross-sections such as circular, triangular, rectangular, trapezoidal, elliptical and parabolic. Currently floods are still a challenge in Kenya and there is a need to design an efficient channel that would transport the maximum amount of water in flood areas to the areas needed for crop irrigation and hydroelectric power generation. The current Government of Kenya focuses on four main agendas: Food security and nutrition, universal health coverage and affordable housing and Manufacturing. This study cuts across the four agendas. Firstly, food security, irrigation of crops from flood waters. Secondly, the Universal Health Survey, floods lead to health hazards such as cholera. Thirdly, Manufacturing, flooding of water to the hydroelectric power plant for the generation of electricity for the manufacturing industry. Finally, affordable housing, flood control, housing and roads will not be destroyed. The goal of this study is to investigate parabolic open channel as an efficient channel that would push excess water out of flooded areas and direct the excess water to crop irrigation and hydroelectric power generation for industrial and domestic use.