Ordinary Differential Equation in Funnel Design for Fastest Bottling Process

Abstract

Most problems common in science and engineering can be modeled. The funnel is more used in industrial and home applications to transfer a material from one container using a funnel. The shape of the funnel according to the concept can produce precise stability. This study can also determine the shortest time to empty the funnel. The correct solution can be analyzed using the method in the software Matlab. Numerical methods are the methods used to obtain accurate, efficient and stable estimates. Methods such as the Heun method, implicit midpoint method, explicit midpoint method and Euler method can be solved by differential equations problems which used to determine the appropriate parameters for short time analysis. The stability of each method can determine the appropriate funnel design based on the graph produced for each parameter. The method will be discussed and compared in terms of accuracy and efficiency to solve differential equations to determining the appropriate parameters for optimum design of funnel. Each method is used to determine the most appropriate method. At the end of the study, numerical results can be obtained indicate that implicit midpoint methods provide greater stability and accuracy than other methods. In conclusion, the proper selection of the funnel design can minimize the cost of the funnel design and optimum funnel designs also control excess wastage or spillage.