This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations. Collocation is performed at Gaussian points to obtain an optimal solution, hence the name orthogonal collocation. The method is used to solve various cases of Burgers’ equations, including the modified Burgers’ equation. The KdV–Burgers’ equation is considered as a test case for the OCFE method using cubic splines. The results compare favourably with existing results. The stability and convergence of the method are also given consideration. The method is unconditionally stable and second-order accurate in time and space.
Separation theory describing the motions of palm kernel and shell on rotating incline was analysed. Two series of differential equations, in order to obtain the dispatch angles of kernel and shell for the separation process were developed respectively. The differences in the motions and physical features of the particles formed the premise for separation. The results obtained from the theory showed a possibility of product separation within the approximate ranges of dispatch angles between 25 and 90 0 for kernels and shells on rotating incline, with specified slide limit, angular velocity and radius of the incline, and comparisons were made between the theoretical and experimental results. The dispatch angles obtained from both theory and experiment reasonably showed significant agreement and therefore suggested validity of the developed theory.
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