Waste materials such as periwinkle shells (PS) and waste cooking oil (WCO) were considered as heterogeneous catalyst and renewable feedstock for biodiesel production respectively in line with the current search for alternatives of the environmentally unfriendly and gradually depleting fossil fuel. PS were size reduced and calcined at 673K for 4 hours to remove carbonaceous and volatile matter in the sample. Physicochemical analyses on the WCO revealed high FFA (2.81%) therefore the need for esterification (0.42%). One factor at a time (OFAT) results show that methanol to oil ratio, catalyst loading, reaction temperature and time had significant effect on the biodisel yield. The transesterification reaction kinetics data was modelled using the zero-order, pseudo-first order and pseudo-second order models. The results presented from the error functions: root mean square error (RMSE), chi-square (χ²), mean absolute error(MAE) and coefficient of determination (R²) adjudged that the pseudo-first order model best described the process. An activation energy of 16.47 KJ/mol was obtained. Gas chromatography result revealed that a biodiesel yield of 73.92% was achieved at 8:1 methanol to oil ratio, 1% catalyst loading, 300 rpm stirring speed, 333K reaction temperature and 90 minutes contact time. The findings suggest potentials of PS as a viable catalyst for biodiesel production.

When a circular body is immersed in a fluid, its interaction with the surrounding water leads to the formation of waves and ripples. This fascinating phenomenon is primarily driven by the fluid encountering a crucial point on the body, known as the complex centre of pressure (iCoP). This point acts as a threshold that instigates disturbances in the fluid, illustrating why the body affects the fluid dynamics even before it is fully submerged. The concept of the iCoP introduces a new dimension to our understanding of fluid dynamics defined by the equation as . The iCoP is symmetric and dependent solely on the diameter of the body, which enables it to pinpoint where fluid disturbances originate in the water. The immersion depth and oscillatory behaviour of the circular body are described by . Here, signifies that the body should be half-immersed, with its centre positioned halfway below the waterline, while the term indicates that the body’s oscillatory movement, with an amplitude of , causes the body to move up and down from this equilibrium position which makes the body not to be totally half immersed as indicated by . Consequently, the immersion depth varies and reflecting both partial immersion and dynamic oscillation. The real part of the iCoP reveals critical locations for fluid displacement, which leads to wave formation, while the imaginary part uncovers the phase shifts that describe the body’s dynamic interaction with fluid motion.