This study presents a green process to synthesize biodiesel using biosynthesized nano-catalyst and a novel methodology for analyzing the impact of influencing factors -methanol/oil ratio, the concentration of nano-catalyst, temperature, and time of reactions-on the yield of biodiesel obtained by heterogeneous nano-catalyst-based transesterification reaction. Nano-calcium oxide (nano-CaO) was obtained as a heterogeneous nano-catalyst using waste eggshells. Waste cooking oil was treated with methanol and nano-catalyst at varying methanol: oil ratios (4 -14:1), nano-catalyst concentration (0.5 -2 %), time of reaction (3 -4.5 hrs), and temperature (50 -65 • C). The superiority and effectiveness of the proposed transesterification indices were accomplished making use of Deluca and Termini fuzzy entropy weighted indexes to obtain optimal reaction conditions with 95.49 % biodiesel yield.
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