Applications of fuzzy differential equation in differential type fluid
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Date
2022-07-12
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UMT Lahore
Abstract
This work highlights the differential type fluid flow through various geometry under a fuzzy environment. Sodium alginate and engine oil are considered conventional base fluids, comprising nanoparticles of copper, silver, titanium and aluminium. The fundamental equations are obtained from the laws of conservation of momentum and energy. These partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations through suitable similarity transformation and then solved by an efficient numerical finite difference scheme known as built-in Matlab bvp4c. The numerical results are presented in the form of graphs and tables for variation in parameters, for example, non-Newtonian parameter, Grashof numbers, material parameters, Prandtl numbers, nanoparticle volume concentration parameter, thermal radiation parameter and Brinkman numbers. The impact of these parameters has been observed on the velocity and temperature profiles of the nanofluid. Generally, fuzziness or uncertainty is inherent in modelling, analysis, and experimentation. Due to uncertain environmental conditions, fuzziness broadly exists in various engineering heat transfer problems. Converted ODEs are transformed into fuzzy differential equations with the help of triangular fuzzy numbers. The triangular fuzzy number is controlled by the - cut which controls the fuzzy uncertainty. The boundary conditions, parameters and nanoparticle volume fractions are said to be triangular fuzzy numbers and explained through the triangular membership functions. Also, discussed was the comparison of nanofluids and hybrid nanofluids through triangular fuzzy membership. In the end, the fuzzy triangular membership functions have not only helped to overcome the computational cost but also give better accuracy.