Fuzzy Finite Element Solution of Uncertain Convection-Diffusion Heat Transfer for a Rectangular Plate

TL;DR

This paper presents a numerical finite element approach incorporating fuzzy uncertainties to analyze the uncertain heat transfer in a rectangular plate, accounting for parameter variability and sensitivity in convection-diffusion problems.

Contribution

It introduces a fuzzy finite element method to model and analyze uncertain heat transfer parameters, providing a novel way to handle uncertainties in convection-diffusion problems.

Findings

Fuzzy parameters significantly affect temperature distribution.

The method effectively captures uncertainty in heat transfer analysis.

Sensitivity analysis identifies key parameters influencing results.

Abstract

Convection-diffusion of heat transfer is one of the important phenomena in fluid flow and industrial problems. The involved parameters, boundary conditions, and material properties are greatly affecting the same. As such, the uncertainness of these parameters, conditions, and properties cannot be ignored. Therefore, the present research work focuses numerical approach to study the uncertain convection-diffusion of heat transfer problem. Here, the finite element method is employed with fuzzy uncertainties to investigate the uncertain temperatures for a plate problem. The uncertainty is considered with a 10% of error and then corresponding fuzzy numbers are generated. These fuzzy numbers are used in the governing differential equation and boundary conditions to get the nodal temperatures. A different combination of fuzzy parameters is considered and the obtained results are reported. Furthermore, the sensitiveness of these parameters is reported in a case study.