Mathematical Methods in Interdisciplinary Sciences

6Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters

Sukanta Nayak¹, Tharasi Dilleswar Rao², and Snehashish Chakraverty²

¹Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, 641112, India

²Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

6.1 Introduction

Diffusion plays a major role in the field of thermal and chemical engineering. It may arise in a wide range of problems, viz., heat transfer, fluid flow, and chemical diffusion. These problems are governed by various linear and nonlinear differential equations. The problem with involved parameters, coefficients, and initial and boundary conditions greatly affects the solution of differential equations. In addition, the parameters used in the modeled physical problem are not crisp (or exact) because of the mechanical defect, experimental and measurement error, etc. In this context, the problem has to be defined with uncertain bounded parameters, which make it challenging to investigate. However, the uncertainties are handled by various authors using probability density functions or statistical methods, but these methods need plenty of data and also may not consider the vague or imprecise parameters. Accordingly, one may use interval and/or fuzzy computation in the analysis of the problems.

As such, this chapter comprises interval and/or fuzzy uncertainties along with ...