July 2020
Intermediate to advanced
464 pages
17h 2m
English
Content preview from Mathematical Methods in Interdisciplinary Sciences
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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 ...
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