Selection of Numerical Methods and Their Application to the Thermo-Ecological Life Cycle Cost of Heat Exchanger Components

Lucyna Czarnowska,Wojciech Stanek,Wojciech Litwin

doi:10.13044/j.sdewes.2015.03.0010

Abstract

Thermo-Ecological Cost with the inclusion of Life Cycle (TEC-LC) is defined as the cumulative exergy consumption of non-renewable natural resources associated with any product and its life cycle, taking into account the necessity to prevent and compensate losses caused by depletion of natural resources and the release of harmful substances into the environment. The problem of collecting data for solving TEC-LC equations is not the only one which can be faced in determining this indicator. The selection of the calculation method could also affect obtained results due to the accuracy of the selected algorithm. Numerical stability is particularly important in the case of large sets of data and in this case operations on large matrixes. The issue with a set of TEC-LC balanced equations is examined and compared on the basis of heat exchanger components.

Highlights

In the inclusion of Life Cycle (TEC-LC) the Gaussian Elimination was used; in this method there is a risk of numerical instability which magnifies the round off and truncation errors
The thermo-ecological cost life cycle should contain as many connections between branches as possible in order to reflect the idea from the cradle to the grave
It is important to use the most accurate numerical method; this matrix does not meet all requirements for any method

Summary

Introduction

In TEC-LC the Gaussian Elimination was used; in this method there is a risk of numerical instability which magnifies the round off and truncation errors. Thermo-ecological cost, Heat exchanger, Math.NET Numerics, Iterative matrix solvers.

Results

Conclusion