Numerical modeling of influence of source in heat transformation: An application in blacksmithing metal heating
Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of mathematics
Abstract
Partial differential equations (PDEs) are used to mimic a variety of real-world physical issues.
A standard parabolic PDE of the form u
; ( > 0) is an 1D heat equation. In a regular
form of domain, the heat equation has an analytical solution. Computing an analytical solution
becomes challenging, if not impossible, any time the domain of such modeled issues has an
uneven shape. In this case, numerical methods can be used to find the numerical solution of
these PDEs. Through the domain’s discretization into a limited number of areas. One of the
numerical techniques used to determine the numerical solutions of PDEs is the finite difference
method (FDM). Here, the FTCSSfor the one-dimensional heat equation and the numerical
computation of its solution using FTCSS are discussed. Furthermore, numerical solution and
analytic solution of heat equation has been compared and analyzed. Additionally, the 1D heat
equation with variable starting conditions (ICs) and numerous initial conditions (ICs)has been
solved numerically using FDMs. Blacksmiths heated the parts at various temperatures and locations
to mold different metals into the necessary shapes. The numerical solution method for
the 1D heat problem given here can be used to solve heat equations used in engineering and
scientific disciplines.
t
= u
xx
Description
Keywords
Heat transformation, Metal heating