Introduction to C++

This tutorial aims to provide an introduction to C++ by developing a real application that models heat transfer during welding.

Background

We will develop a simple heat transfer model based on equations of heat conduction in solids. The spatial variation of the heating or cooling rate in a Cartesian coordinate system can be related to the second derivative of the temperature gradients in the x-, y-, and z-directions¹:

$$\frac{\partial T}{\partial t} = \frac{\lambda}{\rho c}\left [ \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right ]$$ $$= a \left [ \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right ]$$

where $T$ is temperature, $t$ is time, $\lambda$ is thermal conductivity, $rho$ is density, $c$ is specific heat capacity, and $a$ is the thermal diffusivity of the material being welded.

One solution of the generic equation for steady-state distribution of temperature in a plate during arc welding was given by Rosenthal² as:

$$T\{x,R\} = T_0 + \frac{\eta V I}{2 \pi \lambda}\left ( \frac{1}{R} \right ) \mathrm{exp}\left \{ - \frac{v}{2 a} (R + x)\right \};$$ $$R = \sqrt{x^2 + y^2 + z^2}$$

where $T\{x,R\}$ is the temperature as a function of the radial distance ($R$) and distance ($x$) along the welding centerline, $T_0$ is the preheat temperature, $V$ is the arc voltage, $I$ is the welding current, $v$ is the welding speed, $a$ is the thermal diffusivity, and $\eta$ is the arc efficiency.

See the Introduction to Integrated Weld Modeling³ for more details on the model we will be using.

Overview

We will begin by looking at the basic features of C++, including variables, constants, operators, flow of control, and functions. Once we have enough background information, we will begin creating the heat transfer model based on the equations above. The goal will be to create a program that, give initial starting conditions, will output a file that describes the temperature isotherms during the welding process. We will then couple that with the Python plotting program we developed in the Python module to generate a contour plot of the temperature gradients.

References