# Rosenthal equation for multi track

Rosenthal's equation lets one calculate the temperature profile of a moving point heat source analytically for thin and thick plates. For simplicity I use the equation for thick plates defined as: $$T-T_0 = \frac{Q}{2\pi kR}\exp\bigg(-\frac{v(R+x)}{2a}\bigg)$$ Where $$T$$ is the temperature one wants to know, $$T_0$$ is the initial temperature, $$Q$$ is the heat source heat flux, $$R$$ is the radius from heat source center, $$v$$ is the heat source velocity, $$k$$ the thermal conductivity, $$c$$ the thermal capacity, $$\rho$$ the density, $$a=\frac{k}{\rho c}$$ and $$x$$ is the current position of the heat source in traveling direction.

The equation was initially developed to calculate the temperature for single track welding applications. I am wondering how it would be possible to use this equation for multi track welding (where one track is located right next to the last track) and how to capture the effect of the previous track in the new track. Can I simply update the material properties in case of temperature dependent properties and use an updated $$T_0$$ for the new track?

• I think this is a question better suited to a place where people actually know something about welding :-) Commented Dec 11, 2021 at 2:31
• @WolfgangBangerth do you have any websites where my question is better placed? Commented Dec 12, 2021 at 18:42