Master Student Mathematics, Mechanical engineering or similar (f/m/x) - Analytical solution of a 2D heat flux distribution in a glued single-lap joint

As seen in DLR space projects – such as the compact satellite Eu:CROPIS or the small asteroid lander MASCOT – with very lightweight composite structures, the thermal sub-systems participate with a significant portion to the total mass. Also, the structural design itself is highly influenced by the need for additional thermal sub-systems.

Thus, we investigate experimentally, numerically and analytically the effective thermal conductivity in primary structures with a special focus on glued joints. Once this will be completed a corresponding numerical simulation can be set up with improved parameters, which will help to consolidate the prediction of the structure’s heat conduction capability.

Task:
In previous work a single-lap joint was analysed numerically. This joint consists of two carbon-fibre reinforced plastic rods (thickness tlam) that are glued over a length Lj with a glue of thickness ta. Applying a thermal flux Q at one end and holding the temperature Tsink at the other, results in a certain heat flux distribution in the glued joint (highlighted pink box). Next to the numerical solution, an analytical solution with simple boundary conditions is for this twodimensional area in existence.

In a next step, and this is the goal of the thesis, the problem needs to be solved with more refined boundary conditions. This involves an existing Python program that supports in applying a Fourier series as boundary condition and plotting the resulting temperature fields in the jointed area as well as the corresponding heat flux distribution.

Steps:
Specifically, the following points shall to be fulfilled:

• getting familiar with the theoretical background of formulating and solving the partial differential equation for such a problem (2D Laplace)
• formulating the Laplace equation and boundary condition for the single lap joint (neglecting the glue layer)
• solving the Laplace equation
• optional: Including the glue layer in the problem
• summary and documentation of all results (English or German) and presentation of results at the Institute of Lightweight Systems/Institute for Partial Differential Equations

The Master Thesis will be conducted at the German Aerospace Centre (DLR), Institute of Lightweight Systems, Braunschweig and mentored by Dipl.-Ing. Michael Lange, Institute of Lightweight Systems as well as Prof. Dr. Dirk Langemann, TU Braunschweig, Institute for Partial Differential Equations.