Still remember the technical problem above? the picture describes a plate having different temperatures on each side. How is the temperature distribution in the center of the plate? How much temperature at point x = 1, y = 2 or T (1,2) = ?? I need to stress that we are not looking for 100% accurate answers. It is highly unlikely we are looking 100% accurate.
There are 3 approaches to address the above problem. The first way is through technical analysis that requires considerable thinking skills. Things like this are peeled thoroughly in the Master of Mechanical Engineering. We start with a heat transfer formula and then proceed with advanced engineering mathematics. The final solution is a mathematical model using fourier series. We just need to enter the variables x and y and boundary conditions on each side.
The second way is to use numerical methods. We start with the physics formula of heat transfer. Then the formula we rearrange and simplified into a simple algebra that can be done by the computer. Art to reorder and simplify the mathematical model is further learned in Numerical method for engineer and finite element method. Then we simulate this problem using computer software such as ABAQUS or ANSYS. this approach is often referred to as modeling. The most important thing in this modeling is how we validate the model we have created so that the results are nearly accurate.
The third way is to use a technical experiment. We create the plate and on each side we give the boundary condition. Then we measure the temperature on the plate using thermocouple or with the help of infrared camera. This is further studied in infrared thermography articles.
Ideally, the 3 ways mentioned above lead to a convergent answer. If we are already proficient using these three ways, we will feel the beauty of engineering science. Let’s sing a song for engineer.