Understanding PDEs and Boundary Conditions for Heat Transfer in Ice Engineering

[superaznnerd]

help! don't know what to study

so I am a high school student,who has onlly studied basic physics (no AP).
However, I am doing an ice engineering internship this summer, and I want to understand everything in my professors research paper. It seems like its very speciailzed to studying heat, heat transfer, temperature, ect...


part of the research paper is attached...


can someone tell me what/and on what website should I study for my internship??

 

[LostConjugate]

Look up Thermodynamics Lectures

 

[Dickfore]

Will you please erase that awful copypasta? There are file sharing servers for free and you can post a link to the original document.

 

[superaznnerd]

I need more in depth/ specialized/advanced information than that

 

[superaznnerd]

sorry i don't know if I am supposed to release too much info from the research paper...but there are some equations there-i hope you can see them, because they reflect the things I need to study

 

[Dickfore]

Eqn. (4) is called the heat conduction equation. Mathematically, it is a partial differential equation. The methods used for solving these kinds of equations are usually learned in the second part of Mathematical Methods for Physicists courses. Before you can grasp them, you must be very comfortable with both differential and integral calculus.

Every partial differential equation needs some set of boundary conditions and initial conditions to determine its solution uniquely. Here, the boundary conditions are given by eqn. (6). It simply says that there is a fixed heat flux through the left boundary of the film. The initial condition is given by eqn. (7). It simply states that the initial temperature of the film (at time t = 0) was equal everywhere (for all x).

If you want to understand the physics behind these phenomena, you will need to start with a book on Thermal Science, possibly from an engineer's perspective. This is the OpenCourseWare website for such a course in the Mechanical Engineering Department of MIT:

http://ocw.mit.edu/courses/mechanical-engineering/2-51-intermediate-heat-and-mass-transfer-fall-2008/"

 

[superaznnerd]

i have basic knowledge of calculus.
i thought you only need an initial condition to determine the solution. So I'm assuming that a boundary condition is an additional variable (so I have to understand multivariable calculus)??

 

[Dickfore]

i have basic knowledge of calculus.
i thought you only need an initial condition to determine the solution. So I'm assuming that a boundary condition is an additional variable (so I have to understand multivariable calculus)??

Yes. PDEs (Partial Differential Equations) require boundary conditions.