Heated Rod Problem: Solve Equation for Fusion

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In summary, the conversation discusses the equation needed to describe a heated rod composed of two different materials fused together on the x-axis. The heat equation is suggested to be used, with the solution being the sum of two integrals from -infinity to 0 and 0 to +infinity, respectively. The person is unsure of how to solve the problem and requests assistance.
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Homework Statement



I was asked to write the equation that describes the following heated rod: Two rods of different materials that have been fused together on the x-axis at x=0 to form one rod of infinite length.

I was thinking of just using the heat equation integrated from -infinity to 0 with k1 and 0 to +infinity with k2 and having the solution as the sum of these two integrals.

I am really quite unsure of how to go about solving this so any help would be much appreciated.
 
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Homework Equations The heat equation I am looking to use is: ∂u/∂t = k∇2u The Attempt at a Solution I am not sure how to begin this problem. Could someone please help?
 

1. What is the Heated Rod Problem?

The Heated Rod Problem is a mathematical equation used to model the heating and cooling of a rod that is subjected to a constant heat source. This problem is commonly used in thermodynamics and heat transfer studies.

2. What is the equation used to solve the Heated Rod Problem?

The equation used to solve the Heated Rod Problem is known as the heat equation or diffusion equation. It is a partial differential equation that describes how heat is transferred through a medium over time.

3. How is the Heated Rod Problem related to fusion?

The Heated Rod Problem is not directly related to fusion. However, it can be used to model the heating and cooling of materials, which is relevant in fusion reactions where high temperatures are needed to initiate and sustain the fusion process.

4. What are the key assumptions made when solving the Heated Rod Problem?

The key assumptions made when solving the Heated Rod Problem include: 1) the rod is one-dimensional, 2) the rod is homogeneous and has constant properties, 3) there is no internal heat generation, and 4) the heat source is constant and evenly distributed along the length of the rod.

5. How is the Heated Rod Problem solved?

The Heated Rod Problem is typically solved using numerical methods, such as finite difference or finite element methods. These methods discretize the rod into smaller elements and use iterative calculations to solve the heat equation for each element. The final solution gives the temperature distribution along the length of the rod over time.

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