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Multi-layer Sphere Temperature Analysis

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Multi-layer Sphere Temperature Analysis Adam Hickman Brennan Crellin Introduction Rio Tinto seeks a method for determining the slag/matte level of a molten furnace bath. – PowerPoint PPT presentation

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Title: Multi-layer Sphere Temperature Analysis


1
Multi-layer SphereTemperature Analysis
  • Adam Hickman
  • Brennan Crellin

2
Introduction
  • Rio Tinto seeks a method for determining the
    slag/matte level of a molten furnace bath.
  • The decided solution is to house electronic
    sensors in a container capable of withstanding
    the conditions of the molten fluid for between
    20-120 min.
  • The decided container shape is a sphere. The
    sphere will have four layers each layer
    providing different desired attributes. Two
    metallic layers will increase average density, a
    ceramic (or vacuum) layer will insulate, and a
    wax layer will absorb energy to impede heat
    transfer to the electronics.

3
Problem
  • Establish a method for temperature analysis of
    the four-layer sphere. This will allow
    optimization of a sphere that keeps the
    electronics below 250oC.
  • The method should be robust enough to allow for
    material properties and layer thickness to be
    changed.

4
Method (Finite Difference)
  • Initial efforts involved adapting the heat
    equation to the problem in the form presented in
    Equation 2.27 of the text.
  • Because dF and d? are constant, the equation
    becomes
  • Then the method of 5.10.1, Discretization of the
    Heat Equation, was used.
  • This method was abandoned because it only solves
    for interior nodes and assumes a solid sphere.

5
Method (Finite Difference)
  • Final analysis used the general form of the heat
    equation, identified as Equation 5.81 in the
    text
  • Estorage Ein Egenerated
  • Using this equation we analyzed the energy
    balance for multiple cases.

6
Solution
  • The equation was discretized to calculate node
    temperatures at time steps. The equation was
    derived for four node types, contributing to the
    the total solution material change nodes,
    interior nodes, the center node (nmax), and the
    nmax-1 node. Below is the material change node
    equation
  • see the other equations in Appendix A

7
Solution
  • A Screenshot of the working excel solution

8
Conclusion
  • The working excel solution allows for rapid
    numerical analysis of the sphere for various
    material properties and thicknesses.
  • This analytical tool assisted in solving the
    overall problem to optimize the design of the
    sphere for the Rio Tinto application.
  • We found that a sphere of 20cm diameter will last
    for between 50-60 min. given the chosen
    materials.
  • Future work will include further optimization of
    materials and sphere size.

9
Appendix A
  • Interior node
  • Center node (nmax)
  • Node (nmax-1)
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