Mathematical Equation for my experimental data?

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SUMMARY

The discussion focuses on developing a mathematical model to predict heat release through conduction based on experimental data involving different layers of insulation. The equation used is q=(ka(t2-t1))/d, where q represents heat released, k is the thermal conductivity, a is the surface area, t2 and t1 are temperatures, and d is the thickness of the insulation. Experimental results indicate a 50% reduction in heat release from 1 to 2 layers and a further reduction to 34% from 2 to 3 layers, suggesting an exponential trend in heat release reduction with increasing layers. The user seeks guidance on refining their mathematical model for their assignment.

PREREQUISITES
  • Understanding of heat transfer principles, specifically conduction.
  • Familiarity with the equation q=(ka(t2-t1))/d.
  • Knowledge of thermal conductivity and its significance in insulation materials.
  • Basic skills in data analysis and modeling, particularly with exponential functions.
NEXT STEPS
  • Research methods for deriving mathematical models from experimental data.
  • Explore the impact of geometry and surface area on heat transfer in insulation.
  • Learn about exponential decay functions and their applications in thermal analysis.
  • Investigate software tools for modeling heat transfer, such as MATLAB or Python libraries.
USEFUL FOR

This discussion is beneficial for students in physics or engineering, particularly those studying heat transfer, as well as educators looking for examples of mathematical modeling in experimental contexts.

Coolguynice
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Homework Statement


Okay so we're testing the effects different types and number of layers can have the heat released through conduction. in our results we found that the heat released was reduced by 50% for 2 layers compared to 1 layer and that the heat released was reduced to 34% for 3 layers as compared to 2 layer. How would you turn this into a mathematical model that can be used to predict future result? if it helps the graph shows a clear exponential trend.

Homework Equations


q=(ka(t2-t1))/d
so for example using felt for 1 layer we had 250.95j, for 2 layers we had 125.39 and for 3 layers 83.64 (in terms of heat released through conduction)

The Attempt at a Solution


im not exactly sure what to do but one idea i had was to derive the equation of each insulator from a program using the exponential form and roll with that but i would still like to know if there is a better or more correct method that i could help to explain in my assignment.
Any help would be greatly appreciated[/B]
 
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Hi Coolguynice, Welcome to Physics Forums.

If you're looking to create a mathematical model then you'll need to be clear on the system being modeled.

Usually heat transfer depends upon the geometry of the setup, surface areas between regions of different material, and so forth. Can you describe the setup in more detail? How was the "heat released" determined?
 
Presumably "d" in you equation is the thickness of the insulation. Looks like you already have a mathematical model.
 

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