# Optimization and heat transfer model parameter estimation (rho, K, and Cp)

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Sanley Guerrier on 22 May 2024
Commented: Sanley Guerrier on 23 May 2024
Dear experts,
I'm working on a heat transfer model (finite difference method). I have a measured data and I want to fit the model by estimating the input parameters (rho, K, and Cp). Which optimization tool (fmincon, fminbnd, fminsearch, lsqnonlin, etc.) is more suitable to estimate the parameters?
Thank you.
Torsten on 23 May 2024
Edited: Torsten on 23 May 2024
I didn't know the product rho*cp cannot be estimated separately.
You can only estimate the product as one unknown parameter, not rho and cp separately as two unknown parameters. I already mentionned the reason: rho and cp are always used together as the product rho*cp in your model, and there are infinitly many combinations of rho and cp that would give a certain value as their product.
Does that mean if I use "pdepe", it won't be necessary to estimate k?
You will also have to estimate k if you use "pdepe", but you have a reliable integrator which is very important if you want to use its results to estimate parameters with one of the MATLAB tools @Raj suggested.
Sanley Guerrier on 23 May 2024
Thanks much!

Raj on 23 May 2024
The choice of optimization tool depends on several factors including the nature of problem, the characteristics of model, and the specific requirements you have for the optimization process.
1. fmincon- This function is suitable when your optimisation problem has constraints.If your parameters (rho, K, and Cp) satisfy certain bounds or constraints, fmincon might be a good option.
2. fminbnd- This function is is designed for univariate function minimization bounded within a specified range. It is not directly applicable to your case since you are optimizing over multiple parameters.
3. fminsearch- This function finds the minimum of an unconstrained multivariable function. If your problem does not require handling constraints explicitly, it can be an option.
4. lsqnonlin- This function minimizes the sum of squares of nonlinear functions and is particularly suitable for data fitting problems. If your objective function can be expressed as the sum of squares of residuals between the model predictions and measured data, this can be a strong candidate.
Given that you want to fit a heart transfer model to measured data,and you're estimating parameters like density (rho), thermal conductivity (K), and specific heat capacity (Cp), 'lsqnonlin' seems the most suitable option due to its focus onnonlinear least squares problem.
However for a better understanding on the above functions, refer to the following documentation-
Hope you have a better idea now and are able to proceed further!
Sanley Guerrier on 23 May 2024
Thank you, Raj.