Application of genetic algorithms in nonlinear heat conduction problems

Area of Science:

• Computational Heat Transfer
• Thermodynamics
• Applied Mathematics

Background:

• Nonlinear heat conduction problems present challenges in predicting temperature distributions accurately.
• Optimization techniques are crucial for finding optimal thermal performance under specific constraints.
• Minimum entropy generation is a key principle for determining optimal thermodynamic states.

Purpose of the Study:

• To employ genetic algorithms (GA) for optimizing dimensionless temperature in nonlinear heat conduction.
• To analyze the effectiveness of GA in minimizing temperature for three common geometries.
• To apply the minimum entropy generation concept for determining optimum temperatures.

Main Methods:

• Development of dimensionless governing equations for nonlinear heat conduction in selected geometries.
• Implementation of genetic algorithms (GA) using MATLAB for temperature optimization.
• Application of the minimum entropy generation principle to establish optimization constraints.

Main Results:

• Genetic algorithms successfully determined the minimum dimensionless temperature for all analyzed geometries.
• The study validates GA's capability in optimizing temperature distributions in complex heat transfer scenarios.
• Optimal temperature distributions were achieved under the constraint of minimum entropy generation.

Conclusions:

• Genetic algorithms are an effective tool for optimizing dimensionless temperature in nonlinear heat conduction.
• The minimum entropy generation principle provides a valid constraint for thermal optimization.
• The methodology is applicable to various geometries with temperature-dependent thermal conductivity.