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Peak Temperature Optimization in Laser Heating

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In a laser surface heating model the peak temperature achieved on the surface of the material is dependent on the material properties and on the laser parameters. For a given material (Cp, , k) beam size R0 and beam traverse velocity v; the peak temperature Tm can be controlled by the laser power output P. For the global maximum temperature in the model to reach Tm, P is given by:

P=π^(3/2)/2 ((R_0 (T_m-T_0))/A) ((ρC_p kvR_0)/C_1 )^(1/2)

C1 is an equation parameter with a value close to unity which will vary slightly depending on the power distribution in the laser beam.

For any given power distribution I want to find the value of C1 which gives a global maximum peak temperature of Tm. I have two questions:

1. Can I achieve this without the optimization module?
2. If I have to use the optimization module using C1 as the control variable, what would I use as the objective expression?

Many thanks

Dan

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