Modelling equation

[PSEengineer2013]

Hello,

I have a system as attached in the picture. Its a cooking vessel filled with water, resting on a heating plate. The vessel has the
form of a half sphere, with the exception of the area in contact with the heating plate, which is plane.

I derived an equation for the temperature of the vessel which I have also written in the picture under the system. In the equation T is the temperature of the vessel itself, and Tw is the temperature of the water.

In the model a term containing the first derivative of the temperature appears, even though there is only heat conduction (commonly represented by the second derivative of the temperature). I want to know what does the first derivative represent here? (i.e. what is the physical meaning of the first derivative?)

Any help would be appreciated.

Regards

 

[Latexman]

Change in T per change in [Θ]. If [Θ] is time, which is traditional, it is the rate of temperature change.

Good luck,
Latexman

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[cloa]

theta is angle- it looks a totally emperical equation so physical meanings don't apply.

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