@acer 

Thanks very much for your help.

I did notice that you used Units[Simple] not Units[Standard] as I had. When I switch to Units[Standard] the fsolve gives the following result:

fsolve(100*Unit('W')-conv_VerticalPlate_proc(x, 20*Unit('degC'), Unit('m'^2), Unit('m'), .9), x = 10*Unit('degC') .. 100*Unit('degC'));
Error, (in Units:-Standard:-+) the units `W` and `1` have incompatible dimensions
 

It appears that there is more stringent consistency checking in the Standard library but is it recommended to use the Simple library rather than the Standard library?

@Samir Khan 
 

First thanks for adding units to fsolve and for providing the example with units.

With Units[Simple] this example works however if I change it to Units[Standard] it does not.  But if I want to use degC and I use the Standard Units Package I can get the Property functions to work but then fsolve stops working and produces an error.

I seem to only be able to get fsolve to work with units by using the Simple units package.  This requires me to use the convert function to convert degC to kelvin to get the Property functions to work.

Can fsolve only handle units if you use the Simple package or am I doing something wrong?