How can I know the model of my motherboard without opening my desktop..

I cannot know..

Belarc adviser is a good tool and will give you information on your system
Belarc Advisor - Free Personal PC Audit

If it isn't a custom built PC, you may be able to find a list of motherboards that came in that specific model. You may even be able to call the support number for your PC and give them your S/N, and they can let you know.

If these fail, you may be able to use "Belarc Advisor" as Sean suggested. I don't think that'll give you the exact motherboard number, but you'll have the specs for any type of software, and if you really try you may be able to narrow it down, if you can find a list of popular motherboards and their specs.