I have learned that an agile application is done by dividing the development process in form of sprints. How the sprints different from spiral model development? Is there an minimal sprint count for a particular project as constraint?
Agile is not a method, it is an approach towards software development. However, Scrum is a methodology and it is comparable to the Spiral Model. Both have test, plan, and evaluation phases, however Scrum lacks the risk management (when people attack Scrum that is their best move).
The Spiral Model doesn't say much about the length of an iteration - there is not iteration per say in the Model but you can interpret one "circle" as an iteration.
Experts recommend the Spiral Model for long projects that has high risk - the model highly depends on risk management.
In Scrum, there is no such thing as a minimal Sprint count. A project is done, when the customer accepts it. It can happen after one Sprint (very unlikely, but can happen), or after a thousand.
Look beyond just the sprints
Agile is an umbrella term used to describe a general approach to software development. There are many agile methods including Scrum, XP and Kanban. However, they all emphasize responding quickly to change, frequent deliveries of working software, close customer collaboration.
I don't know the specifics of the Spiral model of development that you practice. In order to understand how it is different from Agile, you should look beyond just the sprints:
- Do you start with a requirements document? And do you have a change control process if requirements change? Agile is designed to respond to change. Typically changes are welcome prior to the start of the sprint.
- Do you do up-front design? Agile tries to limit the design to what is needed to convert the stories to deployable code within the sprint. As the sprints progress plan to refactor the code as needed.
- Do you have Product Owners / customers working with the development team daily throughout the project? Agile requires such close interaction and feedback.
To answer your specific question - no there is no minimal sprint count for a project in agile. But, sprints should be short to permit frequent inspection and adaptation. And at the end of each sprint, code should be developed, tested and demo'd to customers in fully ready for deployment condition. Here is some additional info on sprints/iterations.