HC05 and flame sensor combination

Hello, i am working on a very simple project but i don't have the required exeperience to achieve this at all. I have connected an IR Infrared 4 Wire flame sensor and a passive buzzer also with the concept of when flame is being detected , the buzzer goes on in order to alarm . At this point everything is tested and work's fine , but in the limits of my Computer Science lesson i have to go a bit further with this. Everytime that flame is being detected i want to "send a message or something to alert my smartphone" via HC05 Bluetooth module . Is that feasible and do i have to use an application from play store in order to achieve this ?

Probably some loose language here, and a big difference between "message" and "something". A message is not much use, but will do "something" if the phone is on and an app is ready to receive it. If you really want a phone alert, you may find an app, but you might have to do something pretty serious yourself at the phone end. I submit it would be smarter to give up the bluetooth and use a phone shield to send a text instead. This would absolve you from doing anything at the phone end, and you would have something that is actually useful.

Well , yes you are right my topic was a bit loose. But my budget is very limited as a student so i would like to achieve this by using the bluetooth module, even the simplest communication between arduino and bluetooth module is acceptable i mean showing message on phone like serial monitor " Fire alert" . If someone can help me with this would be awesome. I know that by using a GSM module would be more useful but as i said i can't afford to buy it. Thank you in advance.

OK, for the simplest communication, you might find the following background notes useful.

http://homepages.ihug.com.au/~npyner/Arduino/GUIDE_2BT.pdf
http://homepages.ihug.com.au/~npyner/Arduino/BT_2_WAY.ino

If you can already get Arduino to print "Help, I'm on fire!" to the serial monitor, page 1 is all you really need to read - no extra code required, and no special app on the phone either, just a plain vanilla bluetooth terminal.

I searched in playstore for Bluetooth applications , and i found BlueTerm , i guess by doing the correct connection between Arduino and the HC05 module and according to the pdf that you indicated me that code will print a message to the terminal of the application on my phone ?

Yes - provided it is Android.
You may later find that particular app not such a good choice. I'm not sure it can record data in a log file, but most do.