You should first define some parameters of your mission (DeltaV, optimal expansion conditions, altitude) and some constraints on your rocket system (operating pressure, thrust profile, Vieille's law of the specific propellant).
Using the specific impulse definition, you can compute the mass flow rate across the nozzle which, in steady operating conditions, corresponds to the instantaneous mass of burning propellant.
Combustion product properties ( == thermochemical data from tables or NASA CEA program) impose also your throat area since the mass flow rate across the nozzle is now a constraint.
Finally, the equivalence between mass discharge from the nozzle and mass coming from propellant combustion enables you to compute the burning area.
Once you have such constraints, you can start the design of your propellant grain.
You can find details about the process in "Rocket Propulsion Elements" by Sutton and Biblarz.
@ Mr. filippo maggi i am not able to download.one of your pubilcation( Characterization of HTPB-based solid fuel formulations: Performance, mechanical properties, and pollution) please do favor for me.
Solid propellants burn at the exposed surface with nearly constant rate per exposed surface for constant chamber pressure. Primitive rockets burned from the bottom circular surface. Modern rockets also make a hollow core with corrugated profile and surface area about equal to the inside cylinder of the containment vessel. Then the area remains about constant as the fuel burns and can make a much larger surface than the bottom circle.
Usually htpb is accelerated with a second component and you need to specify which burning rate you except at chamber pressure. Assume nozzle area A in square centimeters and pressure at P1 dropping adiabatically to P2 in Newtons per square centimeter meter which is slightly higher than outside pressure.
F = 500 NT = v dM/dt = A ( P1 -P2)( Nozzle coefficient nearly equal to one)
Burning rate mass is dM/dt and velocity is v.
Volume of exhaust gas and area A are used to estimate v.
There is an isentropic constant n based on the composition of the combustion gas, usually around 1.3 for complete combustion. Pressure and volume are related.
P1V1n = P2V2n
Work done is W integral of Vdp.
W = P2V2 (n /(n-1)) ( (P1/P2)((n-1)/n) - 1 )
Volume is based on moles of gas m, combustion temperature T, gas constant R and non ideality Z which is found in tables passed on composition, temperature and pressure.
P1V1 = Z1mRT
Also power is given for burning time t.
v2 = ( V2 / t ) /A
v2 F = W / t
Calculation is done by guessing at dM/dt, P1, and A, then calculating, volume, velocity, and force and making improvements in the guesses.