Mathematical formulas used for the calculation of neutron flux in nuclear reactor.
It is calculated by the assembly enrichment level in each area of the core. Then this value is put in neutron diffusion equation for further calculation.
Generally for detail values computer codes are used for this purpose. One of the simple ways to calculate is given in book “Two Group Reactor Theory” by J. L. Meem.
May be helpful for you.
You can estimate the average thermal neutron flux using the fissile number densities and the thermal power output of the core. First determine the total number of atoms of each fissile element by multiplying core volume by the average number density. Second, multiply the number of atoms of each fissile element by its thermal fission cross section and energy production per fission. Finally, sum these quantities and divide the sum into the thermal power output of the core. Of course, you're then not taking fast fissioning into account, nor the variations in fissile number density and thermal neutron flux across the core, but if you only want an estimate that will normally not matter a great deal.
Neutron Flux can be measured in reactors by different manner and method named Flux mapping experiments. For example by the Foil activation analysis or using proper instruments (detectors) or by a proportional parameters like temperature, power or ,,,, It is a very intersting and extended subject in reactor physics.
I FULLY endorsed Masood Iqbal recommendation, the book “Two Group Reactor Theory” by J. L. Meem., is a brillant work that detailed all the analytical work to calculate the flux a reactivity by hand (today is very easy to calculate that with any worksheet). I used with some students.
I found there only one (strong) limitation, you need the "Tau" of the material mixture. Then I used an analytical model for the Tau of the mixture
Solve 2 group neutron diffusion equation, there are many texts show that
As a summary. The accuracy depens in the efforts that you need to apply.
1) As was said by Brian Gaulke, a first "hand" estimation si by simple:
flux*MacroscopicFissionCrossSection*Volume*EnergybyFission=Power
Then you need to estimatede the average "MacroscopicFissionCrossSection", to do that you need to know the "average neutron energy" (is your reactor thermal, is epithermal, is fast?) and thus obtain the microscopic cross section. Multiply it by the "fuel atomic density (Nf)" of the fissil atoms, BUT WEIGHTED by your estimation on "fuel flux/averageflux" ratio. If you dont have any clue on that, assume 1, and then obtaine the "total fissil atomic density" (Nftot = Volfuel*Nf/Vtot)
2) If the accuracy of approach 1 is not enough (an error of 10 to 20% could be obtain with the formula 1). use a 2 groups approach, with two zones-two groups. Is much more complicated, and is available in the Meen book. Also, as an intermediate approach (as was said by Malik), use a single zone two groups analytical solution (if the system has low leackages or small reflector effect is ok) but the challenge will be always, which is the "ScattXSgroup1 to group2". Only is tabulated for few compositions. If your system match those published number, use ti, if is not. You need to go to Age theory, and using Tau, and obtain "ScattXSgroup1 to group2"