# Discrepancy with phi(mass flowrate) calculation at the patch with buoyantSimpleFoam solver.

### Summary

The problem is related to the way OpenFOAM evaluates the phi(mass flowrate) at the patch with buoyantSimpleFoam solver. In my system, I implemented a codedFixedValue BC for inlet velocity, which enters into the space with some angle from the patch normal. However, the value of phi at the patch produced by the OF is less than the Original value. Upon observation, it seems that only the velocity component perpendicular to the patch was considered to generate the phi. Which disturbs the conservation of heat in the system.

### Steps to reproduce

I have implemented the velocity profile at the inlet patch in such way that all velocity vectors are entering into the space radially with 70deg from the patch normal, as shown in the attached image.

### Theoretically mass flowrate calculations:

- Volumetric flowrate of patch = 0.02831 m3/sec
- Inlet Temperature = 13 deg C
- Corresponding Density,rho = 1.238 kg/m3
- Supply mass flowrate = 0.03485 kg/sec

But from the OF, with 'flowRatePatch' utility, Mass flowrate = 0.01194 kg/sec. Which is in accord with direct summation of 'phi' values on the patch. Nevertheless, there is large difference between the actual supply mass flowrate and OF generated flowrate.

Upon further investigation, based on "compressibleCreatePhi.H" we found the calculation of phi
` surfaceScalarField phi ( IOobject ( "phi", runTime.timeName(), mesh, IOobject::READ_IF_PRESENT, IOobject::AUTO_WRITE ), linearInterpolate(rho*U) & mesh.Sf() );`

The calculation of phi on the face :

- The surface area vector, Sf ( 0,0,4.032e-05)
- The translated velocity vector,U ( 0.93872955,-0.042532896,-0.34202014)
- Mass flowrate = (Sf.U)*rho = (0 + 0 + 1.379e-05)*1.238

##Observations & Queries:

- Why the phi calculations does not taking the contribution of components other than patch normal velocity.
- Based in the above calculations, there is large difference between the actual supply mass flowrate and OF generated flowrate.
- The generated low phi values have also impacted the heat balance of the system.

### Example case

### Relevant logs and/or images

### Environment information

- OpenFOAM version : v1906
- Operating system : Ubuntu 18.04