A novel physiologically based algorithm (PBA) for fast CFD computation of Flow Fractional Reserve (FFR) in Coronary Artery Trees (CATs) is proposed and developed, which, unlike traditional methods, is based on the extension of the Murray’s law for blood vessels at the outlets and extra inlet conditions prescribed alternatively and iteratively. The PBA is then implemented in both SimVascular and Ansys CFD for testing and validation. For validation purpose, 3D models of CATs are built by using their CT images and computational meshes generated for mesh convergence study. Results obtained are then compared with Invasive Coronary Angiographic (ICA) data for validation and evaluation of its accuracy and computational efficiency. It is found that discrepancies between experimental and calculated values of pressure and flow rate at the inlet were less than 0.1% at the end of the 10th round of iteration or less. Further validation shows that the difference between estimated and experimental FFR agree with each other with a maximum difference of 1.62% after convergence is achieved. The PBA is found to be a robust patient-specific and physiologically sound method that can be a good alternative to the existing Lumped Parameter Model (LPM) which is based on empirical scaling correlations using limited population-averaged data and requires nonlinear iterative computation for convergence.