The theme of the ongoing research is to examine the mass and heat transmission phenomena of squeezing flow between two concentric cylinders under the effect of heat sources and magnetic fields. The impacts of the Lorentz force on the behaviour of the liquid flow is elucidated via a magnetic field which is incorporated in the momentum equation. Moreover, the term Q = Q 0 1−βt has been used as a source/sink within concentric cylinders. The proposed model of PDEs formulates the physical phenomena of time-dependent incompressible two-dimensional squeezing flow via modified Navier-Stokes equation, energy equation and mass transfer equation and variable magnetic field. The proposed model involved a highly nonlinear system of PDEs which has been reduced into a system of ODEs via Lie group of similarity transformation and subsequently solved numerically in MATLAB by Parametric Continuation Method (PCM). The direct impact of the squeezing parameter on the profile of temperature and concentration have been observed. Furthermore, an increment in the heat source indicates a decrement in the liquid temperature profile, while an inverse relationship is observed for the concentration profile. In addition, the declining effect of Soret number on the concentration profile is noticed. Beside this, a direct impact of P r, Ω and Ec on the entropy generation has been noticed, while an opposite impact has been noticed at Bejan number. The numerical outcomes of the proposed model that explain the characteristics of fluid flow are quantitatively elucidated by tables, and displayed graphically.