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Abstract The ongoing research aims 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 behavior of the liquid flow are elucidated via a magnetic field incorporated in the momentum equation. Furthermore, within concentric cylinders, the expression $$Q = \frac{Q_0}{1-\beta t}$$ Q = Q 0 1 - β t has been employed as a source/sink. 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. The direct impact of the squeezing parameter on the profile of temperature and concentration has been observed. The results shown that an increment in the heat source indicates a decline in the liquid temperature profile, that an increment in the heat source indicates a decline in the liquid temperature profile. An increment in the heat source indicates a decline in the liquid temperature prof. At the same time, an inverse relationship is observed for the concentration profile. Therefore, we have witnessed a significant increase in the velocity profiles of the flow, mainly as a result of the heat absorption coefficient. In addition, the declining effect of the Soret number on the concentration profile is noticed. It has been found that it enhanced the entropy generation rate for Pr, $$\Omega$$ Ω , and Ec, while an opposite impact has been noticed at the Bejan number. The numerical outcomes of the proposed model that explain fluid flow characteristics and fluid flow characteristics are quantitatively elucidated by tables and displayed graphically. The comparison of two numerical results in the cases are found to be in good agreement, as shown in Tables.