Immiscible fluids find diverse applications across production and engineering sectors. In this study, we are presenting an analytical solution for the dynamics of unsteady immiscible fluid systems incorporating thermal radiation and chemical reactions within the porous medium subjected to a heat source. Initially, we address this complex system by formulating partial differential equations governing momentum, energy, and concentration. By employing nondimensional variables, we convert these equations into forms that have no dimensions, making it straightforward to evaluate them. Following that, we implement the Laplace methods for obtaining accurate solutions for concentration, temperature, and velocity, ensuring that both initial and boundary conditions are maintained. Then by employing MATLAB, we create visual aids to clarify some phenomena existing in the system.