<![CDATA[This study examines the dynamics of fluid flow and heat transfer under impulsive and accelerated motion conditions in non-steady free convective flow systems. It aims to derive and analyze velocity and temperature profiles under the influence of key physical parameters, including the suction/injection parameter, Grashof number, and Prandtl number. A hybrid analytical–numerical method was employed, integrating Laplace transform-based analytical procedures with numerical evaluation techniques. Two cases of non-steady free convective flow, namely impulsive motion and accelerated motion, were considered. Talbot’s method for the inverse Laplace transform was applied in the accelerated motion case to further evaluate the temperature and velocity profiles. The findings show that the suction/injection parameter, Grashof number, and Prandtl number substantially influence both the velocity field and thermal field, thereby shaping the behavior of fluid flow and heat transfer under non-steady convective conditions. This study concludes that the hybrid analytical–numerical approach provides an effective framework for examining transient convective flow problems involving impulsive and accelerated motions. The findings contribute to the literature on fluid mechanics and heat transfer by offering analytical and computational insights relevant to engineering and thermal science applications.]]>
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