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This study aims to explore the idea of solving the problem of squeezing nanofluid flow between two parallel plates using a novel mathematical method.

The unsteady squeezing flow is a coupled fourth-order boundary value problem with flow velocity and temperature as the desired unknowns. In the first step, the conditions that guarantee the existence of a unique solution are obtained. Then following Green’s function-based approach, an iterative method for solving the problem is developed.

The accuracy of the method is examined by comparing the obtained results with existing numerical data, indicating excellent agreement between the two. In addition, the effects of nanoparticle shape and volume fraction on the flow and heat transfer characteristics are addressed. The results reveal that although the nanoparticle shape strongly affects the temperature distribution in the squeezing flow, it only has a slight impact on the velocity field. Furthermore, the highest and lowest Nusselt numbers belong to the platelets and spherical nanoparticles, respectively.

A semi-analytical method with computational support is developed for solving the unsteady squeezing flow problem. Moreover, the existence and uniqueness of the solution are discussed for the first time.