Thermal analysis of unsteady viscous flow in medical engineering: A comparative analysis of numerical and semi-analytical methods

Abstract

The study of thermal and mass transfer in unsteady squeezing flows between parallel plates is crucial for biomedical fluid systems, including drug delivery and medical device design. This research employs a hybrid approach integrating the Akbari–Ganji method (AGM) with the fourth-order Runge–Kutta method, utilizing similarity transformation to convert partial differential equations into ordinary differential equations (ODEs). The analysis focuses on key parameters such as the Prandtl number (0.7–1.5), Squeeze number ([Formula: see text]2–2), Schmidt number (0.5–1.2) and Eckert number (1–2.5). Results show that as the squeeze number increases from [Formula: see text]2 to 2, the velocity profile [Formula: see text] at [Formula: see text] = 0.5 decreases from 0.78 to 0.65, while the temperature profile [Formula: see text] at [Formula: see text] = 0.5 decreases from 2.75 to 1.52. Increasing the Prandtl number from 0.7 to 1.5 raises the temperature, with [Formula: see text] at [Formula: see text] = 0.5 increasing from 1.45 to 1.9. The concentration profile [Formula: see text] at [Formula: see text] = 0.5 increases from 0.7 to 0.74 as the squeeze number increases from [Formula: see text]1.5 to 1.5 while decreasing from 0.84 to 0.71 as the Schmidt number increases from 0.5 to 1.2. The AGM results show excellent agreement with numerical methods, with maximum relative errors of approximately 0.00107% for [Formula: see text], 0.14991% for [Formula: see text] and 0.06368% for [Formula: see text], validating the accuracy of the semi-analytical approach. The theoretical convergence analysis, supported by Python programming simulations, validates the robustness of the methods used. These results provide a solid foundation for the optimization of biomedical fluid systems, particularly in the design of advanced medical devices.

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