International Journal of Science and Technology (IJST)

Polynomial Approximation Analysis of Transient Mixed Convection Flow in A Vertical Micro-Annulus with Viscous Dissipation

This paper presents an analytical assessment of transient mixed convection flow and heat transfer in a vertical micro-annulus, taking into account internal heat generation, viscous dissipation, and temperature-dependent viscosity. The Boussinesq approximation is used to develop the governing momentum and energy equations, which are then translated into dimensionless form. A polynomial approximation method is used to generate closed-form solutions, which are then evaluated via symbolic computation. The effect of critical dimensionless factors, such as the Reynolds number, Peclet number, Eckert number, and heat generation coefficients, on fluid velocity and temperature distributions is investigated. The findings show that internal heat generation greatly increases fluid temperature while decreasing flow velocity. Increasing Eckert and Peclet numbers reduces temperature profiles, while increasing Reynolds numbers decreases fluid velocity. The research also reveals a linked interaction between heat and flow fields, which is controlled by viscosity variations and energy dissipation effects. The findings have important implications for thermal management and flow control in micro-scale systems including microchannels, heat exchangers, and cooling devices, where accurate prediction of linked heat and fluid flow is critical.