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This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

The purpose of this study is the hydrothermal analysis of the natural convection phenomenon within the heat exchanger containing nanofluids using the lattice Boltzmann method (LBM).

The thermal conductivity as well as dynamic viscosity of the CuO–water nanofluid is estimated using the Koo-Kleinstreuer-Li model. The LBM has been used with unique modifications to make it flexible with the curved boundaries. The local as well as total entropy generation assessment, local Nusselt variation, as well as heatline visualization are used.

The solid volume percentage of the CuO–water nanofluid, a range of Rayleigh numbers (Ra) and thermal settings of internal operational fins and bodies are all factors that have been thoroughly researched to determine their effects on entropy production, heat transfer efficiency and nanofluid flow.

The originality of this work is using a novel numerical method (i.e. curved boundary LBM) as well as the local/volumetric second law analysis for the application of heat exchanger hydrothermal analysis.