Thermal performance of a micropolar fluid flowing around a vertical cone with consideration of spatially varying heat source

Here, we have modeled a situation analyse energy transfer in a rotating elastic fluid flow along a vertical cone. Flow from the isothermal cone wall gradually transits into a persistent layer where the fluid motion is driven by buoyancy forces. This layer exhibits smooth, continuous flow (laminar) with variations in temperature and flow properties that are not directly proportional to changes in other variables and not constant across the layer. The scenario is formulated as a system of boundary equations and for parameters reduction, it is said to utilize similarity variables. Then the reduced system was solved using MATLAB and the finite difference method (Keller Box approach), along with the relevant boundary conditions. Assessments are conducted across various parameters on flow affecting quantities. Our analysis reveals several interesting trends. Thermal boundary layer thins when the relaxation period is longer than retardation period since the fluid cools down faster. However, the fluid's overall movement (both linear and angular momentum) increases. Conversely, increasing the Deborah number (elasticity parameter) leads to higher temperatures and micro-rotation, but reduces heat transfer efficiency and flow speed and makes it linear. This study underlines the importance of viscoelastic-micropolar fluids which finds applications as environmental flows, biomedical engineering, polymer processing, rheology. This research shows that longer relaxation periods thin the thermal boundary layer and enhance fluid movement, while higher Deborah numbers increase temperatures and micro-rotation but reduce heat transfer efficiency and flow speed. These findings underscore the importance of viscoelastic-micropolar fluids in applications like environmental flows and biomedical engineering.