Heat Transfer Analysis of Micropolar fluid over a Vertical Cone with Non-Uniform Heat source and sink: Keller Box Method and Industrial Applications

Abstract

A mathematical model is made to look at the heat moves through a micropolar viscoelastic fluid from a vertically isothermal cone to a steady-state free convection boundary layer flow that is laminar, nonlinear, and not isothermal. Using MATLAB programming, we transform the linear momentum, energy, angular momentum equations, and possible boundary conditions using the finite difference methodology (Keller Box method). Higher-order (fourth-order) partial differential equations (PDEs) can be solved using this method up to the Nth first-order partial differential equation (PDE). Evaluations are done on the following parameters: dimensionless stream-wise coordinate, ratio of relaxation to retardation times, Deborah number (De), Erigena vortex viscosity parameter (R), Prandtl number (Pr), non-uniform heat source and sink (A, B), radiation and surface temperature, and angular velocity in the boundary layer regime. The results of the calculations show that temperature (along with the thickness of the thermal boundary layer) drops and linear and angular velocity rise with an increasing ratio of retardation to relaxation periods. Elevating the Deborah number results in increased temperatures and micro-rotation magnitudes, but it also lowers the Nusselt number and linear flow. Viscoelastic micropolar fluid flow finds applications in various areas of fluid dynamics where the behaviour of complex fluids with both viscous and elastic properties, along with micro-rotation effects, plays a significant role. Some applications include polymer processing, biomedical engineering, rheology, environmental fluid dynamics, and complex fluid flows. The skin friction coefficient and the Nusselt number are shown with graphs, streamlines, and tables for changed values of the flow constraints.