A numerical analysis has been conducted to show the effects of magnetohydrodynamic (MHD) and Joule heating on heat transfer phenomenon in a lid driven triangular cavity. The heat transfer fluid (HTF) has been considered as water based hybrid nanofluid composed of equal quantities of Cu and TiO2 nanoparticles. The bottom wall of the cavity is undulated in sinusoidal pattern and cooled isothermally. The left vertical wall of the cavity is heated while the inclined side is insulated. The two dimensional governing partial differential equations of heat transfer and fluid flow with appropriate boundary conditions have been solved by using Galerkin's finite element method built in COMSOL Multyphysics. The effects of Hartmann number, Joule heating, number of undulation and Richardson number on the flow structure and heat transfer characteristics have been studied in details. The values of Prandtl number and solid volume fraction of hybrid nanoparticles have been considered as fixed. Also, the code validation has been shown. The numerical results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The comparison of heat transfer rate by using hybrid nanofluid, Cu-water nanofluid, TiO2 -water nanofluid and clear water has been also shown. Increasing wave number from 0 to 3 enhances the heat transfer rate by 16.89%. The enhanced rate of mean Nusselt number for hybrid nanofluid is found as 4.11% compared to base fluid.

This study explores a spatially distributed harvesting model that signifies the outcome of the competition of two species in a heterogeneous environment. The model is controlled by reaction-diffusion equations with resource-based diffusion strategies. Two different situations are maintained by the harvesting effects: when the harvesting rates are independent in space and do not exceed the intrinsic growth rate; and when they are proportional to the time-independent intrinsic growth rate. In particular, the competition between both species differs only by their corresponding migration strategy and harvesting intensity. We have computed the main results for the global existence of solutions that represent either coexistence or competitive exclusion of two competing species depending on the harvesting levels and different imposed diffusion strategies. We also established some estimates on harvesting efforts for which coexistence is apparent. Also, some numerical results are exhibited in one and two spatial dimensions, which shed some light on the ecological implementation of the model.

With recent technological advances, thermal transport from different electronic and electrical devices is the most vital concern. The microchannel heat sink (MCHS) of liquid cooling is a useful device to remove over thermal load. Ionanofluid is a brand new and super potential cooling fluid for its ionic conductivity, non-flammability, negligible volatility, and high-level heat stability. In this research, the ionanofluid's velocity and thermal field characteristics through a triangular grooved MCHS are investigated using numerical tools. The combination of ionic liquid (IL) 1-Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl)imide [C₄mim]NTf₂ and propylene glycol (PG) is used as base fluid whereas graphene (G) and single-walled carbon nanotube (SWCNT) are chosen as hybrid nanoparticles to make the working ionanofluid. The governing equations of nonlinear partial differential equations describing the physical phenomena along with proper border settings are resolved by applying the finite element method (FEM). Different ratios of hybrid nanoparticles (G: SWCNT) like (1: 0, 1/3: 2/3, 1/2: 1/2, 2/3: 1/3, 0: 1) are suspended in the base fluid mixture. In addition, the base fluid mixture is assumed in different combinations of (IL: PG) as (100: 0, 50: 50, 0: 100). The numerical results are displayed in the forms of streamlines, isothermal lines, and rate of thermal transfer for the pertinent parameters namely forced convection (Re = 100–900) and solid concentration (φ = 0.001–0.05). Also, pressure drop, field synergy number, relative fanning friction feature, relative Nusselt number, and temperature enhancement efficiency are calculated. The results indicate that a higher heat transport rate is found using the IL-based ionanofluid with the highest solid concentration. Moreover, the higher forced convection enhances the thermal efficiency of MCHS. Two linear regression equations along with very good correlation coefficients have been derived from the numerical results.