Rheology of MHD bioconvective nanofluid containing motile microorganisms is inspected numerically in order to analyze heat and mass transfer characteristics. Bioconvection is implemented by combined effects of magnetic field and buoyancy force. Gyrotactic microorganisms enhance the heat and transfer as well as perk up the nanomaterials’ stability. Variable transport properties along with assisting and opposing flow situations are taken into account. The significant influences of thermophoresis and Brownian motion have also been taken by employing Buongiorno’s model of nanofluid. Lie group analysis approach is utilized in order to compute the absolute invariants for the system of differential equations, which are solved numerically using Adams-Bashforth technique. Validity of results is confirmed by performing error analysis. Graphical and numerical illustrations are prepared in order to get the physical insight of the considered analysis. It is observed that for controlling parameters corresponding to variable transport properties c₂, c₄, c₆, and c₈, the velocity, temperature, concentration, and bioconvection density distributions accelerates, respectively. While heat and mass transfer rates increases for convection parameter and bioconvection Rayleigh number, respectively.

The presented communication provides the analysis of entropy generation and heat transport rate in peristalsis of hybrid nanofluid induced by metachronal ciliary beating under magnetic environment for sufficiently large magnetic Reynolds number. Nanoparticles of Cu and Al₂O₃ are suspended in water. Features of their structures are determined by using long-wavelength approximation with zero Reynolds number. Adams Bashforth method has been applied to compute the results of the flow variables as well as entropy generation number from the formulated differential system which are then interpreted graphically to establish physical significance for different values of physical interest. This investigation reveals that thermal performance of fluid can be boosted by utilizing hybrid nanomaterial about the strength of a wall for stability. Irreversibility analysis ensures that entropy reduced for strong magnetic field while thermal heat generation results in an increase in temperature causing an enhancement in entropy of the system. Error analysis has been performed with reasonably accurate tolerance level. The comparative outcomes of both numerical approaches are presented with plentiful graphical as well as numerical demonstrations which demonstrate the importance in terms of robustness, accuracy and stability.

The research community of environmental economics has had a growing interest for the exploration of artificial intelligence (AI)-based systems to provide enriched efficiencies and strengthened human knacks in daily live maneuvers, business stratagems, and society evolution. In this investigation, AI-based intelligent backpropagation networks of Bayesian regularization (IBNs-BR) were exploited for the numerical treatment of mathematical models representing environmental economic systems (EESs). The governing relations of EESs were presented in the form of differential models representing their fundamental compartments or indicators for economic and environmental parameters. The reference datasets of EESs were assembled using the Adams numerical solver for different EES scenarios and were used as targets of IBNs-BR to find the approximate solutions. Comparative studies based on convergence curves on the mean square error (MSE) and absolute deviation from the reference results were used to verify the correctness of IBNs-BR for solving EESs, i.e., MSE of around 10⁻⁹ to 10⁻¹⁰ and absolute error close to 10⁻⁵ to 10⁻⁷. The endorsement of results was further validated through performance evaluation by means of error histogram analysis, the regression index, and the mean squared deviation-based figure of merit for each EES scenario.

The current study is an attempt to analytically characterize the second law analysis and mixed convective rheology of the (Al₂O₃–Ag/H₂O) hybrid nanofluid flow influenced by magnetic induction effects towards a stretching sheet. Viscous dissipation and internal heat generation effects are encountered in the analysis as well. The mathematical model of partial differential equations is fabricated by employing boundary-layer approximation. The transformed system of nonlinear ordinary differential equations is solved using the homotopy analysis method. The entropy generation number is formulated in terms of fluid friction, heat transfer and Joule heating. The effects of dimensionless parameters on flow variables and entropy generation number are examined using graphs and tables. Further, the convergence of HAM solutions is examined in terms of defined physical quantities up to 20th iterations, and confirmed. It is observed that large ${\lambda }_1$ upgrades velocity, entropy generation and heat transfer rate, and drops the temperature. High values of $\delta$ enlarge velocity and temperature while reducing heat transport and entropy generation number. Viscous dissipation strongly influences an increase in flow and heat transfer rate caused by a no-slip condition on the sheet.

Agricultural diversification efforts towards sustainable agriculture generates environmental and economic benefits. Climate change and agricultural production are characterized by a complex cause-effect relationship. In the present study, the primary dataset is collected through an interview-based survey from 410 farmers in 3 districts located in different agro-ecological zones of Punjab, Pakistan. Detailed analysis is conducted by employing the Gaussian treatment effects approach. Results of the study show that the farmers who adopted agricultural diversification to mitigate the impact of climate change were less and insignificantly benefited e.g., on an average of RS 95,260 (US $635) per annum whereas non-adopted farmers lost their farm income on an average of RS 115,750 (US $772) per annum if they had practiced the agricultural diversification. Moreover, determinants of agricultural diversification such as demographic and institutional indicators were significant and larger effects to adopt as compared to social indicators. This study suggests that policies should be designed in the regional context particularly related to the improvement in demographic characteristics and institutional factors such as providing subsidies, training, and awareness to the farmers, particularly to those who practice agricultural diversification. These measures will help to raise the farmers’ adaptive capacity for the adoption of agricultural diversification, and it will enable them to generate tangible benefits by increasing income through adopting sustainable agricultural livelihood.

This research concerns the heat transfer and entropy generation analysis in the MHD axisymmetric flow of Al₂O₃-Cu/H₂O hybrid nanofluid. The magnetic induction effect is considered for large magnetic Reynolds number. The influences of thermal radiations, viscous dissipation and convective temperature conditions over flow are studied. The problem is modeled using boundary layer theory, Maxwell’s equations and Fourier’s conduction law along with defined physical factors. Similarity transformations are utilized for model simplification which is analytically solved with the homotopy analysis method. The h-curves up to 20th order for solutions establishes the stability and convergence of the adopted computational method. Rheological impacts of involved parameters on flow variables and entropy generation number are demonstrated via graphs and tables. The study reveals that entropy in system of hybrid nanofluid affected by magnetic induction declines for β while it enhances for Bi, R and λ. Moreover, heat transfer rate elevates for large Bi with convective conditions at surface.