Chickpea (Cicer arietinum L.) is a dry season food legume largely grown on residual soil moisture after the rainy season. The crop often experiences moisture stress towards end of the crop season (terminal drought). The crop may also face heat stress at the reproductive stage if sowing is delayed. The breeding approaches for improving adaptation to these stresses include the development of varieties with early maturity and enhanced abiotic stress tolerance. Several varieties with improved drought tolerance have been developed by selecting for grain yield under moisture stress conditions. Similarly, selection for pod set in the crop subjected to heat stress during reproductive stage has helped in the development of heat‐tolerant varieties. A genomic region, called QTL‐hotspot, controlling several drought tolerance‐related traits has been introgressed into several popular cultivars using marker‐assisted backcrossing (MABC), and introgression lines giving significantly higher yield than the popular cultivars have been identified. Multiparent advanced generation intercross (MAGIC) approach has been found promising in enhancing genetic recombination and developing lines with enhanced tolerance to terminal drought and heat stresses.

In this study, the entropy formation of an electromagnetohydrodynamic hybrid nanofluid at a stagnation point flow towards a stretched surface in the presence of melting heat transfer, second-order slip, porous medium, viscous dissipation and thermal radiation are investigated. Hybrid nanoparticles alumina (Al₂O₃) and copper (Cu) are considered, with the base fluid water (H₂O). Similarity transformations are used to address the governing partial differential equations (PDEs) that lead to the corresponding ordinary differential equations. The resulting ODEs are solved by employing bvp4c solver numerically in the MATLAB package. The effects of temperature, transport, production of entropy and Bejan number $Be$ are graphically exhibited. Higher radiation parameters $R$ and an electric field $E$ lead to an increase in fluid temperature. The velocity boundary layer is lowered by the magnetic field and porous media parameters. The opposite behaviour is observed in the electric field $E$. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, electronics, heat exchangers, water purification, lubricants and soaps as well.

The objective of this paper is to examine the augmentation of the heat transfer rate utilizing graphene (Gr) and multi-walled carbon nanotubes (MWCNTs) as nanoparticles, and water as a host fluid in magnetohydrodynamics (MHD) flow through an upright plate using Caputo fractional derivatives with a Brinkman model on the convective Casson hybrid nanofluid flow. The performance of hybrid nanofluids is examined with various shapes of nanoparticles. The Caputo fractional derivative is utilized to describe the governing fractional partial differential equations with initial and boundary conditions on the flow model. Exact solutions are obtained for flow transport, temperature distribution besides that heat transfer rate and friction drag in terms of Mittag-Leffler function by using Fourier sine and Laplace techniques as hybrid methods. Further, we provided the limiting case solutions for classic partial differential equations on obtained governing fluid flow models. The influence of various physical parameters with different fractional orders are investigated on hybrid nanofluid’s fractional momentum and energy by plotting velocity and energy curves. Few of the findings suggest that fractional parameters have significant effect on flow parameters and that blade-shaped nanoparticles have a high heat transfer rate. The graphical results reveal that the Grashof number shows a symmetry effect in the case of cooling and heating the plate. Furthermore, the performance of hybrid nanofluid is considerably more effective with the Caputo-fractional derivatives rather than in the classic derivative approach.

This paper presents the problem modeled using Caputo fractional derivatives with an accurate study of the MHD unsteady flow of Nanofluid through an inclined plate with the mass diffusion effect in association with the energy equation. H2O is thought to be a base liquid with clay nanoparticles floating in it in a uniform way. Bousinessq's approach is used in the momentum equation for pressure gradient. The nondimensional fluid temperature, species concentration, and fluid transport are derived together with Jacob Fourier sine and Laplace transforms Techniques in terms of exponential decay function, whose inverse is computed further in terms of Mittag-Leffler function. The impact of various physical quantities interpreted with fractional order of the Caputo derivatives. The obtained temperature, transport, and species concentration profiles show behaviours for $0 < \mathtt{α} < 1$ where $\mathtt{α} $ is the fractional parameter. Numerical calculations have been carried out for the rate of heat transmission and the Sherwood number is swotted to be put in the form of tables. The parameters for the magnetic field and the angle of inclination slow down the boundary layer of momentum. The distributions of velocity, temperature, and concentration expand more rapidly for higher values of the fractional parameter. Additionally, it is revealed that for the volume fraction of nanofluids, the concentration profiles behave in the opposite manner. The limiting case solutions also presented on flow field of governing model.