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This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

An exact analysis is carried out to study the radiation effects on an unsteady natural convective flow of a nanofluid past an impulsively started infinite vertical plate. The nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. The partial differential equations governing the flow are solved by Laplace transform technique. The influence of various parameters on velocity and temperature profiles, as well as Nusselt number and skin-friction coefficient, are examined and presented graphically. An increase in radiation parameter and time leads to fall in temperature of the fluid. The presence of nanoparticles and thermal radiation increases the rate of heat transfer and skin friction. The effect of heat transfer is found to be more pronounced in silver water nanofluid than in the other nanofluids. It is observed that the fluid velocity increases with an increase in Grashof number and time. Excellent validation of the present results is achieved with existing results in the literature.

The objective of this research is to explore the potential of utilizing renewable energy ships (RES) as a sustainable alternative and reducing the need for marine diesel oil (MDO) within the shipping industry. This work concentrates on increasing the thermal performance in RES via the utilization of nanofluids (NFs) that contain a mixture of the base water fluid and titanium dioxide (TiO${}_2)$ nanoparticles. Furthermore, the implementation of the entropy generation minimization and Eyring–Powell fluid model in parabolic trough solar collectors is employed for RES. Moreover, the results indicate that the SFC and LNN supplements resulted in an increase of approximately 1.03% and 0.04% for the SBES, which can be attributed to the greater concentration of the titania nanoparticles. Meanwhile, for the case of USBES, the enhancement was observed up to 1.38% and 0.31%, respectively. Also, the solar radiation parameter played an important role in enhancing the LNN, resulting in an increase of approximately 5.93% and 4.35% for SBES and USBES respectively. This paper provides vital contributions to the sector of sustainable transportation by giving valuable information on the construction and improvement of thermal solar energy technologies.