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The unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, and electrically conducting fluid passing through a vertical plate embedded in a porous medium in the presence of chemical reactions and thermal radiation is investigated. The effects of the Hall current, rotation and Soret are studied. Using the perturbation approach, one can obtain an accurate analytical solution to the governing equations for the fluid velocity, fluid temperature, and species concentration, provided that the initial and boundary conditions are acceptable. It is possible to obtain expressions for the shear stress, rate of heat transfer, and rate of mass transfer for both plates with the ramping temperature and isothermal conditions. On the one hand, the numerical values of the primary and secondary fluid velocities, fluid temperature, and species concentration are presented graphically. On the other hand, the numerical values of the shear stress and rate of mass transfer for the plate are presented in tabular form for various values of the relevant flow parameters. These values are given for a range of pertinent flow parameters. It was determined that an increase in the Hall and Soret parameters over the whole fluid area leads to a corresponding increase in the resulting velocity. The resultant velocity continually climbs to a high level due to the contributions of the thermal and solute buoyancy forces. Lowering the heat source parameter reduces the temperature distribution, resulting in a lower overall temperature. When there is a rise in the chemical reaction parameter over the whole fluid area, there is a corresponding decrease in the concentration. The concentration buoyancy force, Hall current, and Prandtl number reduce the skin friction. On the other hand, the permeability of the porous medium, rotation, chemical reaction, the Soret number, thermal buoyancy force, and mass diffusion all have the opposite effects on the skin friction.

Background: The improvement of the thermal conductivity of nanofluids is practical for different processes such as drug delivery, manufacturing of crystals, polymer processing, food and drink, cancer treatment, oil and gas, paper making and for many more. The bioconvection phenomenon has engrossed the attention of numerous researchers for its many applications in biotechnology, mechanical and electrical engineering. Bioconvection nanofluids are more prominent in the fields of biomedicine, pharmacy, nanodrug delivery, biomedical, automotive cooling and the military. Purpose: The major purpose of the current work was to determine the numerical and statistical analysis of a novel thermal radiation and exponential space-based heat source on the bioconvective flow of a pseudoplastic 3D nanofluid past a bidirectional stretched Riga surface. The behavior of the Arrhenius activation energy (AAE) and thermal radiation are also disclosed. Methodology: Suitable similarity transformations were used to transmute the partial differential equations of the flow-modeled phenomena into the structure of ordinary differential ones. The numerical solutions for the renewed set of ODEs were tackled by the bvp4c shooting algorithm built-in MATLAB software. Furthermore, the statistical analysis was computed by applying response surface methodology (RSM). Research implications: The numerical analysis is valid for the incompressible three-dimensional, magnetized flow of a pseudoplastic bioconvection nanofluid through a bidirectional surface with Riga plate aspects in the occurrence of activation energy. Social implications: The flow across three dimensions has quite important implementations in various fields, for example, polymer production, material production technology, the manufacturing of nano-biopolymer computer graphics, industry, powered engineering, aeroplane configurations, etc. The current analysis is more applicable in nanotechnology. Results: The consequences of flow control parameters over flow profiles were studied and explained under the graphic structures. Numerical outcomes were computed and discussed in detail. From the results, it was noted that the velocity field was increased via a larger mixed convection parameter. The temperature distribution was boosted via the thermal Biot number. The concentration of nanoparticles declined via the greater Lewis number. Furthermore, the motile microorganisms field was reduced via the Peclet number. Originality: Until now, no investigation has been recognized to examine the consequences of the bioconvection flow of three-dimensional pseudoplastic nanofluids past a Riga plate containing motile microorganisms utilizing the shooting method called bvp4c. Conclusions: From the results, it was concluded that nanofluids are more helpful for heat transfer increments. Furthermore, from the experimental design observed, the response declined via the thermophoresis parameter, which was significant from the ANOVA observed model.

In this work, the STEP scheme and several schemes based on the normalized variable diagram (NVD), such as MINMOD, GAMMA, CLAM, NOTABLE, MUSCL, CUBISTA, SMART, WACEB, and VANOS schemes, are evaluated for solving the radiative transfer equation. Two‐dimensional and three‐dimensional rectangular enclosures containing transparent, emitting–absorbing, emitting–absorbing–scattering, or nonhomogeneous participating media are investigated using the modified FTn finite volume method. Although the NVD schemes are much more accurate than the STEP scheme, but they have more time‐consuming and require more iterations. Moreover, most of them often necessitate underrelaxation to ensure convergence. Results show that the MINMOD and GAMMA schemes are still much less accurate than other NVD schemes, but they converge the fastest of the NVD schemes, and do not require underrelaxation. Although the VANOS, WACEB, and SMART schemes give more accurate solutions, they are not competitive with other NVD schemes. However, the CLAM, NOTABLE, and CUBISTA schemes are relatively fast and accurate.

This article describes the incompressible two-dimensional heat and mass transfer of an electrically conducting second-grade fluid flow in a porous medium with Hall and ion slip effects, diffusion thermal effects, and radiation absorption effects. It is assumed that the fluid is a gray, absorbing–emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. It is assumed that the liquid is opaque and absorbs and emits radiation in a manner that does not result in scattering. It is considered an unsteady laminar MHD convective rotating flow of heat-producing or absorbing second-grade fluid across a semi-infinite vertical moving permeable surface. The profiles of velocity components, temperature distribution, and concentration are studied to apply the regular perturbation technique. These profiles are shown as graphs for various fluid and geometric parameters such as Hall and ion slip parameters, radiation absorption, diffusion thermo, Prandtl number, Schmidt number, and chemical reaction rate. On the other hand, the skin friction coefficient and the Nusselt number are determined by numerical evaluation and provided in tables. These tables are then analysed and debated for various values of the flow parameters that regulate it. It may be deduced that an increase in the parameters of radiation absorption, Hall, and ion slip over the fluid region increases the velocity produced. The resulting momentum continually grows to a very high level, with contributions from the thermal and solutal buoyancy forces. The temperature distribution may be more concentrated by raising both the heat source parameter and the quantity of radiation. When one of the parameters for the chemical reaction is increased, the whole fluid area will experience a fall in concentration. Skin friction may be decreased by manipulating the rotation parameter, but the Hall effect and ion slip effect can worsen it. When the parameter for the chemical reaction increases, there is a concomitant rise in the mass transfer rate.

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An experimental validation on laboratory scale has been conducted to investigate and to compare two thermodynamic cycles, Trilateral Flash Cycle (TFC) and Organic Rankine Cycle (ORC). The research covers the heat engine utilizing a hydrothermal resource to compare the performance of TFC and ORC. This research would help to analysis the thermal efficiency and power efficiency for both cycles. TFC shows a higher power production than in ORC for the same applied parameters. ORC, however, can be operated at lower rotational speed than for TFC. This project could help, also, to evaluate the current two phase screw expander for both cycles. It is concluded to propose a larger heat exchanger for TFC as the heat recovery can be more reliable in this cycle than in ORC. This research can be applied to generate electrical power from hydrothermal resources such as geothermal energy and solar thermal.

In this paper, 3-D heterogeneous medium, containing small inhomogeneous zones, subjected to a short-pulse laser has been examined by solving the transient radiative transfer equation. Both curved-line advection method and STEP schemes of the FTn finite volume method have been applied. The curved-line advection method predictions proved that a decrease of the false scattering and ray effects are obtained. In fact, there was a good agreement between the curved-line advection method and the Monte Carlo method. However, the STEP results are slightly mismatching the predictions of the aforementioned reference method. Then, the effects of the absorption coefficient, the size, the number and the position of inhomogeneous zone on the transmittance and reflectance signals have been analyzed. The predictions showed that the increase of the size of the inhomogeneity reduces the intensity of radiation. For both homogenous and heterogonous medium, the change of the detector position varies both the broadening of the signal pulse-width and the time with peak reflectance and/or transmittance. That is can be explained by the effects of the distance and the medium property between the laser-incident source and the detector position. Thus, these both parameters are the main factors for determining the peak position and the pulse broadening. Finally, the effects of the absorption coefficient in the inhomogeneity zone on the absolute values of logarithmic slope has been discussed. The results proved that the absolute values of logarithmic slope may be a perfect indicator for detecting any abnormal absorbing zones in the medium.