This research looked at the effects of thermal radiation and Brownian motion on the mixed convection heat and mass transfer of nanofluid over a porous plate in a Darcy-Forchheimer flow. The controlling partial differential equations are converted to ordinary differential equations and numerically solved by using Runge-Kutta fourth-order alongside shooting approach. Different physical parameters’ effects on temperature, velocity, and concentration distribution are studied. In addition, the results are also graphically represented. The reduced local Nusselt number and Sherwood number are shown and compared to previous investigations; the comparisons are extremely close. According to the results, the rate of heat transfer is lowered by 63.83% when the Brownian parameter is increased from 0.2 to 1 (in case of suction) and by 83.31% when the Brownian parameter is increased from 0.2 to 1 (in the case of injection). Also, in the case of suction, thermophoresis parameters lowered it by 50.48%, and in the case of injection, it was reduced by 65.08%.

fractal analysis of viscous fingering of a reactive miscible flow displacement in homogeneous porous media is investigated and multifractal spectrum, and fractal dimension are introduced as two essential features to characterize the irregularity of finger patterns. The Reaction of the two reactant fluids generates a miscible chemical product C in the contact zone. Considering the similarity between chemical products and coastline, monofractal and multifractal analyzes are performed. In monofractal analysis, the box-counting method is implemented on binary images and in multifractal analysis, due to the image processing; the fractal characteristics of viscous fingering instability are analyzed by means of fractal quantities such as Holder exponent, multifractal spectrum, f (α)-image and fractal dimension dynamics. Fractal analysis shows that the fractal dimension increases with time. Also, by considering five different nonlinear simulations, the results show that in the case both sides of the chemical product C are unstable, the multifractal spectrum curve has the highest peak, which means the more complex finger patterns lead to more values of fractal dimension. In addition, a comparison between different values of Ar is conducted and the results show similar behavior. However, small value of aspect ratio leads to a broader width of the multifractal spectrum curve. Furthermore, f (α)-images of concentration contour were investigated for different precisions and some undetectable finger patterns were observed in these images. It can be concluded that the use of f (α)-image represents more detailed image than concentration contours.

Nanofluid concept was defined over 28 years ago. Since then, a veritable science has been developed around this concept. From 1993 until 2020, up to 18021 articles were published in high-quality journals worldwide. The high scientific interest in nanofluids lies in their exceptional thermophysical properties and their possibilities to design more efficient processes and systems. Although the numerous articles, there is a lack of information on the scope, its social and economic impact, or its future trends. This study provides an overview through bibliometric methods that allow better knowledge of the research field. The main goal is to offer a more generalized and strategic vision to help those researchers interested in this topic with accurate information on its impact. In addition, this study helps to maximize international collaborations and provide relevant information to decision-makers. The analysis reveals that research in nanofluids in the last decade has experienced a great specialization in a wide variety of new applications, reaching more new sectors. The main research communities, the most productive authors, or the most relevant journals are some of the analyzed metrics that provide key parameters for contextualization, allowing a clear vision of the current state of the nanofluids research field.

Combination of Carbon Nanotubes (CNTs) with Human blood as base fluid indicates the enhancement of heat transport in Poiseuille flow and this physical phenomenon could not possible in normal liquids. Usually, when blood cells get touch with external surfaces, the platelets of blood become activated and form blood clots. Therefore, we have considered blood compatible CNT, so that chosen base fluid (blood) can easily pass through it. Due to the higher thermal conductivity, CNTs play an important role to enhance the heat transport in blood flow. These features lead to the novelty of this investigation to study the heat transport of Casson fluid through CNTs in unsteady MHD free convective Poiseuille flow with thermal radiation. Such study consigns practical applications in manufacturing of drugs, biomedical and Tissue engineering, biosensor and other applications in myocardial therapy, neuronal and muscle regeneration. The non-dimensional governing equations are formulated and solved analytically through classical Perturbation Technique and the analysis of results are drawn in smooth curves via MATLAB code. Significant results for different implanted parameters are compared between SWCNT and MWCNT and their significant behaviours are plotted graphically. The obtained results indicate that Casson parameter accelerates the flow velocity for MWCNT and SWCNT. Furthermore, interesting behavior on the outlines of velocity for SWCNT and MWCNT due to the presence of Schmidt number, Peclet number and Reynolds number are detected. Comparison with previously published work has been inspected and originated excellent agreement.

In this comparative examination, the paradox of mass diffusion and heat conduction on the improved surface of weakly hydromagnetic and unsteady fluid flow is examined. Material relaxation time is believed to be one of the contributing factors militating against an effective heat and mass transfer. This flow process is estimated to predict accurately the fluids enhancement and condensation/evaporation properties. With a workable similarity variable, the formulated model of modified Fick’s and Fourier’s laws assumed in the Riga surface-induced flow conveying Casson-Williamson fluids with variable transport properties are transformed to the systems of ordinary differential equations. The spectral iterative technique (SLLM in particular), thus employed to analyze the flow distributions and ascertain the validity of the obtained results. However, cohesion force between the fluid particle establishes abnormalities of both Fick’s and Fourier’s laws indicating that extra time will be required for effective mass and heat convection to the immediate environment. Generalized heat flux parameter minimizes the fluid temperature and accelerated the nanoparticle concentration, relative minimization of the fluid temperature resulted to much more nanoparticle concentration. Moreover, Williamson fluid demonstrated a higher conductivity/diffusivity capacity in constract to the Casson fluid. When compared to Casson fluid, the modified Hartman number has a stronger influence on Williamson fluid.

This paper aims to study the electroosmotic nanofluid flow and heat transfer phenomena in a microchannel with porous walls by paying due attention to the interaction of the injected fluid velocity and the net charge density in the base fluid on the development of zeta potential and electroosmotic slip velocity. The novelty of this study is to obtain the integral expression for electroosmotic slip velocity which is found to converge to Smoluchowski velocity when the injected fluid velocity is low and porous permeability of channel wall becomes negligible. Under a weak electric field condition, the enhancement of pressure gradient is found to increase the normalized temperature and decrease the normalized nanoparticle concentration. The bulk nanofluid temperature is found to follow an almost quadratic relationship with applied pressure gradient. Additionally, in the absence of injection velocity, we observed a new expression for Soret number as a ratio of the cross sectional nanoparticle concentration to Joule heating parameter. Finally, a comparative study on the total entropy generation is carried out to minimize the loss of thermal energy due to irreversible physical mechanisms such as heat transfer, viscous dissipation and Joule heating effects that take place during the fluid flow process in a microchannel. It is thereby observed that the total entropy generation follows a quadratic relation with the Joule heating parameter in the absence of both injection and viscous dissipation. The increment in diffusive Reynolds number reduces EDL thickness near the upper channel bed. With an increment in the applied pressure gradient, the normalized temperature increases whereas the normalized nanoparticle concentration reduces.

The Buongiorno model is utilized for the non-Newtonian third-grade fluid. With non-linear radiation and magnetic action, it incorporates both Brownian motion and thermophoresis processes. Aim this research is to look at non-Newtonian third-grade fluid boundary layer flow with non-linear solar energy thermal radiation and the magnetic effect. The similarity transformation is used to convert nonlinear PDEs into ODEs. Then numerically solved by shooting technique and the sixth-order R-K method. For various physical parameters, derived findings are graphically discussed. We believe that the current findings can be utilized to explain the non-Newtonian properties of second and third-grade fluids, as well as for applications in tribology, the automobile industry, and other fields.

This research’s contribution is towards determining heat transfer characteristics of Ag–C2H6O2 and Cu–C2H6O2 nano fluid over a vertical porous circular cylindrical surface. The mixed convection flow in the presence of electric conductivity, Joule heating and thermal radiation near a stagnation point is considered for investigation. Ethylene glycol is taken as base fluid while copper and silver are nanoparticles. Through similarity transformations, the governing PDEs for momentum, energy, and concentration are turned into ODEs, which are then interpreted using a fourth-order exactness programme (Bvp4c). The parametric impacts on concentration, temperature and velocity are thoroughly discussed graphically while impact on the rate of heat transfer, skin friction and rate of mass transfer is obtained in numeral form. The obtained results are compared to published literature and a comparison between Ag–C2H6O2 and Cu–C2H6O2 nano fluids is demonstrated.

In the present study, the magnetohydrodynamic pulsating flow of chemically reacting Oldroyd-B nanoliquid via channel with the impressions of Ohmic heating, radiative heat and viscous dissipation is studied. The ruling PDEs (partial differential equations) are changed into ODEs (Ordinary differential equations) by utilizing the perturbation procedure and numerically deciphered by adopting the 4th order Runge-Kutta approach with the aid of the shooting process. The novelty of the current work is to inspect the pulsating flow of Oldroyd-B nanoliquid via channel in the occurrence of an applied magnetic field by deploying the Buongiorno nanofluid model. The application of the proposed physical model is energy production, heating and cooling processes, thermoelectric devices, bio-medical applications like brain tumours, cancer treatment, drug targeting. Detailed analysis on the impacts of several pertinent parameters for velocity, temperature, nanoparticles concentration, rates of heat and mass transfer is done. The outcomes predict that the velocity of nanoliquid is improved with augmenting frequency parameter while it is reduced with acceleration in Hartmann number. The temperature rises with an improvement of thermophoresis, viscous dissipation, and Brownian motion while it falls for a given rise in Hartmann number and thermal radiation. Further, the nanoparticle concentration rises with an increasing Brownian motion while it falls over rising chemical reaction, thermophoresis, and Lewis number.

In this communication, the analysis of the entropy generation on magnetohydrodynamic (MHD) Eyring-Powell nanofluid over a stretching sheet with the effects of heat source/sink is reported. The presence of thermophoresis and Brownian motion are responsible for the enhancement in the properties of heat transfer. With the help of suitable similarity transformation entity, the involved governing partially differential equations (PDEs) are converted into nonlinear coupled ordinary differential equations (ODEs). Further, converted differential equations are solved by numerical methods such as Runge-Kutta fourth order correlated with shooting technique. Influence of various pertinent physical parameters is discussed via velocity, temperature, concentration and entropy profiles. The effect of these variables on the quantities of engineering advance such as Nusselt and Sherwood number are furnished in illustrative form and discussed. Further, the major findings of the outcomes are laid down as follows; the Brownian motion of the particles enhances the fluid temperature whereas thermophoresis retards significantly. The entropy generation overshoots due to the increase in the Reynolds number. Nanofluids with high critical heat fluxes and high-power density have the potential to provide the required cooling effect in military ships, submarines, wave energy converters and high-power laser diodes.