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Water-based ‘nanofluid’ flow owing to an unsteady stretched surface is inspected in this paper considering Stefan blowing and thermal radiation. ‘Similarity transformations’ are applied to reduce the governing ‘partial differential equations’ (PDEs) for momentum, energy and concentration into ‘nonlinear’ ‘ordinary differential equations’ (ODEs). By using a shooting technique, those equations are solved numerically with the help of fourth-order ‘Runge–Kutta method’. ‘Wall shear stress’ rises but ‘heat transfer’ as well as ‘mass transfer coefficients’ reduce for the augmentation in ‘Stefan blowing/suction parameter’. ‘Temperature’ and ‘concentration’ of nanoliquid are found to rise but liquid’s ‘velocity’ reduces for the growing of ‘nanoparticle’s volume fraction’. Liquid’s ‘velocity’ and ‘concentration’ are observed to decrease for enhanced ‘Lewis number’. Based on the results presented here as well as their anatomical analysis, the relevant parameters significantly affect the stream, warmth and mass transports.

This paper investigates the dissipative Casson ternary hybrid nanoflow comprising Ag, Cu, and ${\mathrm{\text{MoS}}}_2$ nanocomposite, over a flat plate. Incorporating the thermal source, varying temperature, and concentration provides the required novelty of the study. The physical flow model has been computationally resolved using the Bvp4c approach, after the transformation of the system of PDEs into coupled ODEs. The effects of various parameters on the velocity, temperature, mass distribution profiles, rate of shear stress, Nusselt number, and Sherwood number are shown in figures and tables. The thermo transposition rate in Newtonian, hybrid Newtonian, Casson, and Casson hybrid Newtonian fluids increases by 83%, 115%, 152%, and 183%, respectively, with the enhancement of the dissipation effect. Furthermore, the Sherwood coefficient increases by 31% for each of the four fluid types, while the variable mass index measurement improves. The results indicate a significant advancement in bio-nanofluid dynamics, presenting considerable prospects for optimizing heat transfer in bioengineering. An important concordance between the present investigation and the prior one has also been shown.

The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bioconvection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative analysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence heat, mass and motile micro-organism transfer rates.

In this paper a definitely new analytical technique, predictor homotopy analysis method (PHAM), is employed to solve the problem of two-dimensional nanofluid flow through expanding or contracting gaps with permeable walls. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge–Kutta integration method as well as previously published study results demonstrates high accuracy for this technique. The fluid in the channel is water containing different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The effects of the nanoparticle volume fraction, Reynolds number, wall expansion ratio, and different types of nanoparticles on the flow are discussed.

Blood flow model is recycled to study the influence of magnetic field and nanoparticles in tapered stenosed arteries. The metallic nanoparticles for the blood flow with water as base fluid are not explored so far. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest for pure water and Copper water (Cu-water).

The paper provides an analytical investigation, homotopy analysis method (HAM), of the heat and mass transfer for magnetohydrodynamic Oldroyd-B nanofluid flow over a stretching sheet in the presence of convective boundary condition. The PDE governing equations, which consist of equations of continuity, momentum, energy and nanoparticles, are converted to ordinary differential equations using similarity transformations. The current HAM solution demonstrates very good correlation with those of the previously published studies in the special cases. The influences of different flow physical parameters such as the Deborah numbers in terms of relaxation and retardation times (${\beta }_1$, ${\beta }_2$), magnetic parameter (M), Prandtl number (Pr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Lewis number (Le), and Biot number (Bi) on the fluid velocity component $(f^{\prime }(\eta ))$, temperature distribution $(\theta (\eta ))$ and concentration $(\varphi (\eta ))$ as well as the local Nusselt number $({\mathrm{\text{Nu}}}_x/{\mathrm{\text{Re}}}_x^{1/2})$ and the local Sherwood number $({\mathrm{\text{Sh}}}_x/{\mathrm{\text{Re}}}_x^{1/2})$ are discussed in detail.

In this paper, the swirling nanofluid flow which is driven by a rotating bottom disk of a cylindrical container under magnetic field effect and temperature gradient is considered. Effects of electrical conductivity of cylindrical walls on heat transfer enhancement are numerically analyzed. The governing equations that describe the combined problem (magnetohydrodynamics and mixed convection) under the adoptive assumptions are solved numerically by the finite volume technique. Calculations were made for fixed Reynolds number (Re$=$1000), Richardson number (0$\le$Ri$\le$2), aspect ratio ($H/R=2$), Hartmann number (0$\le$Ha$\le$60), and solid nanoparticle (copper) with volume fraction ($\varphi =0.1$). Five cases are considered in this study: (EI-Walls), (EC-Walls), (EC-Bottom), (EC-Top), and (EC-Sidewall). A decrease in the mean Nusselt number was found with the increase of the Richardson number due to stratification layers. These latter limits the heat transfers between the hot and cold zones of the cylinder. The results indicate that the Nusselt number gets bigger within a certain range of Hartmann numbers, and especially when the rotating lid is electrically conducting. Indeed, average Nusselt number decreases while the Hartmann number increase after it exceeds a critical value. Finally, the electrical conductivity of the rotating lid plays an important role in heat transfer enhancement in nanofluid swirling flow.