Narrow Results

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.

The problem of a steady boundary layer MHD slip flow over a stretching sheet in a water-based nanofluid containing different type of nanoparticles: Cu, Al₂O₃ and Ag has been investigated. An external strong magnetic field is applied perpendicular to the plate and the Hall effect is taken into consideration. The surface of the stretching sheet is assumed to move with a linear velocity and subject to power-law variation of the surface temperature. The governing partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by a Runge–Kutta–Fehlberg method with shooting technique. Effects of the physical parameters on the primary velocity, the secondary velocity and the temperature as well as on the wall shear stress and the rate of heat transfer have been presented graphically and discussed in detail. Investigated results indicate that the nanoparticle volume fraction and the slip parameter produce opposite effects on the skin friction coefficients of the primary and secondary flow. Also, the nanoparticle volume fraction and the types of nanoparticles demonstrate a more pronounced influence on the secondary flow than that on the primary flow and temperature distribution.

The aim of this work is to conduct numerical study of fluid flow and natural convection heat transfer by utilizing the nanofluid in a two-dimensional horizontal channel consisting of a sinusoidal obstacle by lattice Boltzmann method (LBM). The fluid in the channel is a water-based nanofluid containing Cuo nanoparticles. Thermal conductivity and nanofluid’s viscosity are calculated by Patel and Brinkman models, respectively. A wide range of parameters such as the Reynolds number ($\mathrm{\text{Re}}=100$–400) and the solid volume fraction ranging ($\mathrm{\Phi }=0$–0.05) at different non-dimensional amplitude of the wavy wall of the sinusoidal obstacle ($A=0$–20) on the streamlines and temperature contours are investigated in the present study. In addition, the local and average Nusselt numbers are illustrated on lower wall of the channel. The sensitivity to the resolution and representation of the sinusoidal obstacle’s shape on flow field and heat transfer by LBM simulations are the main interest and innovation of this study. The results showed that increasing the solid volume fraction $\mathrm{\Phi }$ and Reynolds number Re leads to increase the average Nusselt numbers. The maximum average Nusselt number occurs when the Reynolds number and solid volume fraction are maximum and amplitude of the wavy wall is minimum. Also, by decreasing the $A$, the vortex shedding forms up at higher Reynolds number in the wake region downstream of the obstacle.

Recently, various ways are investigated to augment heat transfer in different applications such as porous ceramic domain. Adding nanoparticles to fluid is the best operational way to increase the conduction of fluids. In this paper, migration of nanofluid inside a porous duct under the impact of magnetic force is scrutinized. LBM is applied to present comprehensive parametric analysis for various concentrations of nanofluid, Hartmann, Reynolds, and Darcy numbers. Outputs illustrate that Nu augments with improve of Lorentz forces. Augmenting Da significantly enhances the convective flow in our model.

Magnetohydrodynamic flow of nanofluids and heat transfer between two horizontal plates in a rotating system have been examined numerically. In order to do this, the group method of data handling (GMDH)-type neural networks is used to calculate Nusselt number formulation. Results indicate that GMDH-type NN in comparison with fourth-order Runge–Kutta integration scheme provides an effective means of efficiently recognizing the patterns in data and accurately predicting a performance. Single-phase model is used in this study. Similar solution is used in order to obtain ordinary differential equation. The effects of nanoparticle volume fraction, magnetic parameter, wall injection/suction parameter and Reynolds number on Nusselt number are studied by sensitivity analyses. The results show that Nusselt number is an increasing function of Reynolds number and volume fraction of nanoparticles but it is a decreasing function of magnetic parameter. Also, it can be found that wall injection/suction parameter has no significant effect on rate of heat transfer.

Computational studies have been widely applied for the thermal evaluation of the nanomaterial thermal feature in different industrial and scientific issues. The squeezed flow and heat transfer features for Al₂O₃-water nanofluid among analogous plates are investigated using the GOHAM and its validity is verified by comparison with existing numerical results. Novel aspects of Brownian motion and thermal force were accounted in the simulation of nanomaterial flow within parallel plate. Analytical investigation has been done for diverse governing factors namely: the squeeze, chemical reaction factors and Eckert number. The obtained outcomes show that $|C_f|$ has direct relationship with absolute values of squeeze factor. Nu increases for large Eckert number and absolute values of squeeze number.

Lattice Boltzmann method (LBM) was used to simulate two-dimensional MHD Al₂O₃/water nanofluid flow and heat transfer in an enclosure with a semicircular wall and a triangular heating obstacle. The effects of nanoparticle volume fraction ($0\le \varphi \le 0.05$), Rayleigh number $(10^4\le Ra\le 10^6)$, Hartmann number $(0\le Ha\le 60)$ and heating obstacle position (Cases 1–7) on flow pattern, temperature distribution and rate of heat transfer were investigated. The results show that with the enhancing Rayleigh number, the increasing nanoparticle volume fraction and the reducing Hartmann number, an enhancement in the average Nusselt number and the heat transfer appeared. The effect of Ha on the average Nu increases by increasing the Ra. It can also be found that the action of changing the heating obstacle position on the convection heat transfer is more important than that on the conduction heat transfer. The higher obstacle position in Cases 6 and 7 leads to the small value of the average Nusselt number. Moreover, the effect of Ha on average Nu in Case 1 at $Ra=10^6$ is more significant than other cases because the flow pattern in Case 1 is changed as increasing Ha.

In this paper, the natural convection flow in a square cavity filled with nanofluid water-${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ with a hot circular cylinder in the center of the cavity is numerically analyzed. All the walls are in lower temperatures than the circular cylinder. The Navier–Stokes and energy equations in the primitive variable form are discretized and solved by the finite element method (FEM). The effect of the volume fraction, the radius of the circular cylinder, the temperature and Rayleigh number is considered on the average Nusselt number. For the calculation of the viscosity coefficient and thermal conductivity coefficient of water-${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ nanofluid, an experimental model is used which is the function of the volume fraction, temperature and nanoparticles diameter. This model is compared to the Brinkman model for viscosity and Maxwell model for thermal conductivity which are only the functions of volume fraction and are used by many researchers. The results show the experimental model leads to different results in comparison with the Brinkman model and Maxwell model, and indicate that the rate of the heat transfer can increase or decrease with the increase in volume fraction and temperature.

The countless applications of nanofluids in the improvements of nanotechnology, thermal and physical analogies have attracted our attention to frame an unsteady mathematical model for bi-directional flow of a Newtonian nanofluid over a stretching sheet with the potencies of nonzero and zero mass fluxes. Mathematically, this newly presented analysis is more genuine, where the action of a prescribed heat source at a stretching surface is used to control the distribution of heat. Mathematical formulation is carried out using a novel two-phase nanofluid model. Dimensionless forms of governing equations are obtained with the help of a suitable set of variables. The transformed equations are then solved by using an innovative computational technique, namely, Keller–Box approach. Moreover, the convergence of the numerical solution has been discussed via grid-independence tactic. The results for reduced Nusselt and Sherwood numbers have been arranged in the form of a table with CPU run time. Graphical illustrations have been presented for concentration and temperature distributions. It is inspected that escalating amounts of heat distribution indices reduce the mass concentration and the temperature of the nanomaterial. Rate of heat transference is noticed approximately 228.62% higher, while rate of mass transference is observed approximately 16.79% lower when analysis is shifted to zero mass flux environment from nonzero normal mass flux environment.

The impact of various sizes and positions of the heater in a nanofluid-saturated porous lid-driven chamber with a uniform Lorentz force is studied numerically. In this investigation, three different lengths of heater with higher temperature at six different locations along the left sidewall of the cavity are considered. Lower temperature is maintained at the right sidewall. Further, lower and moving upper horizontal walls and the rest of left wall are supposed to be thermally insulated. Based on the finite volume method, the system of nondimensional governing equations is solved by SIMPLE algorithm. The results conclude that the average Nusselt number is reduced with the enhancement of Richardson and Hartmann numbers. When the heater length is reduced from bottom to top, the heat transfer rate is increased for all the considered Richardson, Darcy and Hartmann numbers. In the lower permeability of the porous medium, the effect of solid volume fraction of nanofluid is more vulnerable. In the case of nanofluid, the steady state is reached quickly than the pure fluid.

This communication is to analyze the Marangoni convection MHD flow of nanofluid. Marangoni convection is very useful physical phenomena in presence of microgravity conditions which is generated by gradient of surface tension at interface. We have also studied the swimming of migratory gyrotactic microorganisms in nanofluid. Flow is due to rotation of disk. Heat and mass transfer equations are examined in detail in the presence of heat source sink and Joule heating. Nonlinear mixed convection effect is inserted in momentum equation. Appropriate transformations are applied to find system of equation. HAM technique is used for convergence of equations. Radial and axial velocities, concentration, temperature, motile microorganism profile, Nusselt number and Sherwood number are sketched against important parameters. Marangoni ratio parameter and Marangoni number are increasing functions of axial and radial velocities. Temperature rises for Marangoni number and heat source sink parameter. Activation energy and chemical reaction rate parameter have opposite impact on concentration profile. Motile density profile decays via Peclet number and Schmidt number. Magnitude of Nusselt number enhances via Marangoni ratio parameter.

Motivated by the significant role of nanofluid in pollution cleaning and energy recovery, we decided to explore the unsteady three-dimensional rotating flow of nanofluid driven by the movement of a flat surface with the potencies of prescribed heat distributions. The modeling of the physical model is completed with the help of Buongiorno nanofluid model. Suitable arrangement of similarity variables is implemented to transform the model equations into strongly nonlinear ordinary differential equations. Numerical inspection of the model is made by employing Keller–Box algorithm. Influences of involved parameters on the distributions of heat and mass are discussed graphically, while the potencies of influential parameters on reduced Nusselt and reduced Sherwood numbers are physically discussed through tabular arrangements. It is deduced that increasing the values of Prandtl factor and heat controlling indices diminishes the temperature and concentration distributions, whereas intensification in the amount of rotation factor enhances the temperature as well as concentration distribution. Moreover, negative trends in the amounts of reduced Nusselt and Sherwood numbers are achieved with the escalations in the values of rotation and thermophoresis factors, whereas opposite trend is achieved with the intensification in the choice of Prandtl factor.

The nanofluids are a recent challenging task in a nanotechnology field used in heat transfer enhancement for base fluids. The major purpose of this research is to examine the influences of Hall current on the non-Newtonian power-law nanofluid on an exponentially extending surface. Implementation in the Cattaneo–Christov heat flux and the free stream is performed to analyze the thermal relaxation features. Entropy generation evaluation and Bejan number during the convection flow are investigated. The Runge–Kutta–Fehlberg method is employed to resolve the transformed governing nonlinear equations. The impacts of the key physical factors on the profiles of primary and secondary velocities, temperature and entropy generation are discussed across the graphs. The local skin-friction coefficients, Nusselt and Sherwood numbers are demonstrated in a tabular form under the impacts of key physical parameters. Two different types of power-law indicators including pseudoplastic fluid $(n=0.7)$ and dilatant fluid $(n=1.2)$ are conducted. The results indicated that the flow speed decreases at dilatant fluid compared to pseudoplastic fluid due to higher viscosity. Increasing Hall current parameter powers the axial and secondary velocity profiles. Thermophoresis parameter powers the profiles of the temperature, nanoparticle volume fraction and local entropy generation. The dilatant fluid $(n=1.2)$ gives higher values of $C_{fx},C_{fz},{\mathrm{\text{Nu}}}_x$ and ${\mathrm{\text{Sh}}}_x$ compared to the pseudoplastic fluid $(n=0.7)$.

This paper contains natural convection of Ag–MgO/water micropolar hybrid nanofluid in a hollow hot square enclosure equipped by four cold obstacles on the walls. The simulations were performed by the lattice Boltzmann method (LBM). The influences of Rayleigh number and volume fraction of nanoparticle on the fluid flow and heat transfer performance were studied. Moreover, the effects of some geometric parameters, such as cold obstacle height and aspect ratio, were also considered in this study. The results showed that when the aspect ratio is not large ($\mathrm{\text{AR}}=0.2$ or 0.4), at low Rayleigh number (10³), the two secondary vortices are established in each main vortex and this kind of secondary vortex does not form at high Rayleigh number (10⁶). However, at $\mathrm{\text{Ra}}=10^6$, these secondary vortices occur again in the middle two vortices at $\mathrm{\text{AR}}=0.6$, which is similar to that at $\mathrm{\text{Ra}}=10^3$. At $\mathrm{\text{AR}}=0.2$, the critical Rayleigh number, when the dominated mechanism of heat transfer changes from conduction to convection, is 10⁴. However, the critical Rayleigh number becomes 10⁵ at $\mathrm{\text{AR}}=0.4$ or 0.6. When the cold obstacle height increases, the shape of the vortices inside the enclosure changes due to the different spaces. Besides, at $\mathrm{\text{Ra}}=10^6$, for different cold obstacle heights, the location of the thermal plume is different, owing to the different shapes of vortices. Accordingly, the average Nusselt number increases by increment of the Rayleigh number, nanoparticle volume fraction, cold obstacle height and aspect ratio.

Using an inner complex blockage within a square cavity is spreading massively for the cooling process. This study adopts the time-fractional derivative of the incompressible smoothed particle hydrodynamics (ISPH) method for studying the magnetic field, diffusion-thermo, and thermo-diffusion impacts on the double diffusion of a nanofluid in a porous annulus between a square cavity and an astroid shape. The alterations of the pertinent parameters, fractional derivative order $\alpha$ between 0.9 and 1, dimensionless time parameter $\tau$ between 0 and 0.6, the radius of an astroid $R_a$ between 0.1 and 0.45, solid volume fraction $\varphi$ between 0 and 0.06, Hartman parameter Ha between 0 and 100, Darcy parameter Da between $10^{-2}$ and $10^{-5}$, and Soret number Sr between 0.1 and 2 supplemented by Dufour number Du between 0.6 and 0.03 on the velocity field, temperature, concentration, and mean of Nusselt and Sherwood numbers are discussed. The main findings of the ISPH numerical simulations showed that a decrease in a fractional derivative order $\alpha$ delivers the sooner steady-state of the double diffusion which suppresses the performed calculations. The velocity field’s maximum powers by 19.23% as $R_a$ increases from 0.1 to 0.45 and it decreases by 16.67%, 28.89%, and 97.99% as $\varphi$ powers from 0 to 0.06, Ha powers from 0 to 100, and Da decreases from 10${}^{-2}$ to 10${}^{-5}$, respectively. The outlines of $\overline{\mathrm{\text{Nu}}}$ and $\overline{\mathrm{\text{Sh}}}$ are increasing as $R_a$ and $\varphi$ are increased. A growth in Sr supplemented by a reduction in Du is diminishing the distributed concentration and nanofluid velocity within an annulus.

This work discusses the dual diffusion of a sloshing wavy rod in a nanofluid-filled cavity. The top zone of a cavity is suspended by a porous medium. The boundary treatment in the ISPH method employs a kernel renormalization function. The wavy rod sloshes by an excitation frequency $x=asin(\omega t)$ and it carries $T_h$ and $C_h$. The rigid cavity walls are fixed, adiabatic (horizontal walls), and $T_c$ and $C_c$ (vertical walls). The measurements of pertinent parameters are the Soret number ($0\le$ Sr $\le 2$), nanoparticles parameter ($0\le \varphi \le 0.1$), Rayleigh number (${10}^3\le$ Ra $\le {10}^6$), sinusoidal function ($0.1\le \lambda \le 1$), Dufour number ($0\le$ Du $\le 1.5$), a slope angle of a magnetic field ($0^{\circ }\le \gamma \le 90^{\circ }$), Hartmann number ($10\le \text{Ha}\le 50$), and Darcy parameter ($10^{-2}\le$ Da $\le 10^{-5}$). The performed simulations revealed that the nanofluid flow is accelerated by the Sort number, the sloshing of the rod, and the sinusoidal wavy of the rod. Besides, the dual convection is enhanced by the sinusoidal wavy function and the sloshing of the rod. There is almost no nanofluid flow in a top porous zone of a cavity when Da $\le {10}^{-4}$.

This study describes the Casson (a non-Newtonian fluid) nanofluid bioconvection flow across a spinning disc in the presence of gyrotactic microorganisms, many slips and thermal radiation. Also, the flow is considered as a reversible flow. The esterification process is taken into account. Using the proper variables, a system of extremely nonlinear PDEs is converted into a system of ODEs. To arrive to the solution of such equations, a numerical approach is used. Using the bvp4c approach, nonlinear flow equations can be numerically solved. Investigated are the effects of different numbers on the thermal field, volumetric concentration of nanoparticles and microbiological field. The key characteristics of the parameters in relation to the profiles of the velocity, temperature, concentration and microorganisms are graphically assessed with appropriate physical effects. A graphical explanation is provided for the wall shear stress, local Nusselt number, local Sherwood number and local motile density number. Rate of motile density number shows a prominent difference between reversible and irreversible flows for Brownian motion and Peclet number. The results of the theoretical simulations have dynamic applications in the fields of biotechnology and thermal engineering.

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.

The unsteady flow over a continuously shrinking sheet with wall mass suction in a nanofluid is numerically studied. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations by using similarity transformation. The resulting similarity equations are then solved by the shooting method for three types of nanofluid: copper-water, alumina-water and titania-water to investigate the effect of nanoparticle volume fraction parameter ɸ to the flow in nanofluid. The skin friction coefficient and velocity profiles are presented and results show that dual solutions exist for a certain range of unsteadiness parameter A. It is also found that the nanoparticle volume fraction parameter ɸ and types of nanofluid play an important role to significantly determine the flow behaviour.