Search Results (9)

This research delves into the intricacies of a two-dimensional, steady flow of a ferrofluid within a porous medium, where the thermal conductivity is subject to temperature variations. The study encompasses the influence of magnetic dipoles, radiation, Brownian motion, and thermophoresis phenomena as they interact with a stretching sheet. A novel aspect of this investigation is the detailed analysis of Brownian and thermophoresis effects on nanoparticles while considering Nield’s boundary conditions. The study involves the transformation of flow equations into ordinary differential equations through standard similarity transformations, unraveling the governing equations using the BVP4C method. The outcomes are presented graphically, providing a comprehensive assessment of the factors impacting the fluid properties, including velocity, temperature, and concentration. Notably, this study reveals that an increase in the ferrofluid parameter leads to elevated temperature profiles while causing a decrease in velocity. Furthermore, an increase in the viscosity parameter is associated with a reduction in velocity. Some technological applications of the problem include magnetically controlled actuation and drug targeting. Full article

In the present study, the magnetohydrodynamics (MHD) bio-convective flow and heat transfer of nanofluid, due to the swimming of the gyrotactic micro-organisms over a curved stretched sheet, is examined. In addition, thermophoresis and Brownian motion behaviors are also investigated by assuming slip conditions at the boundary. A non-linear system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). For convergent solutions, the obtained ODE system is solved by the use of the BVP4C routine integrated MATLAB package. In addition, the impacts of different influential parameters on motile micro-organisms, temperature, velocity, and concentration profiles are deliberated. The velocity field is observed to be reduced when the slip parameter increases. As the main results, it is demonstrated that the distribution of motile microorganisms against the curvature parameter decreases significantly. Similarly, it is found that the nanofluid parameters (i.e., Brownian motion and thermophoresis parameters) and the Peclet number reduce the motile micro-organisms’ number. On the other hand, it is evidenced that the motile micro-organisms’ distribution can be improved with an increase in bio-convective Schmidt number. Full article

This study aimed to investigate the consequences of the Darcy–Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno’s model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier–Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others. Full article

This numerical study aims to interpret the impact of non-linear thermal radiation on magnetohydrodynamic (MHD) Darcy-Forchheimer Casson-Water/Glycerine nanofluid flow due to a rotating disk. Both the single walled, as well as multi walled, Carbon nanotubes (CNT) are invoked. The nanomaterial, thus formulated, is assumed to be more conductive as compared to the simple fluid. The properties of effective carbon nanotubes are specified to tackle the onward governing equations. The boundary layer formulations are considered. The base fluid is assumed to be non-Newtonian. The numerical analysis is carried out by invoking the numerical Runge Kutta 45 (RK45) method based on the shooting technique. The outcomes have been plotted graphically for the three major profiles, namely, the radial velocity profile, the tangential velocity profile, and temperature profile. For skin friction and Nusselt number, the numerical data are plotted graphically. Major outcomes indicate that the enhanced Forchheimer number results in a decline in radial velocity. Higher the porosity parameter, the stronger the resistance offered by the medium to the fluid flow and consequent result is seen as a decline in velocity. The Forchheimer number, permeability parameter, and porosity parameter decrease the tangential velocity field. The convective boundary results in enhancement of temperature facing the disk surface as compared to the ambient part. Skin-friction for larger values of Forchheimer number is found to be increasing. Sufficient literature is provided in the introduction part of the manuscript to justify the novelty of the present work. The research greatly impacts in industrial applications of the nanofluids, especially in geophysical and geothermal systems, storage devices, aerospace engineering, and many others. Full article

The aim of this research is mainly concerned with the numerical examination of Darcy-Forchheimer relation in convective magnetohydrodynamic nanofluid flow bounded by non-linear stretching sheet. A visco-elastic and strictly incompressible liquid saturates the designated porous medium under the direct influence of the Darcy-Forchheimer model and convective boundary. The magnetic effect is taken uniformly normal to the flow direction. However, the model is bounded to a tiny magnetic Reynolds number for practical applications. Boundary layer formulations are taken into consideration. The so-formulated leading problems are converted into highly nonlinear ordinary problems using effectively modified transformations. The numerical scheme is applied to solve the governing problems. The outcomes stipulate that thermal layer receives significant modification in the incremental direction for augmented values of thermal radiation parameter R_d. Elevation in thermal Biot number γ₁ apparently results a significant rise in thermal layer and associated boundary layer thickness. The solute Biot number is found to be an enhancing factor the concentration profile. Besides the three main profiles, the contour and density graphs are sketched for both the linear and non-linear cases. Furthermore, skin friction jumps for larger porosity and larger Forchheimer number. Both the heat and mass flux numbers receive a reduction for augmented values of the Forchheimer number. Heat flux enhances, while mass flux reduces, the strong effect of thermal Biot number. The considered problem could be helpful in any several industrial and engineering procedures, such as rolling, polymeric extrusion, continuously stretching done in plastic thin films, crystal growth, fiber production, and metallic extrusion, etc. Full article

The current framework tackles the buoyancy flow via a slender revolution bodies comprising Molybdenum-Disulfide Graphene Oxide generalized hybrid nanofluid embedded in a porous medium. The impact of radiation is also provoked. The outcomes are presented in this analysis to examine the behavior of hybrid nanofluid flow (HNANF) through the cone, the paraboloid, and the cylinder-shaped bodies. The opposing flow (OPPF) as well as the assisting flow (ASSF) is discussed. The leading flow equations of generalized hybrid nanoliquid are worked out numerically by utilizing bvp4c solver. This sort of the problem may meet in the automatic industries connected to geothermal and geophysical applications where the sheet heat transport occurs. The impacts of engaging controlled parameters of the transmuted system on the drag force and the velocity profile are presented through the graphs and tables. The achieved outcomes suggest that the velocity upsurges due to the dimensionless radius of the slender body parameter in case of the assisting flow and declines in the opposing flow. Additionally, an increment is observed owing to the shaped bodies as well as in type A nanofluid and type B hybrid nanofluid. Full article

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport equations are altered into dimensionless self-similar partial differential equations (PDEs) through suitable transformations. The reduced momentum and energy equations are then worked out numerically by employing a new hybrid method called the Gear-Generalized Differential Quadrature Method (GGDQM). The obtained numerical results are incorporated in the calculation of the Bejan number and dimensionless entropy generation. Quantities of physical interest, like velocity, temperature, shear stress and heat transfer rate, are illustrated graphically as well as in tabular form. Impacts of involved parameters are examined and discussed thoroughly in this investigation. Exact and GGDQM solutions are compared for special cases of initial unsteady flow and final steady state flow. Furthermore, a good harmony is observed between the results of GGDQM and those given previously by the Spectral Relaxation Method (SRM), Spectral Quasilinearization Method (SQLM) and Spectral Perturbation Method (SPM). Full article

The primary objective of the present work is to study the effects of heat transfer and entropy production in a nanofluid flow over a curved surface. The influences of Lorentz force and magnetic heating caused by the applied uniform magnetic field and energy dissipation by virtue of frictional heating are considered in the problem formulation. The effects of variable thermal conductivity are also encountered in the present model. The dimensional governing equations are reduced to dimensionless form by introducing the similarity transformations. The dimensionless equations are solved numerically by using the Chebyshev–Gauss–Lobatto spectral method (CGLSM). The rate of increase/increase in the local Nusselt number and skin friction coefficient are estimated by using a linear regression model. The expression for dimensionless entropy production is computed by employing the solutions obtained from dimensionless momentum and energy equations. Various graphs are plotted in order to examine the effects of physical flow parameters on velocity, temperature, and entropy production. The increase in skin friction coefficient with magnetic parameter is high for nanofluid containing copper nanoparticles as compared to silver nanoparticles. The analysis reveals that velocity, temperature, and entropy generation decrease with the rising value of dimensionless radius of curvature. Comparative analysis also reveals that the entropy generation during the flow of nanofluid containing copper nanoparticles is greater than that of containing silver nanoparticles. Full article

The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the energy equation. Appropriate transformations are used to develop the self-similar equations from the governing equations of momentum and energy. The resulting self-similar equations are then solved by the Generalized Differential Quadrature Method (GDQM). For the validation and precision of the developed numerical solution, the resulting equations are also solved numerically using the Runge-Kutta-Fehlberg method (RKFM). An excellent agreement is found between the numerical results of the two methods. To examine the impacts of emerging physical parameters on velocity, temperature distribution and entropy generation, the numerical results are plotted against the various values of physical flow parameters and discussed physically in detail. Full article