Search Results (39)

The present study investigates heat transfer characteristics in the thermally developing region of a porous tube under the local thermal nonequilibrium (LTNE) model. The influence of magnetohydrodynamic (MHD) flow on an electrically conducting fluid flowing through a porous medium under a transverse magnetic field is examined. Under the LTNE framework, two separate energy equations are employed to describe the temperature fields of the fluid and solid phases. The coupled governing equations are solved numerically using the Keller-box method. The results indicate that increasing the interphase heat transfer parameter strengthens thermal coupling between the fluid and solid phases, thereby reducing temperature differences and promoting local thermal equilibrium. In contrast, an increase in the Prandtl number reduces thermal diffusion, leading to larger temperature gradients and greater disparity between the two phases. Furthermore, the magnetic field suppresses both the velocity and temperature distributions through the Lorentz force. An increase in permeability reduces the velocity profiles due to the combined effects of the MHD and Prandtl numbers while increasing the temperature profiles. Increasing the interphase heat transfer rate drives the system from the LTNE to the LTE phase. The study confirms that LTNE effects play a significant role in thermal transfer processes in porous media and are relevant for various industrial heat transfer applications. Full article

In the field of heat and mass transfer applications, non-Newtonian fluids are potentially considered to play a very important role. This study examines the magnetohydrodynamic (MHD) bioconvective Eyring–Powell fluid flow on a permeable cone and plate, considering the viscous dissipation (0.3 ≤ E_c ≤0.7), the uniform heat source/sink (−0.1 ≤ Q₀ ≤ 0.1), and the activation energy (−1 ≤ E₁ ≤ 1). The primary focus of this study is to examine how MHD and porosity impact heat and mass transfer in a fluid with microorganisms. A similarity transformation (ST) changes the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs). The Keller Box (KB) finite difference method solves these equations. Our findings demonstrate that adding MHD (0.5 ≤ M ≤ 0.9) and porosity (0.3 ≤ Γ ≤ 0.7) effects improves microbial diffusion, boosting the rates of mass and heat transfer. Our comparison of our findings to prior studies shows that they are reliable. Full article

Non-Newtonian fluids play a crucial role in applications involving heat transfer and mass transfer. The inclusion of nanoparticles in these fluids improves the efficiency of heat and mass transfer processes. This study employs a numerical solution approach to examine the flow of non-Newtonian hybrid nanofluids over a plumb cone/plate surface, considering the effects of magnetohydrodynamics (MHD) and thermal radiation. Additionally, we investigate how heat and mass transfer are affected by a fluid containing microorganisms. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation to simplify this complex system. We then use the Keller-box finite-difference method to solve these equations. Along with a table presenting the results for skin friction, Nusselt number, Sherwood number, and microbe density number, we present graphical representations of velocity, temperature, concentration, and microorganism diffusion behavior. Our results indicate that the addition of MHD and thermal radiation improves the diffusion of microorganisms, thereby enhancing the rates of heat and mass transfer. Through a comparative analysis with prior research, we demonstrate the reliability of our conclusions. Full article

Numerical and physical simulations of the magnetohydrodynamic mixed convective flow of electrically conducting fluid along avertical magnetized and symmetrically heated plate with slip velocity and thermal slip effects have been performed. The novelty of the present work is to evaluate heat transfer and magnetic flux along the symmetrically magnetized plate with thermal and velocity slip effects. For a smooth algorithm and integration, the linked partial differential equations of the existing fluid flow system are converted into coupled nonlinear ordinary differential equations with specified streaming features and similarity components. By employing the Keller Box strategy, the modified ordinary differential equations (ODEs) are again translated in a suitable format for numerical results. The MATLAB software is used to compute the numerical results, which are then displayed in graphical and tabular form. The influence of several governing parameters on velocity, temperature distribution and magnetic fields in addition to the friction quantity, magnetic flux and heat transfer quantity has been explored. Computational evaluation is performed along the symmetrically heated plate to evaluate the velocity, magnetic field, and temperature together with their gradients. The selection of the magnetic force element, the buoyancy factor $0<\xi <\infty$ , and the Prandtl parameter range $0.1\le \mathrm{Pr}\le 7.0$ were used to set the impacts of magnetic energy and diffusion, respectively. In the domains of magnetic resonance imaging (MRI), artificial heart wolves, interior heart cavities, and nanoburning systems, the present thermodynamic and magnetohydrodynamic issuesare significant. Full article

Nanofluids are engineered colloidal suspensions of nanoparticles in the base fluids. At very low particle concentration, nanofluids have a much higher and strongly temperature-dependent thermal conductivity, which enables them to enhance the performance of machining applications such as the cooling and lubrication of the cutting zone during any machining process, the vehicle’s braking system, enhanced oil recovery (EOR), engine oil, and the drilling process of crude oil. In the current work, the density is assumed as an exponential function of temperature due to larger temperature differences. The main focus of this mechanism is the variable density effects on heat and mass characteristics of nanoparticles across the stretching porous sheet with thermophoresis and Brownian motion to reduce excessive heating in high-temperature systems. This is the first temperature-dependent density problem of nanofluid across the stretching surface. The coupled partial differential equations (PDEs) of the present nanofluid mechanism are changed into nonlinear coupled ordinary differential equations (ODEs) with defined stream functions and similarity variables for smooth algorithm and integration. The changed ODEs are again converted in a similar form for numerical outcomes by applying the Keller Box approach. The numerical outcomes are deduced in graphs and tabular form with the help of the MATLAB (R2013a created by MathWorks, Natick, MA, USA) program. In this phenomenon, the velocity, temperature, and concentration profile, along with their slopes, have been plotted for various parameters pertaining to the current issue. The range of parameters has been selected according to the Prandtl number $0.07\le Pr\le 70.0$ and buoyancy parameter $0<\lambda <\infty$, respectively. The novelty of the current work is its use of nanoparticle fraction along the porous stretching sheet with temperature-dependent density effects for the improvement of lubrication and cooling for any machining process and to reduce friction between tool and work piece in the cutting zone by using nanofluid. Moreover, nanoparticles can also be adsorbed on the oil/water surface, which alters the oil/water interfacial tension, resulting in the formation of emulsions. Full article

This numerical analysis aims to observe and analyze the combined convection characteristics of the micropolar tri-hybrid nano-liquid that moves around a cylindrical object, and, in addition, to compare its thermal behavior to that of hybrid and mono nano-fluids. For this purpose, the problem is modeled by developing the Tiwari and Das models, then the governing model is converted into dimensionless expressions, and finally, the problem is solved using the Keller box approximation. The current findings are compared with previously published results to show that the present method is sufficiently accurate for physical and engineering applications. By examining and analyzing the extent to which skin friction, the Nusselt number, velocity, angular velocity, and temperature are affected by some critical factors, the following points are revealed: A greater value of the micropolar and magnetic factors can result in curtailing the heat transmission rate, velocity, and angular velocity. Higher values of the mixed convection factor can contribute to a better rate of energy transfer and can grant the micropolar tri-hybrid nano-liquid a higher velocity. Regardless of the influencing factors, the maximum value of all considered physical groups is achieved by using ternary hybrid nano-liquids. Full article

The collective effect of thermal and mass convection along with the significance of thermal radiation, heat source/sink, and magneto-nanofluid are considered. A bi-directional stretching device is used to generate the symmetry of the flowing structure. Nonlinear behavior of thermal radiation is considered here. The magnetic field is considered non-uniform and vertically upward. Significances of pedesis motion and Ludwig–Soret are also revealed in an innovative way with heat source/sink effects. The concept of symmetry is used to transmute the transport equations from PDE type to nonlinear ODE type. We solved the transformed setup numerically by adopting Keller-box method criteria with the targeted accuracy rate. Graphical interpretations are explored with code verification. It is important to conclude that friction coefficients decline for incremental values of stretching parameter $\left(0.1\le \mathsf{\alpha }\le 0.9\right)$, magnetic field $\left(0.3\le M\le 0.9\right),$ and unsteady parameter $\left(0.2\le \mathsf{\Lambda }\le 0.9\right)$ along with the bidirectional velocity components, and the rate of heat transmission rises with temperature ratio $\left(1.3\le \mathsf{\Gamma }\le 1.7\right)$ and temperature Biot number $\left(0.3\le B{i}_T\le 0.9\right)$ amplification. Moreso, the rate of mass transfer is enhanced with growing values of pedesis motion $\left(0.2\le N_b\le 0.6\right)$, unsteady parameter and concentration Biot number $\left(0.3\le B{i}_C\le 0.9\right)$ with opposite effect when the Ludwig–Soret parameter $\left(0.3\le N_t\le 0.6\right)$ is boosted. Full article

Nanofluids receive recognition from researchers and scientists because of their high thermal transfer rates. They have impactful industrial and technological modules in daily activities. In recent times, the heat transfer rate has been strengthened even more by a certain type of nanofluid known as “carbon nanotubes”. The water-based magnetohydrodynamic flow with the nanoparticles MWCNT and SWCNT over an axially rotating stretching disk is highlighted in this article. In addition, the perspectives of viscous dissipation and MHD were taken into consideration. In order to formulate the physical problem, Xue’s model is considered with the thermophysical properties and characteristics of carbon nanofluid. The current modeled system of partial differential equations is transformed into an ordinary differential equation system by the suggesting of the best similarity technique. Later, the transformed system of ordinary differential equations is solved numerically by using the Keller box method and the shooting method. Figures and charts are used to study and elaborate the physical behavior of the key subjective flow field parameters. The saturation in the base fluid is considered in both kinds of carbon nanotubes, the single-wall (SWCNTs) and the multiwall (MWCNTs). It is noted that the heat transfer mechanism shows some delaying behavior due to the increase in the Eckert number and the volume fraction elevation values. For the larger volume fraction values and the magnetic parameter, the skin friction increases. In addition, while the temperature profile increases with the Biot numbers, it falls for the increasing values of the Prandtl number. Furthermore, it is noted that the irreversibility of the thermal energy is influenced by the Biot number, temperature difference, Brinkmann number, and magnetic field, which all have dynamic effects on the entropy and the Bejan number. Full article

The heat transfer characteristics along the non-magnetized shapes have been performed in various previous studies numerically. Due to excessive heating, these mechanisms are less interesting in engineering and industrial processes. In the current analysis, the surface is magnetized, and the fluid is electrically conducting, which is responsible for reducing excessive heating along the surface. The main objective of the present work is to analyze convective heat transfer analysis of viscous fluid flow with thermal slip and thermal radiation effects along the vertical symmetric heated plate immersed in a porous medium numerically. The results are deduced for viscous flow along a magnetized heated surface. The theoretical mechanism of heat and magnetic intensity along a vertical surface is investigated for numerical analysis. The nonlinear-coupled partial differential equations (PDEs) for the above viscous fluid flow mechanism with the symmetry of the conditions normal to the surface are transformed and then converted into non-similar formulations by applying appropriate and well-known similarity transformations for integration and solutions. The final non-similar equations are numerically integrated by employing the Keller box method. The discretized algebraic equations are plotted graphically and numerically on the MATLAB R2013a software package. The main finding of the current analysis is to compute physical quantities such as velocity graph, magnetic field graph, and temperature plot along with their slopes, that is, skin friction, magnetic intensity, and heat transfer for different parameters included in the flow model. First, the velocity graph, magnetic field graph, and temperature graph are obtained, and then their slopes are analyzed numerically along the vertical magnetic surface. It is noticed that fluid velocity is increased at lower magnetic force, but minimum velocity is noticed at maximum magnetic force. It is worth mentioning that with the increase in magnetic force, the magnetic energy increases, which extracts the kinetic energy of the fluid and causes the above-said behavior. Furthermore, the current issues have significant implications for the polymer industries, glass fiber production, petroleum production, fiber spinning, plastic film production, polymer sheet extraction, heat exchangers, catalytic reactors, and the production of electronic devices. Full article

The heat transmission properties along the non-magnetized geometries have been numerically obtainedby various researchers. These mechanisms are less interesting in engineering and industrial processes because of excessive heating. According to current studies, the surface is magnetized and the fluid is electrically conductive, which helps to lessen excessive surface heating. The main objective of the current analysis is to numerically compute the temperature-dependent density effect on magnetohydrodynamic convective heat-transfer phenomena of electrical-conductive fluid flow along the vertical magnetized and heated plate placed in a thermally stratified medium. For the purpose of numerical analysis, the theoretical process governing heat and magnetic intensity along a vertical magnetic plate is examined. By using suitable and well-known similarity transformations for integration, the non-linear coupled PDEs for the aforementioned electrical-conductive fluid flow mechanism are changed and subsequently converted into non-similar formulation. The Keller Box method is used to numerically integrate the final non-similar equations. The MATLAB software program plots the transformed algebraic equations graphically and quantitatively. The behavior of the physical quantities such asvelocity graph, magnetic field graph, and temperature plot along with their slopes that arerate of skin friction, the rate of heat transfer, and the rate of magnetic intensity for different parameters included in the flow model. The novelty of the current work is to compute the magneto-thermo analysis of electrically conducting flow along the vertical symmetric heated plate. First, we secure the numerical solution for steady part and then these results are used to find skin friction, heat transfer, and magnetic intensity. In the current work, the fluid becomes electrically conducing due to a magnetized surface which insulates heat during the mechanism and reduces the excessive heating. The results are excellent and accurate because they are satisfied by its given boundary conditions. Additionally, the current problems have a big impact on the production of polymer materials, glass fiber, petroleum, plastic films, polymer sheets, heat exchangers, catalytic reactors, and electronic devices. Full article

The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties. Full article

The radiated flow of magnetized viscous fluid subject to the viscous dissipation phenomenon is numerically studied. The radiative phenomenon is addressed with nonlinear relations. Further, analysis is performed by using the slip effects and convective thermal flow constraints. The transformed problem is numerically evaluated using the Keller Box method. The physical parameter effects, such as the magnetic parameter for the velocity profile, Prandtl number, Brownian motion parameter and Biot number for the energy profile and Lewis number, and the thermophoresis parameter for the concentration profile are discussed. The obtained results suggest applications in enhancing the heat transfer phenomenon, thermal system, energy generation, heat transmission devices, power generation, chemical reactions, etc. Full article

The main theme of the present study is to analyze numerically the effects of the magnetic field on the hybrid nanofluid flow over a flat elastic surface. The effects of the thermal and velocity slips are also analyzed in view of the hybrid nanofluid flow. It is considered a combination of titanium oxide (TiO₂) and copper oxide (CuO) nanoparticles that are suspended in the incompressible and electrically conducting fluid (water). The behavior of the Brownian motion of the nanoparticles and the thermophoretic forces are contemplated in the physical and mathematical formulations. Moreover, the impact of the Joule heating and viscous dissipation are also discussed using the energy equation. The mathematical modeling is simulated with the help of similarity variables. The resulting equations are solved using the Keller–Box method with a combination of finite difference schemes (FDSs). Hybrid nanofluids provide significant advantages over the usual heat transfer fluids. Therefore, the use of nanofluids is beneficial to improve the thermophysical properties of the working fluid. All of the results are discussed for the various physical parameters involved in governing the flow. From the graphical results, it is found that the hybrid nanoparticles improve the concentration, temperature, and velocity profiles, as well as the thickness of the relevant boundary layer. The conjunction of a magnetic field and the velocity slip, strongly opposes the fluid motion. The boundary layer thickness and concentration profile are significantly reduced with the higher levels of the Schmidt number. Full article

In this work, the mixed convection flow of non-Newtonian Eyring–Powell fluid with the effects of temperature dependent viscosity (TDV) were studied together with the interaction of dust particles under the influence of Newtonian Heating (NH) boundary condition, which assume to move over a vertical stretching sheet. Alternatively, the dusty fluid model was categorized as a two-phase flow that consists of phases of fluid and dust. Through the use of similarity transformations, governing equations of fluid and dust phases are reduced into ordinary differential equations (ODE), then solved by efficient numerical Keller–box method. Numerical solution and asymptotic results for limiting cases will be presented to investigate how the flow develops at the leading edge and its end behaviour. Comparison with the published outputs in literature evidence verified the precision of the present results. Graphical diagrams presenting velocity and temperature profiles (fluid and dust) were conversed for different influential parameters. The effects of skin friction and heat transfer rate were also evaluated. The discovery indicates that the presence of the dust particles have an effect on the fluid motion, which led to a deceleration in the fluid transference. The present flow model can match to the single phase fluid cases if the fluid particle interaction parameter is ignored. The fluid velocity and temperature distributions are always higher than dust particles, besides, the opposite trend between both phases is noticed with $\beta$. Meanwhile, both phases share the similar trend in conjunction with the rest factors. Almost all of the temperature profiles are not showing a significant change, since the viscosity of fluid is high, which can be perceived in the figures. Furthermore, the present study extends some theoretical knowledge of two-phase flow. Full article

Current research proposes a model for assessing the flow properties and heat transmission from hybridized nanofluids to solar collectors (SCs). A theoretical investigation that was based on the application of alumina-water (Al₂O₃-H₂O) conventional nanofluid and copper/alumina-water (Cu-Al₂O₃/H₂O) hybrid nanofluid has been considered between two rotating plates in parabolic trough solar collector (PTSC). The Cattaneo–Christov model (CCM) for heat fluxing is used for the thermal boundary layer analysis. The impact of centripetal and Coriolis forces on the swirling flow has been considered. Adequate transformations are utilised for the conversion of the regulating partial differential equations (PDEs) into a group of dimensionless ordinary differential equations (ODEs). Dimensionless ODEs are then tackled by the Keller box method (KBM) in the MATLAB program. The basic concept of this study is to inspect the influences of change in substantial factors on velocities, temperature, and heat transmission rate for both Al₂O₃-H₂O mono nanofluid (MNF) and Cu-Al₂O₃/H₂O hybridized nanofluid (HBNF). The striking feature of the investigation is that the hybrid nanofluid Cu-Al₂O₃/H₂O has a less frictional force and an elevated heat transmission rate (RHT) as assessed with the traditional nanoliquid Al₂O₃-H₂O. Consequently, the rotating factor slows RHT on the surface. In this case study, HBNF is better than the mono NF as a thermal and electrical conductor. Full article