Search Results (39)

This study investigates the flow of a magnetohydrodynamic (MHD) Maxwell fluid over a stretching sheet using a Darcy-Forchheimer (DF) model. We employ numerical analysis with a copper (Cu) nanofluid suspended in water, considering Cattaneo–Christov heat flow, viscous dissipation, and joule heating. Nonlinear ordinary differential equations (ODEs) are solved using the bvp4c method in Matlab and we examine the normalized shear stress, temperature profile, and heat flux rate. Our findings reveal insights for practical applications, showing how parameters such as the relaxation Prandtl number, magnetic parameter, Eckert number parameter, and radiation parameter impact system behaviour. Full article

The physiological system loses thermal energy to nearby cells via the bloodstream. Such energy loss can result in sudden death, severe hypothermia, anemia, high or low blood pressure, and heart surgery. Gold and iron oxide nanoparticles are significant in cancer treatment. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. The present study provides a novel implementation of an intelligent numerical computing solver based on an MLP feed-forward backpropagation ANN with the Levenberg–Marquard algorithm to interpret the Cattaneo–Christov heat flux model and demonstrate the effect of entropy production and melting heat transfer on the ferrohydrodynamic flow of the Fe₃O₄-Au/blood Powell–Eyring hybrid nanofluid. Similarity transformation studies symmetry and simplifies PDEs to ODEs. The MATLAB program bvp4c is used to solve the nonlinear coupled ordinary differential equations. Graphs illustrate the impact of a wide range of physical factors on variables, including velocity, temperature, entropy generation, local skin friction coefficient, and heat transfer rate. The artificial neural network model engages in a process of data selection, network construction, training, and evaluation through the use of mean square error. The ferromagnetic parameter, porosity parameter, distance from origin to magnetic dipole, inertia coefficient, dimensionless Curie temperature ratio, fluid parameters, Eckert number, thermal radiation, heat source, thermal relaxation parameter, and latent heat of the fluid parameter are taken as input data, and the skin friction coefficient and heat transfer rate are taken as output data. A total of sixty data collections were used for the purpose of testing, certifying, and training the ANN model. From the results, it is found that the fluid temperature declines when the thermal relaxation parameter is improved. The latent heat of the fluid parameter impacts the entropy generation and Bejan number. There is a less significant impact on the heat transfer rate of the hybrid nanofluid over the sheet on the melting heat transfer parameter. Full article

This work examines the non-Newtonian Cassonnanofluid’s three-dimensional flow and heat and mass transmission properties over a Riga plate. The Buongiorno nanofluid model, which is included in the present model, includes thermo-migration and random movement of nanoparticles. It also took into account the Cattaneo–Christov double flux processes in the mass and heat equations. The non-Newtonian Casson fluid model and the boundary layer approximation are included in the modeling of nonlinear partial differential systems. The homotopy technique was used to analytically solve the system’s governing equations. To examine the impact of dimensionless parameters on velocities, concentrations, temperatures, local Nusselt number, skin friction, and local Sherwood number, a parametric analysis was carried out. The velocity profile is augmented in this study as the size of the modified Hartmann number increases. The greater thermal radiative enhances the heat transport rate. When the mass relaxation parameter is used, the mass flux values start to decrease. Full article

The movement of microorganism cells in fluid influences various biotic processes, including septicity and marine life ecology. Many organic and medicinal applications need to look into the insight of mechanism in nanofluids containing a microbial suspension. The current paper concerns the bioconvection of a ternary hybrid nanofluid (Al₂O₃-Cu-CNT/water) flow containing motile gyrotactic microorganisms toward three different geometries (a flat plate, a wedge, and a cone) in the occurrence of natural convection, radiation, and heat source/sink. The Cattaneo–Christov theory is employed to develop the model. The equations are solved by using the “bvp4c function in MATLAB”. The influence of the crucial significant factors on the motile microorganisms’ density, velocity, temperature, nanoparticles’ concentration, microbe density gradient, and transmission rates of heat and mass is discussed. The results depict that the heat transmission rate is highest for the flow toward the cone, whereas the mass transmission rate and microbe density gradient are highest for the flow toward the wedge. In addition, the higher estimates of the thermal relaxation parameter corresponding to the Cattaneo–Christov theory act to enhance the rate of heat transmission. The results of the current study will be useful to many microbial-enhanced oil recovery systems, carriage processes, architectural design systems, medicinal fields that utilize nanofluids, and so on. Full article

The purpose of this work is to offer a unique theoretical ternary nanofluid (graphene/tungsten oxide/zirconium oxide) framework for better heat transfer. This model describes how to create better heat conduction than a hybrid nanofluid. Three different nanostructures with different chemical and physical bonds are suspended in water to create the ternary nanofluid (graphene/tungsten oxide/zirconium oxide). Toxic substances are broken down, the air is purified, and other devices are cooled thanks to the synergy of these nanoparticles. The properties of ternary nanofluids are discussed in this article, including their thermal conductivity, specific heat capacitance, viscosity, and density. In addition, heat transport phenomena are explained by the Cattaneo–Christov (CC) heat flow theory. In the modeling of the physical phenomena under investigation, the impacts of thermal nonlinear radiation and velocity slip are considered. By using the right transformations, flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters’ impacts on the velocity and temperature fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using a numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the performance of ternary nanofluid phase heat transfer is improved compared to dusty phase performance. Furthermore, the magnetic parameter and the velocity slip parameter both experience a slowing-down effect of their respective velocities. Full article

In this work, we analyzed the hybrid nanofluid (Ag+CuO+kerosene oil) flow past a bidirectionally extendable surface in the presence of a variable magnetic field. The hybrid nanofluid flow considered is electrically conductive and steady. For the simulation of the problem, the Cattaneo–Christov double-diffusion (CCDD) model was considered, which generalizes Fourier’s and Fick’s laws. The impact of the Hall current produced was taken into account. The physical problem was transformed into a mathematical form with the help of suitable transformations to reduce the complexity of the problem. The transformed system of coupled ordinary differential equations (ODEs) was solved with the semi-analytical method. The results are plotted in comparison with the ordinary nanofluid (CuO+kerosene oil) and hybrid nanofluid (Ag+CuO+kerosene oil). The impact of various parameters $(Pr,Sc,{\gamma }_0,m,M,Nb,Nt,{ϵ}_1,{ϵ}_2)$ on the state variables is described. The velocity gradient under the impact of the mass flux and magnetic parameter shows a decreasing behavior, while the Hall parameter and the stretching ratio show an increasing behavior. Moreover, the skin friction, rate of heat, and mass transfer are numerically displayed through tables. In this work, we found that the thermal and concentration relaxation coefficients showed a decreasing behavior for their increasing trends. For the validation of the implemented technique, the squared residuals are computed in Table 2, which shows that the increasing number of iterations decreases the squared residual error. The results show that Ag+CuO+kerosene oil has good performance in the reduction of the heat transfer rate. Full article

Due to their capacity to create better thermal conductivity than standard nanofluids, hybrid nano-fluids and modified nanofluids have notable applications in aerospace, energy materials, thermal sensors, antifouling, etc. This study aims to the modified and hybrid nanofluid flow with the Carreau fluid over a sloped shrinking sheet. The Cattaneo–Christov heat flux also takes into account. To determine the thermal efficiency of the heat, three different kinds of nanomaterials, copper oxide ($CuO)$, copper $\left(Cu\right),$ and alumina ($A{l}_2{O}_3$), are used. The similarity alteration commutes the insolubility of the model into ODEs. The conclusions are attained by program writing in MATLAB software and dealing with them through the bvp4c solver with the shooting method. The skin-friction amount decreases with the inclined sheet and local Weissenberg parameter for both modified and hybrid nanofluid. An upsurge thermal relaxation parameter declines the skin-friction coefficient for modified nanofluid flow and increases the skin-friction coefficient for hybrid nanofluid flow. The heat transfer rate is upsurged with modified and hybrid nanofluid for thermal relaxation parameter. Furthermore, the presentation includes the development of skin friction coefficient and Nusselt number values for specific parameters. Through benchmarking, numerical solutions are validated using certain limiting situations that were previously published findings, and typically solid correlation is shown. Full article

The objective of this paper is to investigate the 3D non-linearly thermally radiated flow of a Jeffrey nanofluid towards a stretchy surface with the Cattaneo–Christov heat flux (CCHF) model in the presence of a convective boundary condition.The Homotopy Analysis Method (HAM) is used to solve the ordinary differential equation that is obtained by reforming the governing equation using suitable transformations. The equations obtained from HAM are plotted graphically for different parameters. In addition, the skin-friction coefficient, local Nusselt number, and Sherwood number for various parameters are calculated and discussed. The velocity profile along the x- and y-directions decrease with a raise in the ratio of relaxation to retardation times. The concentration and temperature profile rises while magnifying the ratio of relaxation to retardation times. While raising the ratio parameter, the x-direction velocity, temperature, and concentration profile diminishes, whereas the y-direction velocity profile magnifies. Magnifying the Deborah number results in a rise in the velocity profile along the x- and y-directions, and a decline in the temperature and concentration profile. Full article

In this study, we investigated a radiative chemically reactive Casson fluid above a cone, plate, and wedge with gyrotactic microorganisms subjected to the Cattaneo–Christov heat flux model. Newton’s method and the Runge–Kutta methods were employed to solve the physical problem, and a graphical representation of the numerous impacts of non-dimensional parameters on temperature, velocity, and concentration was created. In addition, we also compared recently published solutions with our current solution, which showed good agreement. From this investigation, we concluded that the motile organisms’ momentum, temperature, and concentration density were non-uniform in nature. Here, for engineering importance, we also present the mass transfer and thermal transfer rate over the cone, wedge, and plate cases in a tabular form. We concluded that the mass and heat transfer rate was larger over the cone when compared to the same case over a plate or wedge. The results also highlighted that the local Nusselt and Sherwood numbers and the mass density of the microorganisms depreciated as the Casson fluid parameter decreased. In summary, we concluded that the gyrotactic microorganisms played a role in enhancing the local Sherwood number. Full article

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. The bioconvective motile microorganisms and nanoparticles are taken into consideration. The system of equations for the current flow problems is converted from a highly non-linear partial system to an ordinary system through an appropriate transformation. The effect of the obtained variables on velocity, temperature, concentration and motile microorganism distributions are elaborated through the plots in detail. Further, the velocity distribution is enhanced for a greater Deborah number value and it is reduced for a higher Reynolds number for the two cases of pseudoplastic and dilatant flows. Microorganism distribution decreases with the increased magnitude of Peclet number, Bioconvection Lewis number and microorganism concentration difference number. Two types of graphical outputs are presented for the Sutterby fluid parameter (β = −2.5, β = 2.5). Finally, the validation of the present model is achieved with the previously available literature. Full article

In our research work, we have developed a model describing the characteristics of the bio-convection and moving microorganisms in the flows of a magnetized generalized Burgers’ nanoliquid with Fourier’s and Fick’s laws in a stretchable sheet. Considerations have been made to Cattaneo–Christov mass and heat diffusion theory. According to the Cattaneo–Christov relation, the Buongiorno phenomenon for the motion of a nanoliquid in the generalized Burgers’ fluid has also been applied. Similarity transformations have been used to convert the control system of the regulating partial differential equations (PDEs) into ordinary differential equations (ODEs). The COMSOL software has been applied to obtain mathematical results of non-linear equations via the Galerkin finite element method (G-FEM). Logical and graphical measurements for temperature, velocity, and microorganisms analysis have also been examined. Moreover, nanoparticle concentrations have been achieved by examining different approximations of obvious physical parameters. Computations of this model show that there is a direct relationship among the temperature field and thermal Biot number and parameter of the generalized Burgers’ fluid. The temperature field is increased to grow the approximations of the thermal Biot number and parameter of generalized Burgers’ fluid. It is reasonable to deduce that raising the chemical reaction parameter and concentricity relaxation parameter or decreasing the Prandtl number, concentricity Biot quantity, and active energy parameter can significantly increase the nanoparticles concentration dispersion. Full article

This work aims to offer a mathematical model for two-phase flow that investigates the interaction of Casson nanofluid and dust particles across a stretching surface. MHD Darcy–Forchheimer porous medium and Fourier’s law through Cattaneo–Christove thermal flux are also considered. The governing equations for the two phases model are partial differential equations later transmuted into ordinary ones via similarity transforms. The Runge–Kutta method with the shooting tool is utilized numerically to solve the boundary layer equations computed in MATLAB to obtain numerical results for various pertinent parameters. The numerical outcomes of momentum, temperature, and concentration distribution are visible for both phases. The results of the skin friction, heat transfer coefficients, and the Sherwood number are also visible in the graphs. Furthermore, by comparing the current findings to the existing literature, the validity of the results is confirmed and found to be in good agreement. The fluid velocity is reduced against increasing strength of Casson fluid parameter, enhanced the fluid phase and dust phase fluid temperature. The temperature declines against the growing values of the relaxation time parameter in both phases. Dusty fluids are used in various engineering and manufacturing sectors, including petroleum transportation, car smoke emissions, power plant pipes, and caustic granules in mining. 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

This discussion intends to scrutinize the Darcy–Forchheimer flow of Casson–Williamson nanofluid in a stretching surface with non-linear thermal radiation, suction and heat consumption. In addition, this investigation assimilates the influence of the Brownian motion, thermophoresis, activation energy and binary chemical reaction effects. Cattaneo–Christov heat-mass flux theory is used to frame the energy and nanoparticle concentration equations. The suitable transformation is used to remodel the governing PDE model into an ODE model. The remodeled flow problems are numerically solved via the BVP4C scheme. The effects of various material characteristics on nanofluid velocity, nanofluid temperature and nanofluid concentration, as well as connected engineering aspects such as drag force, heat, and mass transfer gradients, are also calculated and displayed through tables, charts and figures. It is noticed that the nanofluid velocity upsurges when improving the quantity of Richardson number, and it downfalls for larger magnitudes of magnetic field and porosity parameters. The nanofluid temperature grows when enhancing the radiation parameter and Eckert number. The nanoparticle concentration upgrades for larger values of activation energy parameter while it slumps against the reaction rate parameter. The surface shear stress for the Williamson nanofluid is greater than the Casson nanofluid. There are more heat transfer gradient losses the greater the heat generation/absorption parameter and Eckert number. In addition, the local Sherwood number grows when strengthening the Forchheimer number and fitted rate parameter. Full article

In this article, Cattaneo Christov heat transfer analysis in nanofluid (Ferro Fe₃O₄ and Aggregation) flow between two parallel rotating disks with different velocities determined. The relaxation time, velocity slip, heat convective boundary condition, and heat generation are also presented. The governing partial differential equation (PDEs) model is converted into a set of nonlinear ordinary differential equations (ODEs) system by similarity variables. The solution is computed of the resulting ODEs system by using the Runge Kutta (Rk) method. Here a decline is noticed in the tangential velocity for nanoparticles (Fe₃O₄ and Aggregation nanoparticle) for higher values of the porosity parameter (λ₁), slip parameter γ₁, magnetic parameter (M) and Reynolds number ($R{e}_r$), while tangential velocity arises for higher values of rotation parameters (ß₁). This reduces the temperature field for nanoparticles by higher values of Eckert number (Ec), Prandtl number (Pr), Reynolds number ($R{e}_r$), porosity parameter (λ₁), while increases for arising the values of thermal relaxation parameter ${\lambda }_2$, and for both Biot numbers ($B_1$, $B_2$) nanoparticles (Fe${}_3$O${}_4$ and Aggregation nanoparticle). Further we compute the characteristics of physical quantities, namely skin friction and Nusselt number are presented. Full article