Search Results (36)

Magnetohydrodynamic (MHD) flow and heat transfer in porous media are central to many engineering applications, including heat exchangers, MHD generators, and polymer processing. This study examines the boundary layer flow and thermal behavior of an electrically conducting viscous fluid over a porous stretching tube. The model accounts for nonlinear thermal radiation, internal heat generation/absorption, and Darcy–Forchheimer drag to capture porous medium resistance. Similarity transformations reduce the governing equations to a system of coupled nonlinear ordinary differential equations, which are solved numerically using the BVP4C technique with Response Surface Methodology (RSM) and sensitivity analysis. The effects of dimensionless parameters magnetic field strength (M), Reynolds number (Re), Darcy–Forchheimer parameter (Df), Brinkman number (Br), Prandtl number (Pr), nonlinear radiation parameter (Rd), wall-to-ambient temperature ratio (rw), and heat source/sink parameter (Q) are investigated. Results show that increasing M, Df, and Q suppresses velocity and enhances temperature due to Lorentz and porous drag effects. Higher Re raises pressure but reduces near-wall velocity, while rw, Rd, and internal heating intensify thermal layers. The entropy generation analysis highlights the competing roles of viscous, magnetic, and thermal irreversibility, while the Bejan number trends distinctly indicate which mechanism dominates under different parameter conditions. The RSM findings highlight that rw and Rd consistently reduce the Nusselt number (Nu), lowering thermal efficiency. These results provide practical guidance for optimizing energy efficiency and thermal management in MHD and porous media-based systems.: Full article

Highlighting the importance of artificial intelligence and machine learning approaches in engineering and fluid mechanics problems, especially in heat transfer applications is main goal of the presented article. With the advancement in Artificial Intelligence (AI) and Machine Learning (ML) techniques, the computational efficiency and accuracy of numerical results are enhanced. The theme of the study is to use machine learning techniques to examine the thermal analysis of MHD boundary layer flow of Eyring-Powell Hybrid Nanofluid (EPHNFs) passing a horizontal cylinder embedded in a porous medium with heat source/sink and viscous dissipation effects. The considered base fluid is water ($H_{2}O$) and hybrid nanoparticles titanium oxide (${TiO}_2$) and Copper oxide ($CuO$). The governing flow equations are nonlinear PDEs. Non-similar system of PDEs are obtained with efficient conversion variables. The dimensionless PDEs are truncated using a local non-similarity approach up to third level and numerical solution is evaluated using MATLAB built-in-function bvp4c. Artificial Neural Networks (ANNs) simulation approach is used to trained the networks to predict the solution behavior. Thermal boundary layer improves with the enhancement in the value of $Rd$. The accuracy and reliability of ANNs predicted solution is addressed with computation of correlation index and residual analysis. The RMSE is evaluated [0.04892, 0.0007597, 0.0007596, 0.01546, 0.008871, 0.01686] for various scenarios. It is observed that when concentration of hybrid nanoparticles increases then thermal characteristics of the Eyring-Powell Hybrid Nanofluid (EPHNFs) passing a horizontal cylinder. Full article

The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes. 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

Nanomaterials have been the focus of intense study and growth in the modern era across the globe because of their outstanding qualities, which are brought about by their nanoscale size; for instance, increased adsorption and catalysis capabilities plus significant reactivity. Multiple investigations have verified the fact that nanoparticles may successfully remove a variety of pollutants from water, and, as a result, they have been utilized in the treatment of both water and wastewater. Therefore, the current research intent is to examine the nonlinear heat source/sink influence on the 3D flow of water-based silver nanoparticles incorporated in an Eyring–Powell fluid across a deformable sheet with concentration pollutants. Silver particles have been used intensively to filter water, due to their potent antibacterial properties. The leading equations involving partial differential equations are renewed into the form of ordinary ordinary differential equations through utilizing the appropriate similarity technique. Then, these converted equations are solved by utilizing an efficient solver bvp4c. Visual displays and extensive exploration of the different impacts of the non-dimensional parameters on the concentration, temperature, and velocity profiles are provided. Also, the important engineering variables including skin friction, the rate of heat, and mass transfer are examined. The findings suggest that the mass transfer rate declines due to pollutant parameters. Also, the results suggest that the friction factor is uplifted by about 15% and that the heat transfer rate, as well as the mass transfer rate, declines by about 21%, due to the presence of the nanoparticle volume fraction. We believe that these results may improve the flow rate of nanofluid systems, improve heat transfer, and reduce pollutant dispersal. Full article

The numerical investigation of bioconvective nanofluid (NF) flow, which involves gyrotactic microbes and heat and mass transmission analysis above an inclined extending axisymmetric cylinder, is presented in this study. The study aims to investigate the bioconvection flow of nanofluid under the influence of heat sources/sinks. Through proper transformation, all partial differential equations are transformed into a non-linear ODE scheme. A new set of variables is presented in the directive to get the first-order convectional equations and then solved numerically using bvp4c MATLAB, embedded in the function. The proposed model is validated after calculating the error estimation and obtaining the residual error. The influence of various factors on the velocity, energy, concentration, and density of motile microorganisms is examined and studied. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number, the density of motile microorganisms, and Nusselt number. To validate the present study, a comparison is conducted with previous studies, and excellent correspondence is found. In addition, the ND-Solve approach is utilized to confirm the bvp4c. The mathematical model is confirmed through error analysis. This study provides the platform for industrial applications such as cooling capacity polymers, heat exchange, and chemical production sectors. Full article

The main goal of the current research is to investigate the numerical computation of $\mathrm{Ag}/{\mathrm{Al}}_2{\mathrm{O}}_3$ nanofluid over a Riga plate with injection/suction. The energy equation is formulated using the Cattaneo–Christov heat flux, non-linear thermal radiation, and heat sink/source. The leading equations are non-dimensionalized by employing the suitable transformations, and the numerical results are achieved by using the MATLAB bvp4c technique. The fluctuations of fluid flow and heat transfer on porosity, Forchheimer number, radiation, suction/injection, velocity slip, and nanoparticle volume fraction are investigated. Furthermore, the local skin friction coefficient (SFC), and local Nusselt number (LNN) are also addressed. Compared to previously reported studies, our computational results exactly coincided with the outcomes of the previous reports. We noticed that the Forchheimer number, suction/injection, slip, and nanoparticle volume fraction factors slow the velocity profile. We also noted that with improving rates of thermal radiation and convective heating, the heat transfer gradient decreases. The $40\%$ presence of the Hartmann number leads to improved drag force by $14\%$ and heat transfer gradient by $0.5\%$. The $20\%$ presence of nanoparticle volume fraction leads to a decrement in heat transfer gradient for $21\%$ of Ag nanoparticles and $18\%$ of ${\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles. Full article

The fluid flow through blunt bodies that are yawed and un-yawed frequently happens in many engineering applications. The practical significance of deep-water applications such as propagation control, splitting the boundary layer over submerged blocks, and preventing recirculation bubbles is explained by the fluid flow across a yawed cylinder. The current work examined the mixed convective flow and convective heat transfer by incorporating water-based graphene oxide nanofluid around a yawed cylinder with viscous dissipation and irregular heat source/sink. To investigate the heat diffusion across the system of buoyancy effects, the mathematical formulation of the problem was modeled in terms of coupled, nonlinear partial differential equations. The boundary value problem of the fourth-order (bvp4c) solver was operated to find the non-similarity solution. The outcomes indicated that the velocity in both directions enlarged owing to the higher impacts of yaw angle for the phenomenon of assisting flow but decreased for the instance of opposing flow, while the temperature of nanofluid increased because of heightened estimations of yaw angle for both assisting and opposing flows. In addition, with larger impacts of nanoparticle volume fraction, the shear stresses were enhanced by about 0.76% and 0.93% for the case of assisting flow, while for the case of opposing flow, they improved by almost 0.65% and 1.38%, respectively. Full article

The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al${}_2$O${}_3$ and Ag) and (Al${}_2$O${}_3$ and TiO${}_2$) with a base fluid (H${}_2$O), are considered. The governing flow models with accompanying boundary constraints are reshaped into non-linear ODEs by applying the symmetry variables. The reshaped ODEs are numerically computed using Bvp4c in Matlab and the ND solver in Mathematica. The impact of the emerging parameters on the heat transfer, surface shear stress, temperature and velocity profile is scrutinized and expressed in a tabular and graphical structure. It is noticed that the upsurge of the Hartmann number leads to an improvement in the velocity profile. The velocity declines when enriching the porosity parameter. The radiation and Biot number lead to strengthening the temperature profile. The surface shear stress exalts due to a larger modified Hartman number. The radiation and unsteady parameters are downturns in the heat transfer gradient. Full article

This communication predominately discusses the rheological attributes of the Darcy–Forchheimer flow of a nanoliquid over a stretchy sheet with a magnetic impact. The present model considers the two diverse nanoparticles, such as $Cu$ and $Ag$, and water as a base liquid. The heat equation accounts for the consequences of thermal radiation and a nonlinear heat sink/source when evaluating heat transmission phenomena. The current mechanical system is represented by higher-order PDEs, which are then remodeled into nonlinear higher-order ODEs that employ appropriate symmetry variables. The current mathematical systems are numerically computed by implementing the bvp4c technique. The characteristic attitudes of the related pertinent factors on the non-dimensional profiles are sketched via the figures, tables, and charts. The analysis predicts that the speed of the nanoliquid particles becomes slower when there is more presence of a magnetic field and injection/suction parameters. The growing amount of radiation is also pointed out, and the Eckert number corresponds to enriching the thermal profile. Full article

The utilization of hybrid nanofluids (HNs) to boost heat transfer is a promising area of study, and thus, numerous scientists, researchers, and academics have voiced their admiration and interest in this area. One of the main functions of nanofluids is their dynamic role in cooling small electrical devices such as microchips and associated gadgets. The major goal of this study is to perform an analysis of the buoyancy flow of a shrinking/stretching sheet, whilst considering the fascinating and practical uses of hybrid nanofluids. The influence of a nonlinear heat source/sink induced by a micropolar fluid is also inspected. Water-based alumina and copper nanoparticles are utilized to calculate the fine points of the fluid flow and the features of heat transfer. The governing equations are framed with acceptable assumptions and the required similarity transformations are used to turn the set of partial differential equations into ordinary differential equations. The bvp4c technique is used to solve the simplified equations. Dual solutions are presented for certain values of stretching/shrinking parameters as well as the mixed convective parameter. In addition, the shear stress coefficient in the first-branch solution (FBS) escalates and decelerates for the second-branch solution (SBS) with the superior impact of the magnetic parameter, the mass transpiration parameter, and the solid nanoparticles volume fraction, while the contrary behavior is seen in both (FB and SB) solutions for the larger values of the material parameter. 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

The Darcy ternary hybrid nanofluid flow comprising titanium dioxide (TiO₂), cobalt ferrite (CoFe₂O₄) and magnesium oxide (MgO) nanoparticles (NPs) through wedge, cone, and plate surfaces is reported in the present study. TiO₂, CoFe₂O₄, and MgO NPs were dispersed in water to synthesize a trihybrid nanofluid. For this purpose, a mathematical model was calculated to augment the energy transport rate and efficiency for variety of commercial and medical functions. The consequences of heat source/sink, activation energy, and the magnetic field are also analyzed. Such problems mostly occur in symmetrical phenomena and are applicable to engineering, physics, and applied mathematics. The phenomena were formulated in the form of a nonlinear system of PDEs, which are simplified to the system of dimensionless ODEs through similarity replacement (obtained from symmetry analysis). The obtained set of differential equations is resolved through a parametric continuation approach (PCM). Graphical depictions are used to evaluate and address the impact of significant factors on energy, mass, and flow exchange rates. The velocity and energy propagation rates over a cone surface were greater than those of a wedge and plate versus the variation of Grashof number, porosity effect, and heat source, while the mass transfer ratio under the impact of a chemical reaction and activation energy over a wedge surface was higher than that of a plate. Full article

In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle deposition and chemical reaction are taken into the concentration equation in order to investigate the mass transportation in the liquid. To formulate the non-linear ordinary differential equations, the von Karman similarity approach is used in the system of partial differential equations and then integrated numerically by the bvp midrich scheme in Maple programming. Results are provided by graphical framework and tabular form. A quick parametric survey is carried out concerning flow field, thermal, and solutal distributions through graph representation. The curves show that increasing the values of the retardation time parameter decreases the radial velocity while increasing the angular velocity. Additionally, when the relaxation time parameter becomes powerful, the magnitude of the velocity curves decreases considerably in the radial and axial directions. The presence of a radiation parameter indicates that the fluid will absorb a greater amount of heat, which is equivalent to a higher temperature. Further, an increase in the stretching parameter leads to a reduction in the temperature components. Full article

In this paper, we study the magnetohydrodynamics of Darcy flow in a non-Newtonian liquid. The influence of thermophoresis on particle deposition is examined in the Darcy flow of a Maxwell nanofluid. In our model, the temperature distribution is generated by the Fourier law of heat conduction with nonlinear thermal radiation and heat sink/source. We also examine the Soret–Dufour effects in the mass concentration equations. The Brownian and thermophoretic diffusions are assumed to be generated by nanoparticle dispersion in the fluid. The similarity method is used to transform the partial differential equations into nonlinear ordinary differential equations. The transformed flow equations were solved numerically using the BVP Midrich scheme. The results of the computation are displayed graphically and in tabular form. The results obtained show that increasing the Deborah number leads to a decline in radial and angular motion and a decrease in the magnitude of axial flow. As expected, the strength of the heat source and the values of the thermal radiation parameters determine the temperature of the liquid. We also found that as the Soret number rises (or the Dufour number falls), so does the mass transfer rate. Full article