Search Results (188)

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion of nanoparticles in base fluids significantly improves thermal conductivity and enables advanced phase-change technologies. The current work examines Powell–Eyring nanofluid’s heat transmission properties on a stretched Riga plate, considering the effects of magnetic fields, porosity, Darcy–Forchheimer flow, thermal radiation, and activation energy. Using the proper similarity transformations, the pertinent governing boundary-layer equations are converted into a set of ordinary differential equations (ODEs), which are then solved using the boundary value problem fourth-order collocation (BVP4C) technique in the MATLAB program. Tables and graphs are used to display the outcomes. Due to their significance in the industrial domain, the Nusselt number and skin friction are also evaluated. The velocity of the nanofluid is shown to decline with a boost in the Hartmann number, porosity, and Darcy–Forchheimer parameter values. Moreover, its energy curves are increased by boosting the values of thermal radiation and the Biot number. A stronger Hartmann number M decelerates the flow (thickening the momentum boundary layer), whereas increasing the Riga forcing parameter Q can locally enhance the near-wall velocity due to wall-parallel Lorentz forcing. Visual comparisons and numerical simulations are used to validate the results, confirming the durability and reliability of the suggested approach. By using a systematic design technique that includes training, testing, and validation, the fluid dynamics problem is solved. The model’s performance and generalization across many circumstances are assessed. In this work, an artificial neural network (ANN) architecture comprising two hidden layers is employed. The model is trained with the Levenberg–Marquardt scheme on reliable numerical datasets, enabling enhanced prediction capability and computational efficiency. The ANN demonstrates exceptional accuracy, with regression coefficients $R\approx 1.0$ and the best validation mean squared errors of $8.52\times {10}^{-10}$, $7.91\times {10}^{-9}$, and $1.59\times {10}^{-8}$ for the Powell–Eyring, heat radiation, and thermophoresis models, respectively. The ANN-predicted velocity, temperature, and concentration profiles show good agreement with numerical findings, with only minor differences in insignificant areas, establishing the ANN as a credible surrogate for quick parametric assessment and refinement in magnetohydrodynamic (MHD) nanofluid heat transfer systems. Full article

This work investigates the intricate dynamics of the Carreau hybrid nanofluid’s inclined magnetohydrodynamic (MHD) flow, exploring both active and passive control modes. The study incorporates critical factors, including Arrhenius activation energy across a stretched sheet, chemical interactions, and nonlinear thermal radiation. The formulation of the boundary conditions and governing equations is inherently influenced by symmetric considerations in the physical geometry and flow assumptions. Such symmetry-inspired modeling facilitates dimensional reduction and numerical tractability. The analysis employs realistic boundary conditions, including convective heat transfer and control of nanoparticle concentration, which are solved numerically using MATLAB’s bvp5c solver. Findings indicate that an increase in activation energy results in a steeper concentration boundary layer under active control, while it flattens in passive scenarios. An increase in the Biot number ($Bi$) and relaxation parameter ($\mathsf{\Gamma }$) enhances heat transfer and thermal response, leading to a rise in temperature distribution in both cases. Additionally, the 3D surface plot illustrates elevation variations from the surface at low inclination angles, narrowing as the angle increases. The Nusselt number demonstrates a contrasting trend, with thermal boundary layer thickness increasing with higher radiation parameters. A graphical illustration of the average values of skin friction, Nusselt number, and Sherwood number for both active and passive scenarios highlights the impact of each case. Under active control, the Brownian motion’s effect diminishes, whereas it intensifies in passive control. Passive techniques, such as zero-flux conditions, offer effective and low-maintenance solutions for systems without external regulation, while active controls, like wall heating and setting a nanoparticle concentration, maximize heat and mass transfer in shear-thinning Carreau fluids. Full article

This paper explores the complex dynamics of mixed convective flow in a Casson fluid saturated in a non-Darcy porous medium, focusing on the influence of gyrotactic microorganisms, internal heat generation, and multiple convective mechanisms. Casson fluids, known for their non-Newtonian behavior, are relevant in various industrial and biological contexts where traditional fluid models are insufficient. This study addresses the limitations of the standard Darcy’s law by examining non-Darcy flow, which accounts for nonlinear inertial effects in porous media. The governing equations, derived from conservation laws, are transformed into a system of no linear ordinary differential equations (ODEs) using similarity transformations. These ODEs are solved numerically using a finite differencing method that incorporates central differencing, tridiagonal matrix manipulation, and iterative procedures to ensure accuracy across various convective regimes. The reliability of this method is confirmed through validation with the MATLAB (R2024b) bvp4c scheme. The investigation analyzes the impact of key parameters (such as the Casson fluid parameter, Darcy number, Biot numbers, and heat generation) on velocity, temperature, and microorganism concentration profiles. This study reveals that the Casson fluid parameter significantly improves the velocity, concentration, and motile microorganism profiles while decreasing the temperature profile. Additionally, the Biot number is shown to considerably increase the concentration and dispersion of motile microorganisms, as well as the heat transfer rate. The findings provide valuable insights into non-Newtonian fluid behavior in porous environments, with applications in bioengineering, environmental remediation, and energy systems, such as bioreactor design and geothermal energy extraction. Full article

The study examines the onset of magnetoconvection in a Casson fluid-saturated inclined porous layer. Oberbeck–Boussinesq approximation and Darcy law employed to characterize the fluid motion. The stability of the system is examined using both linear and nonlinear stability theories. A basic solution of the governing equation is determined. The linear instability is studied by employing disturbances to the basic flow. The nonlinear instability is analyzed utilizing the energy method. The solution to the eigenvalue problem is derived using the bvp4c routine in MATLAB R2023a. This study evaluates the influence of nondimensional parameters specifically, the Hartmann number, Casson parameter, and inclination angle on both linear and nonlinear instability. The Casson parameter destabilizes the system, whereas the Hartmann number and inclination angle stabilize it. Transverse rolls exhibit greater stability compared to longitudinal rolls. Changes in the Casson parameter significantly affect the presence or absence of transverse rolls; as its value changes, so does the disappearance of transverse rolls. 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

Nanofluids, with their enhanced thermal properties, provide innovative solutions for improving heat transfer efficiency in renewable energy systems. This study investigates a numerical simulation of bioconvective flow and heat transfer in a Williamson nanofluid over a stretching wedge, incorporating the effects of chemical reactions and hydrogen diffusion. The system also includes motile microorganisms, which induce bioconvection, a phenomenon where microorganisms’ collective motion creates a convective flow that enhances mass and heat transport processes. This mechanism is crucial for improving the distribution of nanoparticles and maintaining the stability of the nanofluid. The unique rheological behavior of Williamson fluid, extensively utilized in hydrometallurgical and chemical processing industries, significantly influences thermal and mass transport characteristics. The governing nonlinear partial differential equations (PDEs), derived from conservation laws and boundary conditions, are converted into dimensionless ordinary differential equations (ODEs) using similarity transformations. MATLAB’s bvp4c solver is employed to numerically analyze these equations. The outcomes highlight the complex interplay between fluid parameters and flow characteristics. An increase in the Williamson nanofluid parameters leads to a reduction in fluid velocity, with solutions observed for the skin friction coefficient. Higher thermophoresis and Williamson nanofluid parameters elevate the fluid temperature, enhancing heat transfer efficiency. Conversely, a larger Schmidt number boosts fluid concentration, while stronger chemical reaction effects reduce it. These results are generated by fixing parametric values as $0.1<\varpi <1.5, 0.1<\mathit{Nr}<3.0, 0.2<\mathrm{Pr}<0.5, 0.1<\mathit{Sc}<0.4, \mathrm{and} 0.1<\mathit{Pe}<1.5.$ This work provides valuable insights into the dynamics of Williamson nanofluids and their potential for thermal management in renewable energy systems. The combined impact of bioconvection, chemical reactions, and advanced rheological properties underscores the suitability of these nanofluids for applications in solar thermal, geothermal, and other energy technologies requiring precise heat and mass transfer control. This paper is also focused on their applications in solar thermal collectors, geothermal systems, and thermal energy storage, highlighting advanced experimental and computational approaches to address key challenges in renewable energy technologies. Full article

This study investigates mixed convection flow over a vertical thin needle with variable surface heat, mass, and microbial flux, incorporating the influence of gyrotactic microorganisms. The governing partial differential equations are transformed into ordinary differential equations using appropriate similarity transformations and then solved numerically by employing MATLAB’s Bvp4c solver. The primary focus lies in examining the influence of various dimensionless parameters, including the mixed convection parameter, power-law index, buoyancy parameters, bioconvection parameters, and needle size parameters, on the velocity, temperature, concentration, and microbe profiles. The results indicate that these parameters significantly affect the surface (wall) temperature, fluid concentration, and motile microbe concentration, as well as the corresponding velocity, temperature, concentration, and microorganism profiles. The findings provide insights into the intricate dynamics of mixed convection flow with bioconvection and have potential applications in diverse fields such as biomedicine and engineering. Full article

Bioconvection phenomena play a pivotal role in diverse applications, including the synthesis of biological polymers and advancements in renewable energy technologies. This study develops a comprehensive mathematical model to examine the effects of key parameters, such as the Lewis number (Lb), Peclet number (Pe), volume fraction ($\phi$), and angle of inclination $\left(\alpha \right)$, on the flow and heat transfer characteristics of a nanofluid over an inclined cylinder embedded in a non-Darcy porous medium. The investigated nanofluid comprises nano-encapsulated phase-change materials (NEPCMs) dispersed in water, offering enhanced thermal performance. The governing non-linear partial differential equations are transformed into dimensionless ordinary differential equations using similarity transformations and solved numerically via the Network Simulation Method (NSM) and an implicit Runge–Kutta method implemented through the bvp4c routine in MATLAB R2021a. Validation against the existing literature confirms the accuracy and reliability of the numerical approach, with strong convergence observed. Quantitative analysis reveals that an increase in the Peclet number reduces the shear stress at the cylinder wall by up to 18% while simultaneously enhancing heat transfer by approximately 12%. Similarly, the angle of inclination ($\alpha$) significantly boosts heat transmission rates. Additionally, higher Peclet and Lewis numbers, along with greater nanoparticle volume fractions, amplify the density gradient of microorganisms, intensifying the bioconvection process by nearly 15%. These findings underscore the critical interplay between bioconvection and transport phenomena, providing a framework for optimizing bioconvection-driven heat and mass transfer systems. The insights from this investigation hold substantial implications for industrial processes and renewable energy technologies, paving the way for improved efficiency in applications such as thermal energy storage and advanced cooling systems. Full article

For automobile and aerospace engineers, implementing Hall currents and thermal radiation in cooling systems helps increase the performance and durability of an engine. In the case of solar energy systems, the effectiveness of heat exchangers and solar collectors can be enhanced by the best use of hybrid nanofluids and the implementation of a Hall current, thermophoresis, Brownian motion, a heat source/sink, and thermal radiation in a time-dependent hybrid nanofluid flow over a disk for a Bayesian regularization ANN backpropagation algorithm. In the current physical model of Cobalt ferrite $CoF{e}_2{O}_4$ and aluminum oxide $A{l}_2{O}_3$ mixed with water, a new category of the nanofluid is called the hybrid nanofluid. The study uses MATLAB bvp4c to unravel such intricate relations, transforming PDEs into ODEs. This analysis enables the numerical solution of several BVPs that govern the system of the given problem. Hall currents resulting from the interaction between magnetic fields and the electrically conducting nanofluid, and thermal radiation as an energy transfer mechanism operating through absorption and emission, are central factors for controlling these fluids for use in various fields. The graphical interpretation assists in demonstrating the character of new parameters. The heat source/sink parameter is advantageous to thermal layering, but using a high Schmidt number limits the mass transfer. Additionally, a backpropagation technique with Bayesian regularization is intended for solving ordinary differential equations. Training state, performance, error histograms, and regression demonstration are used to analyze the output of the neural network. In addition to this, there is a decrease in the fluid velocity as magnetic parameter values decrease and a rise in the fluid temperature while the disk is spinning. Thermal radiation adds another level to the thermal behavior by altering how the hybrid nanofluid receives, emits, and allows heat to pass through it. Full article

This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal dispersion. The mass diffusion coefficient and temperature-dependent models of thermal conductivity and species are used to provide thermal transportation. Nonlinear partial differential equations (NPDEs) that go against the conservation laws of mass, momentum, heat, and species transportation are the form arising problems take on. A set of coupled dimensionless partial differential equations (PDEs) are obtained from a set of convective differential equations by applying the proper non-similar transformations. Local non-similarity approaches provide an analytical approximation of the dimensionless non-similar system up to two degrees of truncations. The built-in Matlab (Version: 7.10.0.499 (R2010a)) solver bvp4c is used to perform numerical simulations of the local non-similar (LNS) truncations. Full article

For efficient heating and cooling applications, minimum wall shear stress and maximum heat transfer rate are desired. The current study optimized the local skin friction coefficient and Nusselt number in Al₂O₃-Cu/water hybrid nanofluid flow over a permeable shrinking rotating disk. First, the governing equations and boundary conditions are solved numerically using the bvp4c solver in MATLAB. Von Kármán’s transformations are used to reduce the partial differential equations into solvable non-linear ordinary differential equations. The augmentation of the mass transfer parameter is found to reduce the local skin friction coefficient and Nusselt number. Higher values of these physical quantities of interest are observed in the injection case than in the suction case. Meanwhile, the increase in the magnitude of the shrinking parameter improved and reduced the local skin friction coefficient and Nusselt number, respectively. Then, response surface methodology (RSM) is conducted to understand the interactive impacts of the controlling parameters in optimizing the physical quantities of interest. With a desirability of 66%, the local skin friction coefficient and Nusselt number are optimized at 1.528780016 and 0.888353037 when the shrinking parameter ($\lambda$) and mass transfer parameter ($S$) are −0.8 and −0.6, respectively. Full article

This study investigates the potential of a hybrid nanofluid composed of MoS₂ and ZnO nanoparticles dispersed in engine oil, aiming to enhance the properties of a lubricant’s chemical reaction with the Soret effect on a stretching sheet under the influence of an applied magnetic field. With the growing demand for efficient lubrication systems in various industrial applications, including automotive engines, the development of novel nanofluid-based lubricants presents a promising avenue for improving engine performance and longevity. However, the synergistic effects of hybrid nanoparticles in engine oil remain relatively unexplored. The present research addresses this gap by examining the thermal conductivity, viscosity, and wear resistance of the hybrid nanofluid, shedding light on its potential as an advanced lubrication solution. Overall, the objectives of studying the hybrid nanolubricant MoS₂ + ZnO with engine oil aim to advance the development of more efficient and durable lubrication solutions for automotive engines, contributing to improved reliability, fuel efficiency, and environmental sustainability. In the present study, the heat and mass transformation of a Casson hybrid nanofluid (MoS₂ + ZnO) based on engine oil over a stretched wall with chemical reaction and thermo-diffusion effect is analyzed. The governing nonlinear partial differential equations are simplified as ordinary differential equations (ODEs) by utilizing the relevant similarity variables. The MATLAB Bvp4c technique is used to solve the obtained linear ODE equations. The results are presented through graphs and tables for various parameters, namely, M, Q, β, Pr, Ec, Sc, Sr, Kp, Kr, and ${\varphi }_2*$ (hybrid nanolubricant parameters) and various state variables. A comparative survey of all the graphs is presented for the nanofluid (MoS₂/engine oil) and the hybrid nanofluid (MoS₂ + ZnO/engine oil). The results reveal that the velocity profile diminished against the values of M, Kp, and β, and the temperature profile rises with Ec and Q, whereas Pr decreases. The concentration profile is incremented (decremented) with the value of Sr (Sc and Kr). A comparison of the nanofluid and hybrid nanofluid suggests that the velocity f′ (η) becomes slower with the augmentation of ${\varphi }_2*$ whereas the temperature increases when ${\varphi }_2*$ = 0.6 become slower. Full article

The emerging concept of hybrid nanofluids has grabbed the attention of researchers and scientists due to improved thermal performance because of their remarkable thermal conductivities. These fluids have enormous applications in engineering and industrial sectors. Therefore, the present research study examines thermal and mass transportation in hybrid nanofluid past an inclined linearly stretching sheet using the Maxwell fluid model. In the current problem, the hybrid nanofluid is engineered by suspending a mixture of aluminum oxide $A{l}_2{O}_3$ and copper $Cu$ nanoparticles in ethylene glycol. The fluid flow is generated due to the linear stretching of the sheet and the sheet is kept inclined at the angle $\zeta =\pi /6$ embedded in porous medium. The current proposed model also includes the Lorentz force, solar radiation, heat generation, linear chemical reactions, and permeability of the plate effects. Here, in the current simulation, the cylindrical shape of the nanoparticles is considered, as this shape has proven to be excellent for the thermal performance of the nanomaterials. The governing equations transformed into ordinary differential equations are solved using MATLAB bvp4c solver. The velocity field declines with increasing magnetic field parameter, Maxwell fluid parameter, volume fractions of nanoparticles, and porosity parameter but increases with growing suction parameter. The temperature drops with increasing magnetic field force and suction parameter values but increases with increasing radiation parameter and volume fraction values. The concentration profile increases with increasing magnetic field parameters, porosity parameters, and volume fractions but reduces with increasing chemical reaction parameters and suction parameters. It has been noted that the purpose of the inclusion of thermal radiation is to augment the temperature that is serving the purpose in the current work. The addition of Lorentz force slows down the speed of the fluid and raises the boundary layer thickness, which is visible in the current study. It has been concluded that, when heat generation parameters increase, the temperature field increases correspondingly for both nanofluids and hybrid nanofluids. The increase in the volume fraction of the nanoparticles is used to enhance the thermal performance of the hybrid nanofluid, which is evident in the current results. The current results are validated by comparing them with published ones. Full article

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation ($Rd$). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command ‘nftool’. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index ($R$), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10⁻¹⁰, 1.64 × 10⁻⁹, 1.03 × 10⁻⁹, 302 9.35 × 10⁻¹⁰, 8.56 × 10⁻¹⁰, 1.08 × 10⁻⁹, and 6.97 × 10⁻¹⁰, respectively. It is noted that $f^{\prime }\left(\eta \right)$, $\theta \left(\eta \right),$ and $\varphi \left(\eta \right)$ satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes (${Cf}_x$, ${Nu}_x$, and $S{h}_x$) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase ($M=0.01, 0.05, 0.1$), then the solution bifurcates at different critical values, i.e., ${\lambda }_c=-1.06329,-1.097,-1.17694$. The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement. Full article

This manuscript introduces the first hp-adaptive mesh refinement algorithm for the Theory of Functional Connections (TFC) to solve hypersensitive two-point boundary-value problems (TPBVPs). The TFC is a mathematical framework that analytically satisfies linear constraints using an approximation method called a constrained expression. The constrained expression utilized in this work is composed of two parts. The first part consists of Chebyshev orthogonal polynomials, which conform to the solution of differentiation variables. The second part is a summation of products between switching and projection functionals, which satisfy the boundary constraints. The mesh refinement algorithm relies on the truncation error of the constrained expressions to determine the ideal number of basis functions within a segment’s polynomials. Whether to increase the number of basis functions in a segment or divide it is determined by the decay rate of the truncation error. The results show that the proposed algorithm is capable of solving hypersensitive TPBVPs more accurately than MATLAB R2021b’s bvp4c routine and is much better than the standard TFC method that uses global constrained expressions. The proposed algorithm’s main flaw is its long runtime due to the numerical approximation of the Jacobians. Full article