Thermal Boundary Layer Thickness Research Articles

Heat transfer in 3D radiative Oldroyd-B fluid flow with irregular heat source and activation energy

Heat transfer in 3D radiative Oldroyd-B fluid flow with irregular heat source and activation energy

Computational micropolar model of hybrid nanofluid flow across a wedge

Non-Newtonian flow from wedges is a vital problem in coatings, polymer processing etc. Hence the main aim is to investigate the convective boundary layer flow of micropolar hybrid nanofluid (MHN)from a wedge. It is assumed that the wedge surface is isothermal. The Eringen model is employed to define micropolar fluid. Nanoscale Tiwari–Das formulations are used to study the specific effects of nanoparticles and volume fractions. The dimensionless boundary value problem arises by suitable coordinate transformations as a system of nonlinearly coupled ordinary differential equations. The so-called Falkner Skan flow case is resolved. Dimensionless, transformed, coupled momentum, microrotation, boundary layer equations are resolved using the numerical scheme MATLAB bvp4c. The parameteric investigations are performed on hybrid nanofluids using water as the basis liquid and varying volume fractions from 0 to 8%. Affirmation with previous work is done. The consequence of Eringen micropolar parameter, Hartree pressure gradient parameter, nanoparticle volume fraction, Eckert number, heat absorption (sink) parameter, on the flow and physical characteristics are visualized graphically and in tables. With rising material factor and volume fraction of nanoparticle, temperature is markedly enhanced. Increases in volume fraction dampen angular velocity close to the wedge surface, while farther from the wall, the opposite effect is seen. Temperature and thermal boundary layer thickness are both greatly enhanced by increasing Eckert number. With an increase in the volume proportion of nanoparticles, velocity decreases. Heat generation raises temperatures while a heat sink lowers them. The pressure gradient parameter increases skin friction while decreasing Nusselt number. Nusselt number for hybrid nanofluid is higher than for nanofluid.

An analytical study on the influence of magnetic field-dependent viscosity on viscous and ohmic dissipative second-grade fluid boundary layers

This article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Nanoparticle aggregation kinematics and nanofluid flow in convectively heated outer stationary and inner stretched coaxial cylinders: Influenced by linear, nonlinear, and quadratic thermal radiation

The consequence of nanoparticle aggregation and convective boundary condition on the nanofluid stream past the co-axial cylinder with radiation impact is investigated in the present examination. The influence of linear, nonlinear, and quadratic thermal radiation on the nanofluid flow is analyzed. The outer cylinder stays stable, while the inner cylinder deforms horizontally in the axial direction, allowing fluid to flow. By using similarity variables, the governing equations are transformed into ordinary differential equations (ODEs). Subsequently, the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method is employed to solve the reduced ODEs. The upshot of several nondimensional terms on the temperature and velocity profiles is displayed with graphical representation. The comparison of linear, quadratic, and nonlinear thermal radiation on the thermal profile is illustrated. The upsurge in curvature parameter increases velocity and thermal profile. The increase in radiation parameter intensifies the temperature profile. The thermal profile improves with a rise in the values of radiation parameter. The radiation parameter generates thermal energy in the flow zone, which is why the temperature field has improved. The thermal Biot number exhibits an increasing response with temperature and thermal boundary layer thickness. The linear thermal radiation shows better heat transfer compared to quadratic and nonlinear thermal radiation.

Impact of the Stefan gusting on a bioconvective nanofluid with the various slips over a rotating disc and a substance-responsive species

This paper presents thorough computational and theoretical analyses of steady forced convective flow over a rotating disc submerged in a water-based nanofluid containing microorganisms. It delves into the examination of boundary layer flow characteristics of a viscous nanofluid, considering Stefan blowing effects and multiple slip conditions influenced by a magnetic field. Notably, the study accounts for novel aspects such as thermal radiation and both constructive and destructive chemical reactions. The movement of nanoparticles is elucidated based on thermophoresis and microscopic behaviors, while changes in volume fraction do not affect the thermo-physical properties of the nanofluid. To address the altered nonlinear set of differential equations, an effective numerical approach, the Keller-Box method, is implemented for critical and efficient solutions. These appropriate transformations are defined and applied. When compared to blowing suction, it shows a better enhancement in the rate of heat transfer, mass, and microorganisms. Some of the main observations are there is a decrease in wall skin friction in the directions of radial and tangential as magnetic field strength is increased. The evaluation of thermal boundary layer thickness and temperature is noted for the radiation parameter (Rd) improvement. The present analysis has applications in electromagnetic micro-pumps and nanomechanics. As to the applications in the science and engineering fields, technologies such as micro-electromechanical systems-based microfluidic devices and microfluidic-related technologies will be accepted.

Melting heat transfer features in a B[formula omitted]dewadt flow of hybrid nanofluid ([formula omitted]/water) by a stretching stationary disk

The melting impacts on the three-dimensional hybrid nanofluid flow by a stationary stretching disk is examined. The flow configuration is due to the stretching of the disk. The magnetic field is applied normal to the disk in order to generate the resistance in the liquid. The performance of heat transfer in the liquid, the thermal radiation and heat generation/absorption impacts are taken into consideration. The melting heat transfer impact on the surface is analyzed here. The impact of stretching and rotating mechanisms along with applied physical impacts on the hybrid nanofluid flow and heat features are of the present concern for this physical problem. A conventional transformation is presented to lead to a set of coupled similarity equations which are highly non-linear in nature. A numerical method subject to bvp4c technique is adopted for the solution process. Results reveal that increasing trend of stretching of the disk lowers the boundary layer thickness and consequently highers the rate of heat transfer. It is found the reduction in thickness of thermal boundary layer by the strength of stretching. Additionally, the temperature distribution rises by the influence of melting temperature. Further, the skin fraction coefficient seen to be enhanced with the enlargement of nanoparticles volume fraction.

Consequences of higher order chemical reaction on bioconvective carbon nanotubes flow implementing Buongiorno's model

In recent years, carbon nanotubes have been extensively explored based on numerous applications in fields such as carbon nanotube based electrodes, super capacitors, nanowires, sensors, coating with polymers, biomedical, and mechanical applications. Keeping in view the significance of carbon nanotubes in the heat transfer process in micro-electrochemical systems, this study is conducted to examine the heat transfer attributes of the carbon nanotubes using the mixture base working fluid. The focus of this investigation is to elaborate the consequence of higher chemical reactions on the bioconvective flow of carbon nanotubes. Additionally, modified Buongiorno's nanofluid model has been used, which undertakes thermophoresis and Brownian motion effects. Heated boundary condition has also been incorporated with the migration of motile microorganisms. The hybrid nanofluid mechanism has been followed in this work. Carbon nanotubes of single-layer and multi-layer have been used simultaneously with different working fluids, such as ethylene glycol (EG) and ethylene glycol/water (EG-water). Non-dimensional flow model equations have been tackled with the bvp-4c package. The obtained outcomes have been presented for distinct profiles and tabulated data sets for the surface skin friction and heat transfer coefficient. It has been observed that when the level of Brownian motion increases, the velocity profile decreases abruptly for SWCNT-MWCNT/EG as compared to SWCNT-MWCNT/EG-water hybrid nanofluid. Opposite behavior has been seen with raising values of magnetization. High Prandtl number decrease thermal boundary layer thickness for both types of hybrid nanofluids. The motile microorganism profile expands by raising the level of bioconvective Lewis number. Moreover, the outcomes of drag force and Nusselt number have been compared, and good agreement has been found.

Numerical study of hybrid binary Al2O3-Cu-H2O nanofluid coating boundary layer flow from an exponentially stretching/shrinking perforated substrate with Cattaneo-Christov heat flux, heat source, suction and multiple slip effects

Modern coating systems are increasingly deploying nanomaterials which offer improved thermal performance. The optimization of these systems can benefit from more elegant fluid dynamic models of the coating process. Inspired by these advancements, the present investigation introduces a novel mathematical model to analyze the boundary layer transport in Al2O3-Cu-H2O hybrid binary nanofluid coating deposition on an exponentially stretching porous substrate (sheet). Lateral mass flux (suction) at the wall is also considered a heat source (generation) for hot spot manufacturing effects. To add further sophistication to the thermal conduction model, a non-Fourier approach is adopted which accurately incorporates thermal relaxation effects i.e. the Cattaneo-Christov heat flux (CCHF) model. The Tiwari-Das volume fraction nanoscale formulation is implemented for different combinations of Alumina (Al2O3) and Copper (Cu) metallic nanoparticles in an aqueous base fluid (H2O). Hydrodynamic wall and thermal slip are also included as they feature in coating processes. The fundamental equations governing mass, momentum, and energy conservation, along with the corresponding conditions at the wall (substrate) and free stream, are made dimensionless through suitable scaling similarity transformations. The resulting nonlinear coupled ordinary differential boundary value problem is subsequently addressed using the efficient MATLAB bvp4c routine. Special cases of the non-Fourier model are validated against published results, and the general model is further confirmed through validation using an Adams-Moulton 2-step predictor-corrector algorithm (AMPC). Furthermore, dual solutions of the generalized model are extracted and visualized. A comprehensive study of the effects of key thermophysical key parameters on momentum and thermal characteristics (velocity, temperature, skin friction and local Nusselt number) is conducted and solutions are visualized graphically. The computations show that higher temperatures are present with intensification in the thermal relaxation parameter (Cattaneo-Christov hyperbolic model parameter), which predicts therefore larger temperatures than the classical Parabolic heat conduction model using Fourier analysis. Effectively, thermal relaxation is responsible for finite heat wave propagation and produces more accurate estimations of heat transfer than the Fourier model. An increase in stretching parameter enhances the skin friction coefficient and elevates the local Nusselt number. As the thermal relaxation parameter increases, the temperature magnitudes corresponding to the first and second solutions are both enhanced as are thermal boundary layer thicknesses. An increase in wall suction induces an escalation in the first solution for velocity whereas it reduces the second solution velocity. Stronger wall suction suppresses temperatures. With increasing thermal slip, the boundary layer is cooled i.e. temperature plummets and thermal boundary layer thickness is decreased. Strong deceleration is induced with greater hydrodynamic (velocity) slip. Both first and second solutions for skin friction are elevated with shrinking whereas they are depressed with stretching. With greater velocity slip both the first and second solutions for skin friction are depleted with greater velocity slip for the shrinking case, whereas they are generally enhanced for the very strong stretching case. The computations offer some new insights into multi-physical thermal fluid dynamics of nanofluid-based coating systems.

Nonlinear heat radiation and mass transfer characteristics on MHD Walters’ B fluid flow through a porous medium over a stretching sheet

To handle the continuous thermal power supply is very important in thermal systems and industries, so magnetized heat transport with non-Newtonian fluid is an appropriate platform for thermal power energy. In view of this usefulness, this paper provides a numerical assessment of electrically conducting Walter's B fluid flow through nonlinear permeable stretching sheet subject to mixed convective, porous medium, and Newtonian heating phenomena. Thermophoresis and Brownian motion effects have been included in energy and species diffusion equations to account for the impacts of nonlinear thermal radiation, joule heating, heat source and chemical reaction. The system of governing equations has been reduced to dimensionless nonlinear coupled equations using similarity transformations. The bvp4c technique has been used to obtain the solution for velocity, temperature, and concentration distributions. We consider both regions of assisting and opposing flow and provide various tables and graphs to examine the impact of varying values of emerging factors. Heat source and thermal radiation characteristics are found to enhance the thermal boundary layer thickness, which may be used to dissipate heat. The magnetic parameter augmented the fluid temperature and decelerated the velocity field. The chemical reaction parameter accelerated the concentration distribution. Further, the Sherwood number, Nusselt number, and skin friction coefficient have been determined and compared well to prior research that has been published.

Insight of Jeffrey flow over a stretching Riga plate with activation energy and viscous dissipation: Melting heat transfer regime

AbstractPresent article highlights the significance of Arrhenius activation energy along with viscous dissipation in Jeffrey fluid over a Riga plate. Riga plate is basically an actuator made up of array of magnets and electrodes scaled on a plane surface to tackle the weaker electrical conductivity during fluid flow. In order to ensure the novelty, a reliable melting heat surface condition has been incorporated on nonlinear stretching Riga plate of variable thickness to reconnoiter features of heat transfer. Moreover, stagnation point has been retained in this study. Adequate transformations are employed in order to attain system of nonlinear ordinary differential equations. A well known semi analytical technique (Homotopy analysis method) is utilized to obtain series solutions of prevailing dimensionless equations. Influence of several apposite parameters on velocity, thermal and concentration distributions is analyzed graphically. Physical evaluation and graphical sketch is presented for drag force coefficient and rate of heat transfer. Analysis of velocity as well as associated boundary layer thickness gives the growing up impact for the strength of modified Hartmann number. Enhancement of dimensionless reaction rate and endothermic/exothermic reaction parameter results in increment for heat flux over stretching Riga plate. Increase in thermal distribution takes place for higher Eckert number while thermal boundary layer thickness depicts opposite trend in this case. Concentration boundary layer thickness enhances while concentration profile declines for higher Schmidt number. Velocity distribution is found to be incremented for intense melting process. Higher dimensionless activation energy parameter is analyzed to be responsible for growing up concentration field.

Formation and evolution of laminar thermal structures: correlation to the thermal boundary layer and effects of heating time

We report an experimental study of the formation and evolution of laminar thermal structures generated by a small heat source, with a focus on their correlation to the thermal boundary layer and effects of heating time $t_{heat}$ . The experiments are performed over the flux Rayleigh number ( $Ra_f$ ) range $2.1\times 10^6 \leq Ra_f \leq 3.6\times 10^{7}$ and the Prandtl number ( $Pr$ ) range $28.6 \leq Pr \leq 904.7$ . The corresponding Rayleigh number ( $Ra= t_{heat}\,Ra_{f}/\tau _0\,Pr$ ) range is $900 \leq Ra \leq 4\times 10^{4}$ , where $\tau _0$ is a diffusion time scale. For thermal structures generated by continuous heating (i.e. starting plumes), their formation process exists three characteristic times that are well reflected by changes in the thermal boundary layer thickness. These characteristic times, denoted as $t_{emit}$ , $t_{recover}$ and $t_{static}$ , correspond to the moments when the plume emission begins and completes, and when the thermal boundary layer becomes quasi-static, respectively. Their $Ra_f$ – $Pr$ dependencies are found to be $t_{emit}/\tau _0\sim Ra_f^{-0.41}\,Pr^{0.41}$ , $t_{recover}/\tau _0\sim Ra_f^{-0.48}\,Pr^{0.48}$ and $t_{static}/\tau _0\sim Ra_f^{-0.49}\,Pr^{0.33}$ , respectively. Thermal structures generated by finite $t_{heat}$ exhibit similar evolution dynamics once $t_{heat} \ge t_{emit}$ , with the accelerating stage behaving like starting plumes and the decay stage like thermals (i.e. a finite amount of buoyant fluids). It is further found that their maximum rising velocity experiences a transition in the $Ra$ -dependence from $Ra$ to $(Ra\ln Ra)^{0.5}$ at $Ra \simeq 6000$ ; and their maximum acceleration reaches the value of starting plumes at $t_{heat}\simeq t_{recover}$ , and remains unchanged for larger $t_{heat}$ . In particular, the maximum rising velocity for the cases with $t_{heat} = t_{recover}$ follows a scaling relation $Ra_f^{0.37}\,Pr^{-0.37}$ , in contrast to the relation $Ra_f^{0.48}\,Pr^{-0.48}$ for starting plumes. This study provides a more comprehensive understanding of laminar thermal structures, which are relevant to a range of processes in nature and laboratory systems such as Rayleigh–Bénard convection.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Theoretical analysis and numerical study of natural convection inside combined solar chimney

AbstractSolar chimneys may induce natural ventilation through solar radiation. However, sufficient theoretical studies are needed as a basis to fully exploit passive design in practical green building design. In this work, we investigate the heat transfer properties of turbulent natural convective flows in a combined solar chimney with a thermal flux at the absorption wall by means of theoretical analysis and numerical simulations. Two different flow patterns have been found, one with a clear thermal boundary layer flow pattern and the other without, based on high Rayleigh numbers. For flow development in these two flow regimes, the transient scaling analysis is performed separately and the control mechanism for each phase is presented. Some new scale relationships are established to characterize the ventilation performance of solar chimneys, including thermal boundary layer thickness δT, velocity vT, mass flow m, and so on. For the distinct thermal boundary layers, δT,s ~ HΓ2/5/Bo1/5κ2/5, vT,s ~ Bo2/5κ4/5Γ1/5/H, m ~ ρBo1/5κ2/5Γ3/5. For nonobvious thermal boundary layers, vT,f ~ Bo1/3κ/H2/3W1/3, m ~ ρBo1/3κ/A2/3. The important scale relationships are validated using corresponding numerical simulation data, such as the mass flow rate scale M ~ (Γ/κ)3/5Bo1/5 in the distinct thermal boundary layer flow state, and so on. The air changes per hour and heat exchange efficiencies are calculated for a solar chimney with a fixed height‐to‐width ratio to provide a basis for the design of a solar chimney.

Analysis of boundary layer characteristics in supergravitational turbulent thermal convection

We investigate the boundary layer characteristics within annular centrifugal Rayleigh–Bénard convection (ACRBC) considering a Rayleigh number Ra∈[108,1011], a Prandtl number Pr = 10.7, and an inverse Rossby number Ro−1=16. Our study is based on the temperature and velocity data obtained from direct numerical simulations. Different from the flow over a flat plate, the ACRBC system bifurcates into three regions: the plume-impacting regions, plume-ejecting regions, and plume-sweeping regions, and all three regions are moving with the zonal flow. Our focus is primarily on the temperature dynamics within the plume-sweeping region, where the wind of large-scale circulation shears the boundary. We determine the transient thermal boundary layer thickness over time using the slope method, relying on the temperature curve's orientation relative to the wall. Notably, the probability density function distribution of the thermal boundary layer thickness is reminiscent of traditional RBC systems, albeit with a more extended exponential tail. Employing a dynamic frame based on time resampling, we discern that the temperature boundary layer traits align with the Prandtl–Blasius boundary layer theory. In conclusion, we show that the exponential decay index for the thermal boundary layer thickness harmonizes with the system's heat transfer scaling law. It is found that the ratio between the inner and outer boundary layer thickness remains stable, providing theoretical guidance for the design and control of the internal flow field of high-speed rotating machinery.

Multi-dimensional investigation of ceiling jet temperature characteristics beneath curved ceiling produced by fire in the utility tunnel

To study the temperature profile beneath the curved ceiling from a multi-dimensional perspective, an experimental investigation was conducted in utility tunnels with two different sizes, and a series of models were established to predict a two-dimensional longitudinal temperature profile and transverse temperature attenuation in this study. The prediction models for the two-dimensional longitudinal temperature profile were developed by modeling the vertical temperature distribution, thermal boundary layer thickness, Gaussian thermal layer thickness and maximum longitudinal temperature attenuation. Through the experimental validation on two sizes, it is found that the proposed prediction model can express the longitudinal temperature profile from a two-dimensional view within the relative error range of 20%. Besides, the prediction model for transverse temperature attenuation was established by the definition of characteristic tilt angle, and the three detailed expressions of this model were proposed according to different types of ceiling jets after impingement. The proposed prediction model for transverse temperature attenuation was also validated, and the verification results showed that the relative error of the transverse temperature attenuation prediction model can be controlled within a 25%. The developed prediction models in this study can be applied in the fire protection engineering of utility tunnels.

Time-resolved measurement of acoustic density fluctuations using a phase-shifting Mach-Zehnder interferometer.

Phase-shifting interferometry is one of the optical measurement techniques that improves accuracy and resolution by incorporating a controlled phase shift into conventional optical interferometry. In this study, a four-step phase-shifting interferometer is developed to measure the spatiotemporal distribution of acoustic density oscillations of the gas next to a rigid plate. The experimental apparatus consists of a polarizing Mach-Zehnder interferometer with a polarization camera capable of capturing four polarization directions in one shot image and it is used to measure the magnitude and the phase of density fluctuations through a duct of rectangular cross section connected to a loudspeaker. The results are compared with the well-established thermoacoustic theory describing the thermal coupling between acoustic oscillations and rigid boundaries, and the results show a very good agreement for various ratios of the (frequency-dependent) thermal boundary layer thickness to the plate spacing. This measurement technique could be advantageously employed to analyze more complex heat transfer processes involving the coupling of acoustic oscillations with rigid boundaries.

Analysis of Magnetohydrodynamic Free Convection in Micropolar Fluids over a Permeable Shrinking Sheet with Slip Boundary Conditions

The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the partial slip condition at the sheet, allowing a realistic representation of the fluid flow near the boundary. The governing equations for the flow, heat, and mass transfer are formulated using the conservation laws of mass, momentum, angular momentum, energy, and concentration. The resulting nonlinear partial differential equations are transformed into a system of ordinary differential equations using suitable similarity transformations. The numerical solutions are obtained using robust computational techniques to examine the influence of various parameters on the velocity, temperature, and concentration profiles. The impact of slip effects, micropolar fluid characteristics, and permeability parameters on the flow features and heat transfer rates are thoroughly analyzed. The findings of this investigation offer valuable insights into the behavior of micropolar fluids in free convection flows over permeable shrinking sheets with slip, providing a foundation for potential applications in various industrial and engineering processes. Key findings include the observation that the velocity profile overshoots for assisting flow with decreasing viscous force and rising magnetic effects as opposed to opposing flow. The thermal boundary layer thickness decreases due to buoyant force but shows increasing behavior with heat source parameters. The present result agrees with the earlier findings for specific parameter values in particular cases.

Multiple slips on Darcy–Forchheimer unsteady flow manifested with Cattaneo–Christov heat flux over a stretching sheet

This primary goal of this analysis is to investigate how several slips affect the flow, heat, and mass performance of Darcy–Forchheimer unstable behavior beyond a stretching sheet using a numerical analysis of the Soret effect. The novel constitutive model Cattaneo–Christov is illustrated to analyze the features of thermal relaxation time. The Cattaneo–Christov method is used to predict heat and mass transport. A surface that slanders and has varying thicknesses propels the flow. Through the use of local similarity transformations, the governing nonlinear partial differential equations reduce to the coupled ordinary differential equations and include the momentum, energy, and concentration equations. The altered ODEs are calculated numerically using the Runge–Kutta Fehlberg scheme and an efficient shooting procedure. The physical properties of the temperature, concentration, and fluid velocity profiles are shown visually and shed light on the change of several governing parameters. For example, in comparison to the classical Fourier’s heat model, our result suggests that the Cattaneo–Christov heat flux constitution has lower temperature and thermal boundary layer thickness. In the meantime, a high wall thickness parameter greatly upgrades the rate of heat transfer, and thermal relaxation has the opposite effect. Discussion is held regarding the effects of various miscellaneous variables on temperature, concentration, and velocity.

Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation

This article, motivated by hybrid magnetic coating manufacturing developments, utilizes a neural network-based computational program to study the dynamics of hybrid magnetic nanofluids with entropy generation. A new physico-chemo-mathematical model has been presented to simulate the hybrid magnetic nano-coating flow along a stretching surface to a porous medium with viscous heating. A Rosseland flux model is used for radiation heat transfer and Darcy’s model for the isotropic porous medium. The stretching sheet is porous, and wall suction or injection are possible. A robust neural network has been deployed to optimize the physical parameters controlling the transport characteristics of hybrid nanofluids. Specifically, two hybrid nanoparticle combinations are addressed, namely graphite oxide (GO)-molybdenum disulfide ( Mo S 2 ) and copper (Cu)-silicon dioxide ( Si O 2 ), both with engine oil as the base fluid. The dimensional boundary layer model is transformed via suitable scaling variables from a partial differential system into a dimensionless non-linear coupled ordinary differential system. The transformed boundary value problem is solved numerically with the BVP4C subroutine in the symbolic software MATLAB, which achieves exceptional accuracy. Validation with previous simpler studies is conducted and a good correlation is obtained. The neural network optimization analysis incorporates Bayesian regularization as the training algorithm. The Bejan entropy generation minimization (EGM) analysis shows that with increasing radiation parameter R d , both entropy generation rate and Bejan number are increased. Furthermore, an elevation in Brinkman number Br leads to an upsurge in entropy generation rate and a downtrend in the Bejan number. The numerical solution of the boundary value problem reveals that with an increment in nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , surface injection parameter ( s < 0 ) , Eckert number Ec and radiation parameter R d and with a decrement in suction parameter ( s > 0 ) and Prandtl number Pr , there is a strong enhancement in temperature magnitude and thermal boundary layer thickness. With greater nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and a reduction in thermal buoyancy parameter λ , strong flow deceleration is induced, and momentum boundary layer thickness is increased. The skin friction coefficient is substantially boosted with lower values of magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and higher values of thermal buoyancy parameter λ . There is a significant decrement also computed in Nusselt number with a greater radiation parameter R d . The simulations provide a good benchmark for future extensions that may consider non-Newtonian behavior.

Bi-directional Forced Convective Stagnation Points Flow of Oldroyd-B Liquid with Joule Heating Effects: A Finite Difference Simulations

The impact of Joule heating for the three-dimensional stagnation point flow of non-Newtonian liquid (namely Oldroyd-B) nanomaterial has been inspected. The influence of mixed convection and the magnetic force is also considered. The flow is induced by the bidirectional stretched surface which moves linearly. The partial differential equations for the developed model are altered into dimensionless statements first. The numerical simulations with the implementation of a finite difference scheme are used for the numerical description. The physical description of parameters is presented against the flow parameters. The results reveal that there is a reverse change in velocity observed for both the relaxation time constant and the retardation constant. Furthermore, the heat transfer rate decreases as the ratio parameter increases. The thickness of the boundary layer increases due to the retardation time and can also be regulated by the application of a magnetic field. An increase in the magnetic parameter leads to an enhancement in temperature and an increase in thermal boundary layer thickness.