Thermal Boundary Layer Thickness Research Articles

Effect of Cattaneo-Christov approximation for viscoelastic fluid with carbon nanotubes on flow and heat transfer.

The current work studies the motion of viscoelastic liquid saturated with carbon nanotubes over a stretching surface in a Darcy porous medium analytically below an influence of Cattaneo-Christov heat flux. The carbon nanotubes (CNTs) act as nanoparticles which are then appended into the base fluid. Water and kerosene are used as a base fluid with two types of CNTs, namely, Single-wall carbon nanotubes and Multiwall carbon nanotubes. Carbon nanotubes possess a wide range of industrial and biomedical applications including energy production, nuclear reactor cooling, and galaxy cooling applications because they can expand the thermal and mechanical properties of base things. As a result, the carbon nanotubes used in the mentioned fields are being investigated for their potential in heat transfer applications. Governing equations formulated using the Partial differential equations have converted to Ordinary differential equations exhausting the appropriate comparison transformation process. An influence of some relevant constraints on velocity and temperature is evaluated in details. The Cattaneo-Christov heat transfer model is utilized to investigate the heat transfer individualities with varying thermal conductivity consuming the attributes of the Appell hypergeometric function. The impacts of the emerging parameters on the profiles are depicted through graphical representations and analytically constructed tables. Considering its usefulness in modulating temperature distribution in different industrial application, including solar collector design, electronic cooling, building ventilation, etc. According to our findings, the temperature profile exhibits an enhancement with the thermal radiation parameter and the viscous-elastic fluids. In addition, when compared to the classical Fourier's law of heat conduction, the temperature profile and thermal boundary layer thickness for the Cattaneo-Christov heat flux model are lower.

Heat transport and temperature boundary-layer profiles in closed turbulent Rayleigh–Bénard convection with slippery conducting surfaces

We report direct numerical simulations (DNS) of the Nusselt number$Nu$, the vertical profiles of mean temperature$\varTheta (z)$and temperature variance$\varOmega (z)$across the thermal boundary layer (BL) in closed turbulent Rayleigh–Bénard convection (RBC) with slippery conducting surfaces ($z$is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length$L = H$and width$W = H/4$($H$is the sample height), and two-dimensional rectangles with aspect ratios$\varGamma \equiv L/H = 1$and$10$. The slip length$b$for top and bottom plates varied from$0$to$\infty$. The Rayleigh numbers$Ra$were in the range$10^{6} \leqslant Ra \leqslant 10^{10}$and the Prandtl number$Pr$was fixed at$4.3$. As$b$increases, the normalised$Nu/Nu_0$($Nu_0$is the global heat transport for$b = 0$) from the three samples for different$Ra$and$\varGamma$can be well described by the same function$Nu/Nu_0 = N_0 \tanh (b/\lambda _0) + 1$, with$N_0 = 0.8 \pm 0.03$. Here$\lambda _0 \equiv L/(2Nu_0)$is the thermal boundary layer thickness for$b = 0$. Considering the BL fluctuations for$Pr>1$, one can derive solutions of temperature profiles$\varTheta (z)$and$\varOmega (z)$near the thermal BL for$b \geqslant 0$. When$b=0$, the solutions are equivalent to those reported by Shishkinaet al.(Phys. Rev. Lett., vol. 114, 2015, 114302) and Wanget al.(Phys. Rev. Fluids, vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For$b > 0$, the derived solutions are in excellent agreement with our DNS data for slippery plates.

A novel nonlinear diffusion model of magneto-micropolar fluid comprising Joule heating and velocity slip effects

The impact of heat-conduction and substantial rheological model of non-Newtonian micropolar fluid, which usually features linear reflection, could not properly grab the true performance. A novel nonlinear substantial model of micropolar fluid with magnetohydrodynamic, viscous dissipation, and Joule heating is applied for the heat transfer and boundary layer flow. Like shear thinning or thickening fluids, a nonlinear power-law model describes the angular velocity, which effectively explains the non-Newtonian attributes of micropolar fluids, and it is generalized successfully by the n-diffusion theory. Further, we have used the velocity slip conditions. The non-similar equations are derived and solved numerically by bvp4c MATLAB built-in function. The results are verified in the limiting case. Graphical results for the heat and fluid flow and also for the Nusselt number help to see the impact of emerging parameters. It is observed through this study that the skin friction and Nusselt number both decline for the increasing power-law index and the micro-rotational and transient velocity both get slow for the higher slip parameter. Further, the thermal boundary layer thickness dramatically reduces for the very large Prandtl number.

Numerical study on the effect of fin length variation on the thermal performance of a bus duct conductor

This article presents a finite volume-based simulation study on the effect of fin length variation on the thermal performance of a bus duct conductor. The study was conducted by developing a numerical model using ANSYS FLUENT. IEC 60439-1 and IEC 60439-2 standards were employed as a guideline to conduct the experimental setup. It was found that increasing the fin length increases the total heat transfer rate. This is due to an increase in the surface area exposed to the fluid and a decrease in the thermal boundary layer thickness. However, it was observed that longer fin lengths contributed to greater frictional forces on the fluid that resulted in a drop in convective heat transfer coefficient. The current numerical study is expected to provide a better understanding of the effect of fin length on the thermal performance of a bus duct conductor.

NUMERICAL STUDY OF THE INFLUENCE OF TEMPERATURE-DEPENDENT VISCOSITY ON THE UNSTEADY LAMINAR FLOW AND HEAT TRANSFER OF A VISCOUS INCOMPRESSIBLE FLUID DUE TO A ROTATING DISC

In this article, the effect of temperature-dependent viscosity (TVD) on the unsteady laminar flow and heat transfer (HT) of a viscous incompressible fluid due to a rotating disc (RD) has been investigated numerically by exploiting an in-house numerical code. A set of time-dependent, axisymmetric, and non-linear partial differential equations which govern the fluid flows and heat transfer are reduced to non-linear local non-similarity ordinary differential equations by introducing a newly developed group of transformations for different time regimes. Three different solution methods, such as, (i) perturbation solution method for small t, (ii) asymptotic solution method for large t, and (iii) implicit finite difference method for the entire t regime, have been applied to solve the resulting equations treating t as the time-dependent rotating parameter. The local radial skin friction, tangential skin friction and the heat transfer are computed at the surface of the disc for different numerical parameters, such as, Prandtl number, Pr and the viscosity-variation parameter, e. Besides, the key dimensionless quantities such as velocity and temperature profiles, which are inherently linked with the boundary layer thickness, are presented graphically for different values of e while Pr = 0.72. It is found that the dimensionless radial, tangential and axial velocity profiles decrease as e increases, and consequently, the momentum boundary layer thickness is decreased. On the other hand, the non-dimensional temperature profiles are increased owing to the increasing values of e, and this effect eventually leads to a small increment in the thermal boundary layer thickness.

Computational treatment of MHD Maxwell nanofluid flow across a stretching sheet considering higher-order chemical reaction and thermal radiation

The present analysis reports a computational study of Magnetohydrodynamic (MHD) flow behaviour of 2D Maxwell nanofluid across a stretched sheet in appearance of Brownian motion. The substantial term thermal radiation and chemical reactions have been employed extensively in the current research. Nanofluids are usually chosen by researchers because of their rheological properties, which are important in determining their appropriateness for convective heat transfer. The present research reveals that the fluid velocity augments for the enhanced values of all the parameters. Heat source, as well as the radiation parameters, ensure that there is enough heat in the fluid, which implies escalation of the thermal boundary layer thickness by accruing radiation parameter. Moreover, streamlines and isotherms have been investigated for the different parametric values. The suggested model is valuable because it has a wide range of applications in domains including medical sciences (treatment of cancer therapeutics), microelectronics, biomedicine, biology, and industrial production processes.

Cattaneo-Christov dual diffusive non-Newtonian nanoliquid flow featuring nonlinear convection

A theoretical study is presented of the transport characteristics in double diffusive tangent hyperbolic (non-Newtonian) nanofluid boundary layer flow from a stretching flat surface. The Cattaneo–Christov (non-Fourier and non-Fickian) double diffusion model is deployed in the formulations for energy and species conservation, to determine more precisely temperature and concentration distributions with thermal and solutual relaxation times. Non–linear mixed convection and heat generation/absorption are included. The nanofluid approach combines Brownian motion and thermophoresis. Suitable transformations are deployed to render the nonlinear partial differential system into a system of dimensionless coupled ordinary nonlinear differential equations. The non-dimensional boundary value problem is then solved with the homotopic analysis method (HAM). The distributions of velocity, temperature and concentration of nanoparticles are depicted and investigated for the effects of multiple emerging parameters. Velocity is reduced (and momentum boundary layer thickness elevated) with increasing power–law index and Weissenberg number whereas velocity is elevated (and momentum boundary layer thickness reduced) with increment in mixed convection variable. Temperature is suppressed (and thermal boundary layer thickness depleted) with increasing thermal relaxation variable, heat sink parameter, Prandtl number whereas temperature is enhanced (and thermal boundary layer thickness boosted) with greater heat source parameter, Brownian motion parameter and thermophoresis parameter. Nanoparticle concentration is depleted (and concentration boundary layer thickness reduced) with greater Schmidt number and Brownian motion parameter whereas the opposite effect is induced with greater thermophoresis parameter and solutal relaxation time. Skin friction is strongly reduced with increasing values of nonlinear thermal and concentration convection variables. The simulations are relevant to nano-polymer coating operations.

Unsteady stagnation-point flow of CNTs suspended nanofluid on a shrinking/expanding sheet with partial slip: multiple solutions and stability analysis

The purpose of the study of single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) mixed water-based nanofluid having unsteady stagnation-point flow on shrinking/expanding sheet with velocity and thermal slip effects is to decode the heat transfer mechanism to know the high cooling rate criteria. Governing boundary layer coupled partial differential equation (PDEs) are converted into ordinary ones. The transformed equations are numerically solved by shooting method with RK-4 scheme. The impacts of different parameters are described graphically and a comparison between current and previous results is made in tabular form. Existence of multiple solutions along with unique solution appears for specific cases of shrinking and expanding velocities. The investigation also reveals that SWCNT-nanoparticles have more dominating heat and momentum transfer rates than MWCNT-nanoparticles. Velocity slip delays the boundary layer separation, but maximum surface drag-force does not alter. Thermal slip and unsteadiness reduce heat transfer rate, whereas velocity slip enhances it. For high shrinking velocity compared to free stream velocity, the surface cooling rate drops down with Prandtl number and thermal boundary layer thickness significantly reduces for all types of nanofluids and for both solution branches. For both nanofluids, the temperature near the sheet decreases with thermal slip. For non-uniqueness of the similarity solution, a linear stability analysis is conducted and it verifies that upper branch of the obtained solutions is stable, while lower branch is unstable for high shrinking velocity and the unique solution is stable for expanding and low shrinking velocities.

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

AbstractThe current article focuses on mass and thermal transfer analysis of a two‐dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature‐dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.

On the links between unsteady separation and Nusselt number deterioration during vortex-wall interaction

A CFD study of an axisymmetric vortex ring interacting with a flat, constant-temperature, heated wall is conducted to study the physical nature of the mechanisms leading to deterioration in wall heat transfer due to the unsteady boundary layer separation resulting from vortex-wall interaction. The study utilizes a supplemental computation of a hypothetical flow configuration in which slip is allowed at the heated wall to eliminate separation of the boundary layer during the interaction. Comparison between the physical and hypothetical cases enables “isolation”, and hence understanding of the role of separation in the deterioration of Nusselt number (Nu). It is found that the nature of the near-wall upwash velocity leading to Nu deterioration is fundamentally altered by the presence of spearation. Without separation, the upwash is driven directly by the primary vortex ring. In contrast, with separation, the near-wall upwash is modified significantly by blockage from boundary layer separation and interaction with the secondary vortex ring. The modification is associated with the development of a near-wall “sublayer” that is responsible for the deterioration of Nu independent of the behavior of the overall thermal boundary layer thickness.

MHD boundary layer flow of couple-stress fluid over a bidirectional moving surface with non-Fourier heat flux

This work is addressed to the study of MHD boundary layer couple-stress fluid flow considering the non-Fourier Cattaneo-Christov hyperbolic heat transfer model over a bidirectional movable surface. The group of continuous symmetry transformations is adopted to determine invariant solutions of governing equations for boundary layer fluid flow with heat transfer. Using Lie symmetry analysis, the governing equations having boundary conditions are converted into self-similar equations under a group of transformations only when initial prescribed velocity distributions are in linear form. The similar velocity and temperature profiles are obtained and the effects of the magnetic field and hyperbolic heat-flux are explored. The study revealed that the flow boundary layer thickness becomes thicker due to the increase of the couple-stress parameter, while the thermal boundary layer thickness becomes thinner for increasing relaxation time of heat-flux. The couple-stress parameter acts in the flow field in opposite style to the magnetic parameter. Also, for an increase in the couple-stress parameter and the thermal relaxation-time parameter, the higher wall heat transfer is exhibited.

Particle convective heat transfer near the wall in a supercritical water fluidized bed by single particle model coupled with CFD-DEM

Supercritical water fluidized bed (SCWFB) is a promising reactor to gasify biomass or coal. Its optimization design is closely related to wall-to-bed heat transfer, where particle convective heat transfer plays an important role. This paper evaluates the particle convective heat transfer coefficient (hpc) at the wall in SCWFB using the single particle model. The critical parameters in the single particle model which is difficult to get experimentally are obtained by the computational fluid dynamics-discrete element method (CFD-DEM). The contact statistics related to particle-to-wall heat transfer, such as contact number and contact distance, are also presented. The results show that particle residence time (τ), as the key parameter to evaluate hpc, is found to decrease with rising velocity, while increase with larger thermal boundary layer thickness. τ follows a gamma function initially adopted in the gas–solid fluidized bed, making it possible to evaluate hpc in SCWFB by a simplified single particle model. The theoretical predicted hpc tends to increase with rising thermal gradient thickness at a lower velocity (1.5 Umf), while first decreases and then increases at higher velocity (1.75 and 2 Umf). hpc occupies 30%–57% of the overall wall-to-bed heat transfer coefficient for a particle diameter of 0.25 mm. The results are helpful to predict the overall wall-to-bed heat transfer coefficient in SCWFB combined with a reasonable fluid convective heat transfer model from a theoretical perspective.

Fluid flow over a vertical stretching surface within a porous medium filled by a nanofluid containing gyrotactic microorganisms

In this paper, the boundary layer flow of a nanofluid containing gyrotactic microorganisms over a vertical stretching surface embedded in a porous medium. The fluid contains gyrotactic microorganisms. Nonlinear velocity stretches the surface, and the surface is isothermal. The governing boundary layer equations for steady, laminar, and two-dimensional are transformed into ordinary differential equations using a suitable similarity transformation. The fourth/fifth-order Runge–Kutta method solved the system of equations after linearization. The shooting method guesses the missing boundary conditions. Pertinent results are presented graphically and discussed quantitatively with respect to variation in the controlling parameters such as bioconvection Lewis number (Lb), Lewis number (Le), Peclet Lewis number (Pe), buoyancy ratio parameter (Nr), bioconvection Rayleigh number(Rb), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Richardson number (Ri), motile parameter (sigma), porosity parameter (user2{ }lambda), and Prandtl number (Pr) on dimensionless velocity, temperature, nanoparticle concentration, and microorganisms conservation. It is observed that increasing the porosity parameter retards the thermal boundary layer thickness which from application point of view, it is obvious that the surface cooling effect is enhanced and thus nanofluids are appropriate as heat transfer fluids. The comparison with the previous validates the applied numerical scheme.

Characterization of laminar and turbulent supercritical carbon dioxide slot jet impingement heat transfer

Supercritical carbon dioxide (sCO2) has recently been proposed as a promising alternative to conventional fluids for thermal management because of its unique thermophysical properties near the critical point. Jet impingement is also recognized as one of the most effective configurations for high intensity heat transfer. Therefore, leveraging the favorable thermophysical properties of sCO2 in microscale jet impingement may lead to high performance thermal management solutions. However, the effects of thermophysical property variations in the pseudo-critical temperature range on the flow and heat transfer behavior in such configurations is not well understood. The present investigation seeks to address this need through computational simulations of laminar and turbulent slot sCO2 jet impingement. Large eddy simulations (LES) are validated and employed for turbulent cases. The studied range of conditions span reduced pressures of Pr=1.03−1.10, Reynolds numbers Re=225−11,000, dimensionless jet lengths H/W=2−4, jet inlet temperatures Tin=294−330K, and impingement plate temperatures Tplate=270−370K. The turbulent simulations reveal varying spatial distributions of heat transfer coefficient with different jet and plate temperatures, which can be explained in terms of the temperature-dependent properties of sCO2. Heat transfer deterioration (HTD) is observed for both laminar and turbulent flows. HTD is found to be most significant in the stagnation zone, and its relative magnitude decreases downstream more sharply for turbulent flows than laminar. Heat transfer enhancement (HTE) is observed when both the jet inlet and impingement plate temperatures are at opposite ends of the pseudo-critical temperature range. For cooling applications, HTD and HTE effects can be explained in terms of opposing temperature-dependent variations in boundary layer thermal conductivity and overall thermal boundary layer thickness with Prandtl number. Considering the dependence of thermophysical properties on Pr, a thermal management system control strategy is proposed in which Pr is adjusted depending on Tplate to achieve optimal performance over varying operating conditions.

Entropy analysis in a second‐grade nanoliquid influenced by an exponential space‐dependent heat source and Arrhenius activation energy

AbstractAddressing the second‐grade nanofluid flow over a porous stretching sheet based on entropy generation is done in this study. In the mathematical modeling, the revised Buongiorno model is utilized. Employing exponential space‐dependent heat generation and Heat transfer subject to melting effect is implemented. Energy and concentration expressions are retained based on the impact of activation energy, Joule heating, nonlinear thermal radiation, and viscous dissipation. Implementation of solutions for a standard transformation, governing equations, and the numerical procedure is done. Several governing parameters are discussed based on the effect of comprehensive effects of the flow region. A thicker thermal boundary layer is obtained by increasing the magnetic strength and Brownian movement. Thermophoresis increases similarly while the trend takes place, and for the melting parameter, the reverse order is noted. Melting parameter increases with increase in entropy generation rate and Brinkman number increases with reduction in Bejan number. In the literature, it is found that the situation is limited for the obtained results in the model. Higher entropy generation rates are exhibited for the demonstration of magnetic force. From the results, it is observed that the design parameters will consequently optimize the heat transfer in the assessment of industrial processes.

Entropy analysis with the Cattaneo–Christov heat flux model for the Powell–Eyring nanofluid flow over a stretching surface

The recent trend of research in fluids' transport along with heat transfer processes is focused on entropy minimization in thermal systems. This leads to the introduction of nanofluids as operating fluids, use of non-Newtonian fluid models, the type, shape, and sizes of nanoparticles, and the effect of variable thermophysical properties. In the present research, a numerical investigation is carried out for the entropy generation in a time-dependent, thermodynamically stable Powell–Eyring nanofluid flow over a flat, porous and non-linear horizontal stretching surface. The Cattaneo–Christov model for the heat flux is assumed for the thermal boundary layer analysis. The effects of the uniform thermal radiation, nanoparticle's shape and the boundary slip is also included in the mathematical model. The governing equations are abridged under the assumptions of the usual boundary layer flow and the Roseland approximations. Partial differential equations are first transformed to a system of ordinary differential equations by using appropriate similarity transformations. The Keller box scheme is then adopted to find the approximate solutions for the reduced ordinary differential equations. Two different classes of nanofluids, copper-water () and titanium-water () are considered for our analysis. Numerical results are presented graphically to study the effect of various thermophysical parameters. Numerical results show material parameters, velocity slip, nanoparticle concentration and fluid injection increase the thermal boundary layer thickness and reduce the rate of heat transfer at the surface. Moreover, increasing the strength of these reduces fluid movement within the boundary layer and increases the overall entropy of the system.

Aligned Magnetohydrodynamics Free Convection Flow of Magnetic Nanofluid over a Moving Vertical Plate with Convective Boundary Condition

Due to its substantial applications in physics, chemistry, and engineering, some emphasis has been given in recent years to explore the boundary layer flow of magnetohydrodynamic (MHD) nanofluids. The numerical study is conducted to investigate the behaviour of MHD free convection flow of magnetic nanofluids over a moving vertical plate with convective boundary conditions by taking a few types of parameters into consideration. The similarity transformation was used to reduce the partial differential governing equations into ordinary differential equations. Then, the reduced equations were solved using fourth-fifth order Runge–Kutta–Fehlberg and coded into Maple Software. The results of velocity and temperature profiles were illustrated graphically while the results of skin friction coefficient and Nusselt number were presented in tabulated data. As a result, inclination angle of magnetic field parameter, magnetic interaction parameter, Grashof number and Biot number improve the velocity field and lowers the momentum boundary layer thickness. However, the nanoparticle volume fraction parameter, and the Biot number parameter boost the temperature field and raise the thermal boundary layer thickness. The Nusselt number of the moving plate with the flow is the highest, whereas the skin friction coefficient of the moving plate against the flow is the highest. Fe3O4-kerosene has a better influence to the velocity and temperature profiles as well as skin friction coefficient and Nusselt number.

Chemically reactive Maxwell nanoliquid flow by a stretching surface in the frames of Newtonian heating, nonlinear convection and radiative flux: Nanopolymer flow processing simulation

AbstractThe effects of a chemical reaction and radiative heat flux in a nonlinear mixed thermo-solutal convection flow of a viscoelastic nanoliquid from a stretchable surface are investigated theoretically. Newtonian heating is also considered. The upper-convected Maxwell (UCM) model is deployed to represent the non-Newtonian characteristics. The model also includes the influence of thermal radiation that is simulatedviaan algebraic flux model. Buongiorno’s two-component nanofluid model is implemented for thermophoretic and Brownian motion effects. Convective thermal and solutal boundary conditions are utilized to provide a more comprehensive evaluation of temperature and concentration distributions. Dimensionless equations are used to create the flow model by utilizing the appropriate parameters. The computed models are presented through a convergent homotopic analysis method (HAM) approach with the help of Mathematica-12 symbolic software. Authentication of HAM solutions with special cases from the literature is presented. The impact of various thermophysical, nanoscale and rheological parameters on transport characteristics is visualized graphically and interpreted in detail. Temperatures are strongly enhanced with Brownian motion and thermophoresis parameters. Velocity is boosted with the increment in the Deborah viscoelastic number and mixed convection parameter, and the hydrodynamic boundary layer thickness is reduced. A stronger generative chemical reaction enhances concentration magnitudes, whereas an increment in the destructive chemical reaction reduces them and also depletes the concentration boundary layer thickness. Temperature and concentration are also strongly modified by the conjugate thermal and solutal parameters. Greater radiative flux also enhances the thermal boundary layer thickness. Increasing the Schmidt number and the Brownian motion parameter diminish the concentration values, whereas they elevate the Sherwood number magnitudes,i.e.enhance the nanoparticle mass transfer rate to the wall.

Space-fractional heat transfer analysis of hybrid nanofluid along a permeable plate considering inclined magnetic field

In this study, the Caputo space-fractional derivatives of energy equation are used to model the heat transfer of hybrid nanofluid flow along a plate. The plate is considered permeable and affected by an inclined magnetic field. We use the space-fractional derivative of Fourier’s law to communicate between the nonlocal temperature gradient and heat flux. The hybrid nanofluid is formed by dispersing graphene oxide and silver nanoparticles in water. The new fractional integro-differential boundary layer equations are reduced to ordinary nonlinear equations utilizing suitable normalizations and solved via a novel semi-analytical approach, namely the optimized collocation method. The results reveal that the increment of the order of space-fractional derivatives and the magnetic inclination angle increase the Nusselt number. Also, an increase in the order of space-fractional derivatives leads to a thicker thermal boundary layer thickness resulting in a higher temperature. It is also found that the temperature of the fluid rises by changing the working fluid from pure water to single nanofluid and hybrid nanofluid, respectively. What is more, the proposed semi-analytical method will be beneficial to future research in fractional boundary layer problems.

Computational Framework of Magnetized MgO-Ni/Water-Based Stagnation Nanoflow Past an Elastic Stretching Surface: Application in Solar Energy Coatings.

In this article, motivated by novel nanofluid solar energy coating systems, a mathematical model of hybrid magnesium oxide (MgO) and nickel (Ni) nanofluid magnetohydrodynamic (MHD) stagnation point flow impinging on a porous elastic stretching surface in a porous medium is developed. The hybrid nanofluid is electrically conducted, and a magnetic Reynolds number is sufficiently large enough to invoke an induced magnetic field. A Darcy model is adopted for the isotropic, homogenous porous medium. The boundary conditions account for the impacts of the velocity slip and thermal slip. Heat generation (source)/absorption (sink) and also viscous dissipation effects are included. The mathematical formulation has been performed with the help of similarity variables, and the resulting coupled nonlinear dimensionless ordinary differential equations have been solved numerically with the help of the shooting method. In order to test the validity of the current results and the convergence of the solutions, a numerical comparison with previously published results is included. Numerical results are plotted for the effect of emerging parameters on velocity, temperature, magnetic induction, skin friction, and Nusselt number. With an increment in nanoparticle volume fraction of both MgO and Ni nanoparticles, the temperature and thermal boundary layer thickness of the nanofluid are elevated. An increase in the porous medium parameter (Darcy number), velocity slip, and thermal Grashof number all enhance the induced magnetic field. Initial increments in the nanoparticle volume fraction for both MgO and Ni suppress the magnetic induction near the wall, although, subsequently, when further from the wall, this effect is reversed. Temperature is enhanced with heat generation, whereas it is depleted with heat absorption and thermal slip effects. Overall, excellent thermal enhancement is achieved by the hybrid nanofluid.