Convection Of Fluid Research Articles

First order chemical reaction response in mixed convective Falkner-Skan Sutterby fluid with Cattaneo-Christov heat and mass flux model

The complex phenomenon of heat transfer plays a pivotal role in a broad spectrum of mechanical and industrial applications, ranging from space and nuclear reactor cooling to medicinal applications like magnetic drug targeting, energy production, heat conduction in biological tissues, among others. Historically, Fourier's law of heat conduction has served as a predictive model for heat transfer in numerous practical scenarios. However, this model's limitation is its generation of a parabolic energy expression, implying an immediate influence on the system by any initial disturbance. Numerous researchers have attempted to address this issue, leading to the Cattaneo's modification to Fourier's law, which introduces a relaxation time for heat flux, meaning the time needed to achieve stable heat conduction following the imposition of a temperature gradient. Christov later tweaked this model into a material invariant version, integrating the upper-connected derivative from the Oldroyd model. These models, now collectively termed as the Cattaneo-Christov (CC) model, form the core of the present study. In this study, we explore the mixed convective MHD Falkner-Skan Suttberby nanofluid flow towards a wedge surface, in the presence of a mixed convection. A two-phase nanofluid based C–C model is utilized to apply the nano-concept. The nonlinear equation system is solved using the bvp4c technique in MATLAB. The effects of various parameters including the magnetic field strength, wedge angle, nanoparticle volume fraction, and Prandtl number on the velocity and temperature profiles are discussed. The results show that the velocity increases with the magnetic parameter, wedge angle, and nanoparticle fraction, while the temperature decreases or increases depending on the suction or injection conditions. The Nusselt numbers and solutal transport rate are also reported for different parameter values. Overall, the study demonstrates that the non-Fourier C–C model yields significantly different solutal and heat transfer characteristics compared to the classical Fourier law. The results provide useful insights into the heat transfer behavior of nanofluids in stagnation point flows over geometries with complex shapes, which have practical applications in areas such as aerodynamics and thermal management of electronic devices.

Effects of Activation Energy Diffusion Thermo and Nonlinear Thermal Radiation on Mixed Convection Casson Fluid Flow Through a Vertical Cone with Porous Media in the Presence of Brownian Motion and Thermophoresis

In this paper, analyze the impact of Activation energy, Diffusion thermo and nonlinear thermal radiation of mixed convection casson fluid flow through a vertical cone with porous material in the presence of Brownian and thermophoresis has been studied. Numerical techniques, namely Runge–Kutta integration and the shooting method, were applied to obtain solutions to similarity-transformed equations governing continuity, momentum, energy and concentration. The study examined the distributions of flow velocity, temperature and concentration under the interactive effects of the fluid. The results revealed that the activation energy of the Arrhenius equation plays an important role in fluid transport mechanisms within a chemically reactive system involving the Soret effect for a low-Schmidt-number fluid. When the activation energy parameter E was greater within the range 0 < E < 5, the wall shear stress was stronger, heat transfer rate increased, and mass transfer rate decreased.

Dissolution-driven convection of low solubility fluids in porous media

Geological sequestration represents a promising strategy for storing CO2. In order to further elucidate this process, we simulated the dissolution-driven convection of a CO2-brine system with a free interface in a porous medium, based on a novel Darcy-Cahn-Hilliard model that accounts for the low solubility of CO2 with brine. We consider a range of unstable Rayleigh numbers Ra, and we derive a quantitative relationship for the dimensionless solute flux. This flux exhibits distinctly different behaviors during the various stages of the flow. In particular, during the free convection stage, larger Ra-values result in a moderate decrease of the solute flux, while the solute flux is approximately independent of Ra during the constant flux stage. In order to evaluate the solute flux during the shutdown stage, we employ simulations in the two-sided Rayleigh-Bénard cell configuration. With a correction factor a=0.67 to account for the damping effect of the bottom boundary, the model can reproduce the solute flux during the shutdown stage. By accounting for the effects of partial miscibility, the simulation approach developed here holds the potential to yield more accurate estimates of the solute flux in the context of CO2 sequestration and related applications.

The heat transfer enhancement of the converging-diverging tube in the latent heat thermal energy storage unit: Melting performance and evaluation

Latent heat thermal energy storage (LHTES) has emerged as a promising approach to settle the intermittent and fluctuant of renewable energy but heat transfer enhancement is necessary due to the low thermal conductivity of the phase change material (PCM). This study numerically investigated the heat transfer enhancement effect of the typically converging-diverging tubes (CDTs) inside a shell-and-tube LHTES unit. The evolution of melting behavior was analyzed to describe the heat transfer enhancement mechanism of the CDT. Based on the enhancement effect and pump power consumption associated with the CDT, a modified performance evaluation criterion (PEC) was established to evaluate the feasibility of current designs. The arrangement of CDTs was found to significantly improve the heat transfer performance of LHTES. The triangle CDT exhibited the maximum melting time reduction of 20.77%. The heat transfer enhancement effect of CDT was attributed to the enhanced natural convection of PCM and forced convection of heat transfer fluid. The analysis of the evaluation ensures the feasibility of the new criterion and its specific application field. Moreover, it was worth to note that the triangle CDT achieved the best cost performance of 0.363 ω, where ω represented the return factor.

Steam-side heat transfer analysis in spirally corrugated tube for grate furnace superheater

In the case of low Reynolds number, the structure of the spirally corrugated tube will make the solid particles in the fluid be affected by the centrifugal force, and be more evenly distributed in the fluid to achieve anti-fouling effect. Therefore, it can be used in heat exchangers with serious fouling problems to improve heat exchange efficiency. In this paper, the first stage low-temperature superheater in the grate furnace is selected as application equipment. The local resistance coefficient, local Nusselt number and local heat flux are analyzed, the thermal-hydraulic characteristics of different sample points are evaluated. Combinatorial method of central composite design and Latin hypercube design is used to select four representative sample points, and effect of the corrugation pitch ratio and depth ratio on the convective heat transfer intensity, fluid resistance and fluid work consumption of the steam side is studied. The research results show that as the corrugation depth increases, the local heat transfer coefficient in the circumferential direction increases, and more heat is transferred from the flue gas to the steam, but the pump power consumed in the flow process has also increased. Due to the existence of spiral structure, the local heat flux density of the wall is symmetrically distributed in the circumferential direction, which represents that the temperature gradient increases, and the heat flow is improved.

Lattice Boltzmann simulation of cavity flows driven by shear and internal heat generation for both Newtonian and viscoplastic fluids

Following our recent investigation [G. Kefayati, “Internally heated convection of viscoplastic fluids in enclosures using a lattice Boltzmann method,” Phys. Fluids 35, 013108 (2023)], this paper centers on exploring the influence of shear on internally heated convection and its flow within a square cavity. The study delves into the behavior of both Newtonian and viscoplastic fluids within this setup. The cavity features two vertical side walls that consistently maintain low temperatures, serving as isotherms. Meanwhile, the horizontal walls are adiabatic and provide thermal insulation. In this work, we present dimensional macroscopic equations and introduce innovative non-dimensional macroscopic equations. To generate shear, the top lid is continuously translated, and we quantify its intensity using the corresponding Richardson number. For investigating the viscoplastic behavior and defining the yielded (fluid) and unyielded (solid) zones, we employ an exact Bingham model, which relies on a unique tensor. To tackle the problem effectively, we develop a dimensionless lattice Boltzmann method to derive the specified macroscopic non-dimensional equations and subsequently solve the fluid motion scenario. Throughout the study, we introduce modified non-dimensional parameters, including the introduced yield number (Y), Reynolds number (R) ranging from 0 to 400, Prandtl number (Pr) ranging from 0 to 100, and the modified Grashof number (G) within the range of 104–106. By varying these parameters, we analyze their influence on streamlines, isotherms, and the regions of yield and unyielded zones. The obtained results revealed that shear plays a significant role in influencing fluid flow, heat transfer, and the behavior of the unyielded section within the enclosure.

Non-Oberbeck–Boussinesq effects in two-dimensional Rayleigh–Bénard convection of different fluids

Non-Oberbeck–Boussinesq (NOB) effects in three representative fluids are quantitatively investigated in two-dimensional Rayleigh–Bénard convection. Numerical simulations are conducted in air, water, and glycerol with Prandtl numbers of Pr=0.71,4.4, and 2547, respectively. We consider Rayleigh number Ra∈[106,109] involving temperature difference (Δθ̃) of up to 60 K. The velocity and temperature profiles are found to be top-bottom antisymmetric under NOB conditions. As Pr increases, the time-averaged temperature of the cavity center ⟨θc⟩t increases under NOB conditions and the value of ⟨θc⟩t is only weakly influenced by Ra for all fluids. For Pr = 4.4 and 2547, with the enhancement of NOB effects, ⟨θc⟩t linearly increases and the maximum θ rms decreases/increases, and its location shifts toward/away from the wall near the bottom/top wall. Dispersed ⟨θc⟩t points and opposite phenomenon are observed in Pr = 0.71. The Nusselt number (Nu) and thermal boundary layer thickness at hot and cold walls (λ¯h,cθ) of the three fluids are comparable, and the Reynolds number (Re) significantly decreases as Pr increases. Under the NOB conditions with Pr = 4.4 and 2547, Nu decreases, Re increases, and λ¯hθ (λ¯cθ) thins (thickens) in an approximately linear fashion. Furthermore, the NOB effects on Nu, Re, and λ¯h,cθ are relatively small for Pr = 0.71 and 4.4, whereas the modifications caused by NOB effects at Pr = 2547 are more significant. The power-law scaling factors of Nu, Re, and λ¯h,cθ are demonstrated to be robust to Pr, as well as NOB effects.

Investigation of the heat transfer coefficient for a red clay brick

AbstractThere is a need for the development of materials for thermal isolation. Heat energy is used in different ways, for example, for house warming or production of electricity from solar power plants. However, to use the heat energy efficiently isolating materials are needed. There are different materials available to isolate houses and heat storage containers. However, those materials are expensive and some are over engineered. The best available material for thermal isolation would be air that has the thermal coefficient . Thus, materials that trap a large amount of air are good isolators. On the other hand, some isolating materials are harmful for the environment, for example, glass wool, asbestos. An alternative are red clay bricks because red clay is a natural product that is present everywhere on the planet. But the thermal coefficient of red clay bricks is high . To reduce the thermal coefficient cavities can be added in the brick. The cavities trap air and reduce the thermal coefficient of the brick.We simulate the heat transfer through a hollow brick. The holes in the brick are cavities. In order to determine the heat transfer coefficient we solve the heat flux through the hollow brick. For that a model of the brick is formulated as sequence of a solid and a fluid part. In the solid part only heat conduction is present and in the fluid heat transfer is present in form of conduction, convection and radiation. The flow field in the fluid part is modelled with the velocity‐vorticity formulation of the incompressible Navier‐Stokes. It is assumed that the Rayleigh number is below 106, hence, natural convective laminar fluid flow is present in the cavities. The cavities are also heated by heat radiation of the surrounding walls.The numerical realisation is done with the Boundary‐Domain Integral Method (BDIM). To handle suitable geometries the complexity of the BDIM is reduced from quadratic to logarithmic or almost linear by applying the ‐methodology. M is the number of unknown domain nodes. Numerical studies will be presented.

Fluid-inertia torque on spheroids in pseudo-plastic fluid flows: effect of shear-thinning rheology

Fluid-inertia torque remarkably affects the orientation of non-spherical particles in Newtonian flows whereas this torque induced by convective fluid inertia in particle-laden pseudo-plastic flows is still unknown. In the present study we numerically investigate the fluid-inertia torque on a neutrally buoyant spheroid in the Carreau-type pseudo-plastic fluid flows at finite Reynolds numbers with the immersed boundary method. The results show that compared with the fluid-inertia torque in Newtonian flows, the magnitude of the fluid-inertia torque on spheroids is remarkably attenuated by the shear-thinning rheology in pseudo-plastic fluid flows. The deviation of fluid-inertia torque between pseudo-plastic and Newtonian flows is more significant with decreasing Reynolds numbers, indicating the importance of the effect of shear-thinning rheology at small Reynolds numbers. Moreover, the spheroid rotation rate is reduced in pseudo-plastic fluids, and the equilibrium orientation of oblate spheroids changes non-monotonically with the shear-thinning effect in the linear shear flow of pseudo-plastic fluids. The present findings imply the importance of the effect of shear-thinning rheology on the torques of spheroids, which could be potentially applied for the control of particle orientations in pseudo-plastic fluids in the future.

Impact of bioconvection on Darcy‐Forchheimer flow of MHD Carreau fluid with Arrhenius activation energy

AbstractThis research examines the bioconvection impact on mixed convective Carreau fluid flowing toward permeable stretched surface with joule heating and Darcy‐Forchheimer effect. The evaluation has been attained in the presence of convective conditions, Joule heating, thermal radiative, mixed convective and motile microorganisms, which have not been dreamed before. Flow in permeable medium is characterized by utilizing Darcy‐Forchheimer model. Appropriate similarity factors are utilized to obtain the ordinary differential equations (ODEs). The derived mathematical formulation is now numerically solved with the help of R‐K 4th order scheme based on shooting approach. The results of the motile microorganism number, velocity, Sherwood number, temperature, motile density number, drag coefficient, concentration, and local Nusselt number are revealed graphically. The effect of bioconvection Lewis number on the motile microorganisms and motile density profile are quite inverse. Further, higher values of Schmidt number decrease the concentration field.

Experimental studies on two-phase immersion liquid cooling for Li-ion battery thermal management

The thermal management of lithium-ion batteries (LIBs) has become a critical topic in the energy storage and automotive industries. Among the various cooling methods, two-phase submerged liquid cooling is known to be the most efficient solution, as it delivers a high heat dissipation rate by utilizing the latent heat from the liquid-to-vapor phase change. In this study, a novel two-phase liquid immersion system was proposed, and the cooling performance of an 18650 LIB was investigated to evaluate the effects of thermal management on the performance of the battery pack. Four cooling strategies, namely natural, forced convection, mineral oil (single-phase), and SF33 fluid (two-phase) cooling, were compared under different discharge rates and dynamic load conditions. The results suggest that two-phase immersion cooling with SF33 fluid was highly effective to keep the cell temperature under 34 °C under all tested conditions, and the temperature change of the battery did not exceed 5 °C. A large amount of heat from the battery during high C discharge was absorbed by the boiling of SF33, allowing it to effectively maintain the cell temperature in an optimal temperature range (33–34 °C). Finally, the mechanism of pool heat transfer was determined through visual analysis. Initially, small bubbles appeared near the wires and battery terminals, which acted as gasification cores. Subsequently, small bubbles arose around the surface of the battery body, most of which grew to reach the interface. Eventually, the vapor condensed near the top condenser coils. This study provides a foundation for the further development of direct two-phase liquid-cooling technology, which can be an effective method for enhancing the life and safety of LIBs.

Analysis of entropy generation in the flow of MHD water–ethylene glycol nanofluid over a spinning down pointing vertical cone

ObjectivesEntropy generation is investigated by considering the consequence of Magnetic field in H2O − C2H6O2 (50:50) mixture based Al2O3 and Fe3O4 nanoparticles. The 2D magnetohydrodynamic mixed convective boundary layer fluid flow characteristics are assumed to be independent of time at every point. The boundary conditions are mathematically formulated with the slip conditions (velocity and thermal). Significant outcomesThe investigation discloses that the F′(η) (tangential and swirl) drops for the increasing effects of the M. Fe3O4 shows a rise in velocity compared to Al2O3. In case of Magnetic parameter Fe3O4 shows 0.71% and 0.89% of Cf and Nu respectively compared to Al2O3. For changed estimation of the Brinkman number, both the Entropy generation and Bejan number shows opposite behavior. To verify the exactness of the numerical method, a comparison is made between the obtained outcomes and previously published results, corresponding to the skin friction and Nusselt number and the results are reliable. Practical implicationsThis work is developed to multiply the rate of energy transference and increasing the execution as well as effectiveness of energy delivering in industrial field. This model considers the effect of magnetic field, since it helps in achieving energy circulation in numerous devices like refrigerators and in other heating applications. Especially using the magnetized nanofluid helps in improved energy transmission in biomedical imaging. Additionally, the entropy generation model is verified using the thermodynamics second law.

Influence of symmetric/asymmetric boundaries on axisymmetric convection in a cylindrical enclosure in the presence of a weak vertical throughflow

The linear and nonlinear stability of axisymmetric convection of a viscous fluid in a cylindrical enclosure heated from below is investigated for various radius to height ratios. A weak vertical throughflow is imposed in a gravity-aligned or a gravity-opposing manner. Symmetric and asymmetric boundaries of free-free, rigid-rigid and rigid-free types are considered for lower and upper boundaries with isothermal temperature boundary condition. The side-walls are assumed to be rigid and adiabatic. A convergent Maclaurin series representation is considered for the finding of axial trial eigenfunctions. In order to corroborate the results of the present study with those of a previous investigation, the critical Rayleigh number and the number of radial rolls manifesting for any given aspect ratio are determined in the case of no throughflow and an exact match is found. Further, the influence of boundaries and the effect of throughflow on chaotic and periodic regimes of motion are studied with the help of a time series solution and the largest Lyapunov exponent as indicators of chaos. The novelty of the present study is the use of a Maclaurin series representation for the eigenfunctions of the linear problem and using the same in determining the solution with the convective mode.

Mineralization age of the Xiangshan uranium ore field, South China redefined by hydrothermal apatite U-Pb geochronology

The Xiangshan volcanic-related uranium ore field, located in the Ganzhou-Hangzhou Uranium-Polymetallic Metallogenic Belt (GHMB) in South China, has been the country’s largest historic uranium producer. Although this ore field has been intensely studied for decades, the absolute age of uranium ore formation was still debated. Conventional U-Pb dates on U-minerals (i.e., pitchblende, brannerite) and Ar-Ar dates on associated alteration minerals (i.e., illite) from different uranium deposits yield a wide range of ages (122 to 85 Ma). The uncertainty regarding the exact timing of uranium mineralization at Xiangshan has limited the development of accurate ore genesis models and precluded a better understanding of the links between metallogenesis and regional-scale geodynamics during the Cretaceous-Tertiary period in South China.In this work, we focus on applying in-situ LA-ICP-MS U-Pb geochronology to magmatic and hydrothermal apatite from two typical uranium ore deposits at Xiangshan, intending to indirectly constrain the exact timing of uranium mineralization and reconstruct the magmatic-hydrothermal history. U-Pb age determinations on magmatic zircon and apatite from the three types of ore-hosting volcanic rocks yielded precise crystallization ages of 133 to 136 Ma and 135 to 140 Ma, respectively. These results are identical within uncertainty to previously reported U-Pb dates obtained in the study area, and thereby tightly constrain the emplacement age of the Xiangshan volcanic complex that hosts uranium deposits. Moreover, the potassium feldspar-biotite Ar-Ar dating for the major volcanic rocks demonstrates that these host rocks were cooled and completely solidified through the biotite/potassium feldspar closure temperature (below 300 °C) at 133–131 Ma. Subhedral or anhedral aggregates of hydrothermal apatite ubiquitously formed in the high-grade uranium ores at the Shannan and Zoujiashan deposits and are commonly intergrown with fluorite, illite and uranium minerals. Relative to magmatic apatite from the host rocks, the hydrothermal apatite is typically characterized by much higher U and Th contents, depletion of LREEs, enrichment in HREEs and a much more pronounced negative Eu anomaly. As such, the hydrothermal apatite is unequivocal of hydrothermal origin and formed synchronously with uranium mineralization. LA-ICP-MS U-Pb dating of these hydrothermal apatite crystals yielded an absolute 206Pb/238U age of 126.7 ± 0.6 Ma for the Shannan deposit and 131.3 ± 7.2 Ma for the Zoujiashan deposit. The new ages are much older (>10 Ma) than those previously reported ages on ore or gangue minerals such as pitchblende and illite. Thus, one unidentified mineralization event likely occurred at ca. 131–127 Ma, soon after solidification and subsequent brittle deformation or faulting within the volcanic caldera. We, therefore, proposed that volcanic magmatism was highly likely to be the ‘heat engine’ driving hydrothermal fluid convection and possibly provide the essential conditions (i.e., magmatic fluids, U sources) for the formation of the U mineralization. Another implication of this study is that dating hydrothermal apatite with high U concentrations associated with uranium mineralization could be considered a complementary geochronological tool in the study of analogous hydrothermal uranium deposits worldwide.

Finite elements simulation MHD free convection in a rectangular embedded corrugated rods cavity filled with CuO/water nanofluid

The convective heat transfer and fluid is investigated in a rectangle chamber along with corrugated heated rods. For preferable novelties, this study considered porous media, micropolar fluid and an inclined magnetic field effect. The physical illustrations of nanofluid flow is assimilated in terms of differential equations. We use the finite element approach to tackle the fluid flow and heat transfer in rectangular chamber. Flow regulating parameters are Rayleigh number, Darcy number and Hartman number. The horizontal and vertical velocities and temperature distribution are provided through the use of contour plots and line graphs. The results show that heat transmission rates increase due to the increasing values of Hartmann number. Because Lorentz forces are resistive, the velocity profile tends to flatten down as long as Hartman number increases. The Nusselt number and velocity profile have greater values around the heat boundaries.

A Novel Thermal Lattice Boltzmann Method for Numerical Simulation of Natural Convection of Non-Newtonian Fluids

A modified thermal Bhatnagar–Gross–Krook Lattice Boltzmann (BGK-LB) model was developed to study the convection phenomenon of non-Newtonian fluids (NNFs). This model integrates the local shear rate into the equilibrium distribution function (EDF) of the flow field and keeps the relaxation time from varying with fluid viscosity by introducing an additional parameter. In addition, a modified temperature EDF was constructed for the evolution equation of the temperature field to ensure the precise recovery of the convection–diffusion equation. To validate the accuracy and effectiveness of the proposed model, numerical simulations of benchmark problems were performed. Subsequently, we investigated the natural convection of power–law (PL) fluids and examined the impact of the PL index (n = 0.7–1.3) and Rayleigh number (Ra = 103–5 × 105) on the flow and temperature fields while holding the Prandtl number (Pr = 7) constant. The obtained results indicate that, for a given value of n, the convective intensity exhibits a positive correlation with Ra, which is illustrated by the rising trend in the average Nusselt number (Nu¯) with increasing Ra. Additionally, shear-thinning fluid (n < 1) exhibited increased Nu¯ values compared to the Newtonian case, indicating an enhanced convection effect. Conversely, shear-thickening fluid (n > 1) exhibits reduced Nu¯ values, indicating weakened convective behavior.

Rayleigh–Bénard convection of viscoelastic fluids in three-dimension finite cavity

The Rayleigh–Bénard convection (RBC) with viscoelastic fluids has captured wide attention in the past decades, caused by its ubiquitous uses in the heat transfer process. However, the numerical technique for simulating the viscoelastic fluid flows developed slowly until recent years because of the numerical instability raised by the hyperbolic characteristics of the viscoelastic constitutive equation. In the present work, a novel numerical scheme was developed to simulate the three-dimension (3D) RBC with viscoelastic fluids, where the quasi-linear treatment was applied to the hyperbolic terms of the momentum equation and the viscoelastic constitutive equation. The in-house solver was also optimized in the aspect of time cost. The results show that the critical value of convection onset in 3D is near to that in the two-dimension (2D); however, the flow pattern displays the wave characteristics in the horizontal direction. The viscoelastic kinetic energy budget of oscillating convection in 3D still conforms to the energy transport law of that in 2D [Zheng et al., Phys. Rev. Fluids 8, 023303 (2023)].

Soret-induced convection of ternary fluid in a horizontal porous layer heated from below

The present paper deals with the investigation of the Soret-induced convection of a three-component mixture of hydrocarbons in a horizontal porous layer. This problem is important for geological applications. The first part of the paper is devoted to the linear stability of the conductive state. The longwave instability is studied analytically by the expansion into the power series with respect to the wave number. A new long-wave oscillatory instability mode existing at negative separation ratios is found out. It is shown that this mode is more dangerous than the long-wave monotonic instability mode in the entire range of its existence. The instability to the perturbations with nonzero wave numbers is studied numerically by the shooting method. Stability map is obtained. The results confirm the predictions of the longwave analysis. In the second part of the paper, the nonlinear convection regimes are studied by the finite difference method. The calculations give the results consistent with the linear stability analysis. It is found that the primary bifurcation as a result of which the conductive state losses its stability is supercritical. The transformations of the convective flow structure with the change in the Rayleigh–Darcy number are accompanied by the hysteresis phenomena.

Squeeze flow of a Maxwell fluid between two parallel disks or two spheres

In this study, we investigated the squeeze flow of an upper convected Maxwell fluid between two rigid disks or spheres. It has been proved that the velocity field of the Maxwell squeeze flow between two disks is similar to Newtonian at low Deborah numbers. Based on the Newtonian fluid velocity field, we analyze the pressure distribution between two parallel disks and develop a theoretical model of normal squeeze force. We also use the same method to analyze the interaction between two nearly contacting, arbitrary rigid spheres. We obtained the analytical expression of the pressure distribution and normal squeeze force, which can be implemented into the contact model for the discrete element simulation of a wet particle system with the Maxwell fluid.

Comparative analysis of analytical and numerical approximations for the flow and heat transfer in mixed convection stagnation point flow of Casson fluid

A mathematical description of non-Newtonian mixed convective Casson fluid stagnation point flow and transfer of heat exists in terms of partial differential equations. We considered the same to study it further under the effects of unsteadiness and varied film thickness parameters. For inclusion of these parameters in the flow model study we modified the available similarity transformations. The governing equations with three independent variables are converted into ordinary differential equations by employing the modified invertible transformations. For the mass and heat transfer in the mixed convection stagnation point unsteady flow of Casson fluid over a stretching sheet, a detailed comparative analysis is carried out in this paper, of the analytical and numerical approximation techniques. The Homotopy Analysis Method is applied for the analytical solutions while the Runge-Kutta with a Shooting Method (RKF45) and Finite Difference Method are used for obtaining the numerical solutions. With these solution schemes we present an analysis of velocity and temperature profiles under the effects of embedded parameters such as the Casson fluid parameter, unsteadiness parameter, mixed convection parameter, Prandtl number, Eckert number, and stretching ratio. The results are presented in both graphical and tabulated forms and they illustrate the dependence of mass and heat transfer characteristics of Casson fluid upon the embedded parameters. Further, we have shown an agreement between the analytical and the approximate solutions for the considered flow and heat transfer which reflects a validation of the results presented here.