Thin Film Flow Research Articles

A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber

When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. Recent studies verified that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically, making numerical simulations challenging. In this paper, we present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting. A series of comparisons to laboratory experiments and previously proposed numerical methods supports the validity of our numerical method. We also prove that our method is second-order consistent in space and satisfies the entropy estimate.

Water-based nanofluid flow and heat transfer in thin film over an unsteady stretching sheet: An entropy analysis

The transfer of thermal energy is intrinsically associated with the generation of entropy. Here, we investigate the entropy generation number in nanofluid thin film flow over a radiated stretching sheet subject to different shapes of titanium oxide and copper nanoparticles in base fluid water. In addition, the impact of the magnetic field, viscous dissipation, and Joule heating were also considered. Using a suitable similarity transformation, the momentum and energy equations that describe the flow are converted into ordinary differential equations. These equations are then solved numerically using bvp4c in MATLAB. Graphs and explanations show how different physical parameters affect the velocity profile, temperature distribution, Nusselt number, skin friction coefficient, entropy generation number, and Bejan number. As the Brinkman number went up, fluid friction and Joule loss caused more entropy generation, but the Bejan number showed the opposite trend. In a certain situation, it is also important to note that as the value of the radiation parameter goes up, the irreversibility of heat transfer becomes more important. In addition, spherically shaped nanoparticles have the lowest entropy among all other forms. Hence, nanoparticles have the ability to reduce the amount of energy lost in any physical process and increase the overall productivity of systems. Understanding the flow and heat transmission within a thin film has many practical applications in industry, including aerodynamic lamination of plastic sheets, wire and fiber coating, food processing, annealing and thinning of copper wires, reactor fluidization, and many more.

Rimming flow in a rotating horizontal cylinder with phase change at the interface

The two-dimensional solutions and stability analysis are presented for an evaporating thin viscous liquid film flowing inside a uniformly heated rotating horizontal cylinder. A non-linear, fourth-order, partial differential evolution equation is obtained by simplifying mass, momentum, and energy conservation equations within the lubrication approximation. The effect of evaporation, gravity, viscous drag, surface tension, thermocapillary stress, and intermolecular forces has been taken into account. The numerical solutions of the model are validated against the existing experimental as well as the numerical results, along with the analytical result for the limiting cases of the present model. The film thickness model is solved to elucidate two-dimensional spatiotemporal solutions and their stability for a wide range of thermal and other parameters. The evaporative mass flux at the liquid–air interface results in unsteady solutions which are oscillatory in nature, and the amplitude of the oscillations increases with an increase in the evaporative flux. The film ruptures after some time and the rupture time is found to be inversely proportional to the evaporation number, a non-dimensional number quantifying the rate of evaporation. The linear stability analysis shows that the thermocapillary stresses as well as the long-range molecular forces destabilize the film. A negative disjoining pressure is shown to reduce the rupture time and vice versa. Evaporation (condensation) plays a destabilizing (stabilizing) role in the thin film flow. Non-linear computations are carried out for the steady profiles, validating the growth rates obtained from the linear stability analysis.

Thin film flow, heat transfer and viscous dissipation effects on vertical stretching sheet for different shapes of (Au-Np) dispersed in water

In this article, we present numerical investigation and analysis of thin film flow and heat transfer effects for different shapes of gold nanoparticles on a vertical stretching sheet. There are several uses for thin liquid films, including antireflection coating for lenses. Coating systems must have a smooth, polished surface, low friction, clarity, and strength to satisfy the demands of all of these applications. We consider thin film flow of nanoparticles on a vertical stretching sheet due to their numerous applications. Additionally, we employed water as the base fluid and considered different shapes of gold nanoparticles (blades, cylinders, and platelets). After formulating the problem, we convert nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs) using a transformation. The resulting nonlinear differential equations have been computed by the BVP4c method. It is examined and graphically assessed how the Nusselt number, temperature, skin friction, and fluid velocity are related. This research suggests that the blade shape has the maximum heat transfer rate and the lowest skin friction coefficient value.

Instability of Liquid Film with Odd Viscosity over a Non-Uniformly Heated and Corrugated Substrate.

The effect of odd viscosity on the instability of liquid film along a wavy inclined bottom with linear temperature variation is investigated. By utilizing the long-wave approximation, the non-linear evolution equation of the free surface is derived. By applying the normal mode method, the linear instability of thin film flow is investigated. With the help of multi-scale analysis methods, the weakly non-linear instability of thin film flow is also investigated. The results reveal that the Marangoni effect caused by non-uniform temperature distribution promotes the instability of the liquid film, while the odd viscosity has a stabilizing effect. In addition, for a positive local inclination angle θ, an increase in bottom steepness ζ inhibits the instability of the liquid film flow. In contrast, with a negative local inclination angle θ, increased bottom steepness ζ promotes the instability of the liquid film flow. The results of the temporal linear instability analysis and the weakly non-linear instability analysis have been substantiated through numerical simulations of the non-linear evolution equations.

Extended integral boundary layer method for reactive species mass transfer in rotating films

AbstractThe present work extends the Integral Boundary Layer (IBL) Method to centrifugal force driven thin film flow with mass transfer. The proposed hybrid approach combines the IBL based solution of the flow field with a Finite Difference based solution of the mass transport equation, avoiding any concentration profile assumptions and restrictions on surface chemistry. In comparison against results from highly resolved Computational Fluid Dynamics (CFD) simulations, the proposed concept is proven as a computationally efficient and accurate method well applicable to infinitely fast surface reactions as well as finite rate kinetics.

Chemically reactive and thin film flow analysis of cross nano-liquid over a moving surface

Vapour generalized liquids hydrodynamics plays a pivotal role in the absorption columns or design of distillation using structured packing since they indomitable the fluid dynamics restrictions of the columns and control rates of mass balance which is the main purpose of this particular work. Particularly, a first attempt is made regarding this work to explore an investigation for time-dependent thin film flow of Cross nano-liquid over a moving surface. Additionally, some physical aspects during this illustration in terms of heat absorption/generation, thermal radiation, magnetic field, non-constant thermal conductivity, and activation energy with chemical reaction are studied. Some of the suitable similarity variables are introduced to convert the leading problem in the form of ordinary differential equations and then the transformed problem is approximated by one of the built-in collocation methods by using MATLAB. Very interesting results in terms of monotonic reduction in the film thickness for various uplifting values of unsteadiness and magnetic parameters and vice versa for the Wessenberg number are found. Moreover, temperature and concentration are concluded as enhancement functions of variable thermal conductivity and activation energy, respectively. The last comparative work is presented to validate the entire approach and where the method shows an excellent correlation with the previously published results.

Thermocapillary thin film flow upon a porous heated stretchable cylinder

AbstractEarlier research work related to the unsteady flow of thin liquid film on a heated stretching cylinder has considered the boundary‐layer approximation under the assumption that the film thickness is thick. In this article, we have considered the full set of Navier–Stokes equations to study the unsteady film development over a porous heated stretching cylinder with the assumption that film height either coincides or lies within the boundary‐layer thickness. The effects of magnetic field, suction/injection, and cooling or heating of the cylinder have been considered for investigation. The governing set of coupled nonlinear partial differential equations is solved numerically by the implicit finite difference scheme (Crank–Nicolson). It was found that the film thinning rate diminishes with rising values of the porosity parameter and Hartmann number. It is also noted that the film thickness is enhanced for injection whereas opposite results are observed for suction through the porous cylinder. The thermocapillary effect showed that the thinning rate of the liquid film decreases or increases according to the surface of the cylinder being heated or cooled. It is observed that continuously increasing the stretching speed of the cylinder produces faster thinning of the liquid film. The temperature of the liquid film is the maximum at the surface of the cylinder and it decreases toward the free surface when the cylinder is heated. But the opposite phenomenon occurs when the cylinder is cooled.

Thin liquid films on a slippery vertical cylinder in presence of chemical reaction

In industrial settings, chemical reactions often affect thin liquid films that flow down vertical cylinders. However, the effect of non-isothermal reactions on the dynamics of these films is not fully comprehended. To address this issue, this study investigates the behavior and stability of thin film flows on uniformly heated vertical cylinders that exhibit wall slippage when subjected to a pseudo-zero-order exothermic or endothermic chemical reaction. A reduced model is developed for thin liquid films flowing down vertical cylinders in the presence of exothermic or endothermic chemical reactions, assuming the film thickness is much smaller than the cylinder radius. The heat from the reaction and/or wall heating initiates a thermocapillary Marangoni effect, which is further enhanced by wall slippage, directly affecting the dynamics of the free surface. Linear and weakly nonlinear stability analyses show that wall slip amplifies the instability, while exothermic reactions stabilize the system and endothermic reactions destabilize it. It is also found that chemical reactions significantly influence the supercritical stable, subcritical unstable, unconditional stable, and explosive zones of the thin film. A direct numerical simulation confirms the results of linear and weakly nonlinear analyses.

Thermocapillary thin film flows on a slippery substrate with odd viscosity effects

This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.

Flow instabilities of second-grade fluid over a stretching sheet

The work at hand studies thin-film flow instabilities in a non-Newtonian second-grade fluid moving over a stretching sheet. The analysis considers the free surface evolution equation of the thin second-grade viscoelastic fluid model based on the long-wave approximation method. We undertook a linear stability analysis using a normal mode approach and obtained expressions for the linear time growth rate, linear phase speed, and critical wavenumber, which illustrates the linear stability structure of the flow system. Furthermore, the multi-scale analysis of the fluid’s weakly non-linear stability characteristics reveals the presence of subcritical instability in the linear stability zone. The study shows that the varying flow parameters affect the threshold amplitude, which influences the stable and unstable zones in the subcritical region. The outcomes show a stabilizing effect spanning the range of non-dimensional parameters, such as the second-grade parameter ranging from 0 to 100 in values, the surface tension parameter ranging from 0 to 100 in values, and the modified Froude number from 0 to 100 in values.

Heat transfer analysis of temperature dependent viscosity Johnson–Segalman fluid film flow on a vertical heated belt

Understanding the behaviour of temperature dependent viscosity thin film flows on a vertically upward moving heated belt is crucial for improving predictive models in various engineering applications, such as in coating and lubrication processes. This paper presents the heat transfer analysis of temperature-dependent viscosity fluid flow on a vertical upward moving heated belt. The formulated coupled system of nonlinear ordinary differential equations is solved using the Adomian decomposition method. The study investigates the impact of flow controlling parameters: Stokes number St, Brinkmann number Br, variable viscosity parameter β, Weissenberg number We, effective viscosity ϕ and slip parameter e is observed on velocity, temperature, and stationary points. It is perceived that the temperature of the fluid decreases with the increase of St, Br, β, and ϕ, while it increases with the increase of We and e. Positions of stationary points relocate towards the heated belt surface by the increment of St, Br, β, and ϕ. On the other hand, their positions relocate away from the heated belt surface by the increment of We and e. The analysis also highlights the influence of heat generated by viscous dissipation and heat transported by thermal diffusion on the velocity, temperature, and stationary points. Moreover, the flow variables discussed for the temperature dependent viscosity Johnson–Segalman fluid are also discussed for the temperature dependent viscosity Newtonian fluid, and an analogy between both is provided.

Heat and mass transfer of Ag–H2O nano-thin film flowing over a porous medium: A modified Buongiorno’s model

Due to their numerous applications, such as fibre and wire coating, polymer preparation, etc., thin films have recently come into focus in the analysis of heat and mass transport. As a result, the current article’s main objective is to investigate how heat and mass are transferred when an Ag−H2O(sliver–water) thin film flows past a stretching sheet that is subject to thermal and velocity slips. The research takes into account other variables including porosity, thermal radiation, thermophoresis, and Brownian motion, among others, to ensure that the outcomes are consistent with real-world conditions. Along with these parameters, the impact of the nanoparticle volume fraction is also analysed by incorporating the modified model of the existing Buongiorno model. The resulting mathematical model is transformed into ordinary differential equations with the help of appropriate similarity transformation. The system of equations thus obtained is solved by employing the RKF-45 technique and the outcomes are expressed in terms of graphs and tables. The major outcomes indicate that the increase in the mixed convection parameter causes enhancement in the temperature profile while a reduction in the velocity profile. The thermophoresis is found to increase both the temperature and concentration profiles of the thin film. Whereas, the greater values of the volume fraction of the nanoparticles enhance the temperature and diminishes the velocity.

Newly Developed Method for Liquid Thin Film Thickness Measurement Using Optical Fiber–Based Reflective Probe

A new ray-tracing–based calibration method for an Optical-fiber-based Reflective Probe (ORP) was developed. This technique enables thickness measurement in micrometers in wavy thin liquid film flow, which is simpler and quicker than other liquid film measurements. First, the relationship between the film thickness and ORP signal was calculated through the ray-tracing simulator. The signal trend showed a steep rate of change within a few-hundred-micron thicknesses, thanks to the emission nature of the step index multimode fiber. The ray-tracing–based calibration was established using the calculated relationship. Second, the calibration method was validated under quiescent conditions. The calibrated ORP measured the thickness and then was compared to visualization. Good agreement was confirmed between the two results at a maximum difference of 20% under 1000 μm in thickness. Finally, thickness measurement for the wavy thin film flow was performed. Airflow (jG = 40 to 75 m/s) was introduced into the rectangle test section, and a small amount of tap water (Q = 30 to 90 mL/min) was injected into the channel plate. The difference in the measured thickness between ORP and high-speed visualization was around 20%. The effectiveness of the new calibration method and ORP measurement including its uncertainty will be discussed.

Structural Design of Dual-Type Thin-Film Thermopiles and Their Heat Flow Sensitivity Performance.

Aiming at the shortcomings of the traditional engineering experience in designing thin-film heat flow meters, such as low precision and long iteration time, the finite element analysis model of thin-film heat flow meters is established based on finite element simulation methods, and a double-type thin-film heat flow sensor based on a copper/concentrate thermopile is made. The influence of the position of the thermal resistance layer, heat flux density and thickness of the thermal resistance layer on the temperature gradient of the hot and cold ends of the heat flow sensor were comprehensively analyzed by using a simulation method. When the applied heat flux density is 50 kW/m2 and the thermal resistance layer is located above and below the thermopile, respectively, the temperature difference between the hot junction and the cold junction is basically the same, but comparing the two, the thermal resistance layer located above is more suitable for rapid measurements of heat flux at high temperatures. In addition, the temperature difference between the hot and cold contacts of the thin-film heat flux sensor increases linearly with the thickness of the thermal resistance layer. Finally, we experimentally tested the response-recovery characteristics of the sensors, with a noise of 2.1 μV and a maximum voltage output of 15 μV in a room temperature environment, respectively, with a response time of about 2 s and a recovery time of about 3 s. Therefore, the device we designed has the characteristic of double-sided use, which can greatly expand the scope of use and service life of the device and promote the development of a new type of heat flow meter, which will provide a new method for the measurement of heat flow density in the complex environment on the surface of the aero-engine.

Experimental characterization of the flowline of a lithium film formed using an electromagnetic thruster for a RAON prototype charge stripper

This paper describes the variable optimization of a lithium charge-stripper device for the Rare isotope Accelerator complex for ON-line experiences (RAON) and the experimental characterization of a lithium film formed for the charge removal of uranium using a magnetohydrodynamic liquid metal circulation system. To this end, liquid lithium charge stripper was fabricated to form a thin lithium film flow through collisions between a liquid lithium jet and a planar deflector. The flow characteristics of the lithium film were analyzed through simulation and waterjet experiments in terms of the liquid lithium film thickness. To circulate the liquid lithium, a mechanically safe electromagnetic thruster with precise pressure control was designed by analyzing its electromagnetic and hydraulic parameters through finite element simulation. The analysis of the geometrical arrangement of the permanent magnet and input current of the thruster revealed that compared to existing electromagnetic thrusters, the nominal input current of the newly-constructed thruster was reduced to 57% and its weight reduced to 6%, while facilitating easy maintenance. The optimized nozzle diameter and angle of the lithium charge stripper was 0.7 mm and 34°, respectively. Further, the formation of a 22-µm thick liquid lithium thin film required to obtain the 79+ charge state of uranium was confirmed at an input current of 107 A.

Insight into the thermocapillary radiative flow of hybrid nanoliquid film over an infinite rotating disk with entropy generation and heat source

Research into hybrid nanofluid flow over a disk surface is growing due to numerous processes in marine or gas turbines, rotating disk reactors for biofuels generation, cooling of spinning equipment components and other industrial applications. The purpose of this research study is to examine the entropy generation for the transient thermocapillary flow of hybrid nanoliquid thin films across a disk surface with different shapes of nanoparticles. To analyze the nanomaterial, the Tiwari–Das hybrid nanofluid flow model is established, and in doing so, Prandtl’s boundary layer theory is incorporated into this model. The energy equation considers the impacts of thermal radiation, two different kinds of heat sources — namely an exponentially space-dependent heat source and a linear thermal heat source — and viscous dissipation. The nonlinear partial differential equations, which explain the flow processes, are transformed into the nondimensional ordinary differential equations (ODEs). Once the ODEs have been constructed, they are next solved using the bvp4c technique. In addition, the surface drag force and the rate of heat transfer are both evaluated as functions of the shape factor of the nanoparticles that are disseminated in the base fluid. The influence of significant parameters on the flow fields is depicted graphically, and adequate physical explanations are provided for each representation. One of the important findings of this study indicates that the largest amount of heat transfer can be accomplished at the disk surface by employing nanoparticles with blade shape, while this physical quantity is the least when nanoparticles with spherical shapes are used. The temperature profile grows as the thermal and exponential heat sources increase. Entropy generation improves with the increase in either the magnetic parameter or the Brinkman number.

Heat transfer of thin-film Casson hybrid nanofluid flow across an unsteady stretching sheet

Hybrid nanoparticles copper and alumina effect on the heat transfer of thin-film blood flow toward an unsteady permeable stretching sheet is studied. The influence of suction is considered. The governing partial differential equations together with boundary conditions are reduced into the set of ordinary differential equations by implementing the similarity transformations. The Keller-box method is used to solve the momentum and heat equations. The characteristics of the blood flow and heat transfer under the effect of unsteadiness parameter, nanoparticles volume fraction, Casson parameter, and intensity of suction for different thin-film thickness are discussed. The numerical results of the velocity and temperature profiles are graphically displayed. The physical interest such as the local skin friction and Nusselt number are depicted in a tabular form.

Heat transfer in MHD thin film flow with concentration using lie point symmetry approach

Heat and mass transfer in a viscous film on an unsteady stretching surface in the presence of a variable magnetic field is investigated using Lie symmetry analysis. Combination of translational and scaling Lie point symmetries is used to obtain invariants of the model. The deduced invariants provide a new generalized class of similarity transformations that have not been used before. These transformations restructure the governing problem in a system of eight-parameter nonlinear ordinary differential equations. Analytic series solutions are obtained for the resulting system of equations for different values of these parameters and are illustrated graphically. We found that coefficients of the translational symmetries do not have any effect on the solutions however, coefficients of the scaling symmetries significantly affect the variation of temperature and concentration distribution across the fluid film and help in controlling the heat and mass transfer rates. Also, increasing the value of unsteadiness and magnetic parameter decreases the film thickness and promotes a uniform temperature and concentration across film thickness. Furthermore, we found that at the lower values of Prandtl and Schmidt number, diffusion dominates the heat and mass transfer while at the higher values advection dominates the heat and mass transfer.

Thin film flow of blood-based hybrid nanoparticles subject to slip effects: A stability assessment

The objective of this research is to predict the thermal observations for hybrid nanofluid conveying the thin film flow influenced by the suction phenomenon and slip consequences. The copper and aluminum nanoparticles are utilized to explore the hybrid nanofluid features. In addition, a uniform magnetic field perpendicular to the motion of the nanoliquid has been generated. By utilizing appropriate dimensionless quantities, partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs). The controlling method for boundary value problems (BVP4C) has been applied against the thermal profile. The coating film’s thickness has been kept fixed. The skin friction and Nusselt number distribution are calculated for blood over the shrinking sheet in the attendance of the radiation and velocity slip parameters. The effects of various variables and spray rate through coating are clearly represented. The numerical calculation is computed for assessing the wall shear force. It is observed that a dual branch has been discovered. In addition, a stability analysis has been conducted and the upper branch has been determined to be the stable branch.