Forward Roll Coating of a Williamson’s Material onto a Moving Web: A Theoretical Study

This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg’s number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate.

Roll-over-web coating analysis of micropolar-Casson fluid: a theoretical investigation

The theoretical model of micropolar-Casson fluid is studied in roll-coating over a moving substrate based on the lubrication theory. Closed-form solutions for the velocity, pressure gradient, and microrotation are attained, while a numerical technique employed to compute interesting engineering variables such as pressure, roll-separating force, separating point, and power input. The influence of involved parameters on the physical and engineering quantities are displayed via graphs and table. The coupling number (N) and viscoplastic parameter (β) provide the controlling mechanism for the exit sheet thickness, separating force, and power input. Also, the pressure gradient and pressure profile in the nip region enhances for large values of coupling number (N) whereas the viscoplastic parameter (β) gives the opposite behavior.

Analysis of calendering process of non-isothermal flow of non-Newtonian fluid: A perturbative and numerical study

This paper numerically solves the third-order fluid flow during calendering with slip condition at the rolls. The basic equations are transformed into dimensionless forms and simplified by adopting LAT (Lubrication Approximation Theory). The flow equations are then solved with the perturbation technique. Whereas a finite difference scheme along with TDMA (Tridiagonal Matrix Algorithm) is implemented to solve the energy equation. Engineering parameters like power input, exit distance, and roll separating force are computed. The impact of slip parameter [Formula: see text] and material parameter [Formula: see text] on the velocity profile, pressure, pressure gradient, temperature profile, power input, detachment point, and roll separating force is portrayed through graphs and discussed. It is noticed that both the parameters [Formula: see text] and [Formula: see text] exhibit opposite behaviors and give insight to the mechanisms that control the physical and engineering parameters.

Analysis of the lubrication approximation theory in the calendering/sheeting process of upper convected Jeffery’s material

This paper analyses an isothermal calendering for an upper convected Jeffery’s Material. Lubrication Approximation Theory (LAT) is applied to simplify the flow equations. Analytical solutions of velocity, flow rate, and pressure gradient are carried out. Outcomes of sheet thickness, detachment point, roll separating force, power input to the roll, and pressure distribution are obtained. The effects of some involved parameters are displayed through graphs and tables. It is noted that the material parameter is a controlling device for sheet thickness, flow rate, detachment point, roll separating force, power input, and the pressure distribution. We observed that as the material parameter increases, the detachment point increases which results in increased sheet thickness.

Numerical analysis of the calendering process by using Giesekus fluid model

A numerical study of the calendering process is presented. The material to be calendered is modeled by using Giesekus constitutive equation. The flow equations are first presented in dimensionless forms and then simplified by incorporating the lubrication approximation theory. The resulting equations are analytically solved for the stream function. The pressure gradient, pressure, and other engineering parameters related to the calendering process, such as roll-separating force, power function, and entering sheet thickness, are numerically calculated by using Runge–Kutta algorithm. The influence of the Giesekus parameter and the Deborah number on the velocity profile, pressure gradient, pressure, power function, roll-separating force, and exiting sheet thickness are discussed in detail with the help of various graphs. The present analysis indicates that the pressure in the nip region decreases with increasing Giesekus parameter and Deborah number. The power function and the roll-separating force exhibit decreasing trends with increasing Deborah number. The exiting sheet thickness decreases up to a certain entering sheet thickness, as compared to the Newtonian case. Beyond this entering sheet thickness, the exiting sheet thickness increases with increasing entering sheet thickness.

Mathematical Analysis of the Coating Process over a Porous Web Lubricated with Upper-Convected Maxwell Fluid

The present study offers mathematical calculations of the roll-coating procedure lubricated with an upper-convected Maxwell fluid. An incompressible isothermal viscoelastic fluid was considered, with both the roll and the porous web having uniform velocities. By using the lubrication approximation theory, the desired equations of motion for the fluid applied to the porous web were modelled and analyzed. The suction rate on the web and the injection rate at the roll surface were proportionately anticipated. Results for the velocity profile and pressure gradient were received analytically. Fluid parameters of industrial significance (i.e., detachment point, pressure, sheet/roll separating force, power contribution, and coating thickness) were also calculated numerically. A substantial and monotonic increase was witnessed in these quantities with the increase of flow parameters.

Role of Roll Separating Force in High-Speed Twin-Roll Casting of Aluminum Alloys

The role of the roll separating force in the high-speed twin-roll casting of aluminum alloys was examined. In horizontal-type twin-roll casting, as the casting speed increased upon decreasing the roll separating force, the strip texture changed from a shear and rolling texture to a random texture. Direct temperature measurements during high-speed twin-roll casting showed that the roll separating force played a significant role in maintaining a good contact between the strip and the roll surface. This resulted in a high cooling rate around the roll nip and enabled the fabrication of a sound strip with a fine microstructure. Moreover, the high casting speed and lowered roll separating force gave a band structure consisting of fine globular grains in the mid-thickness region of the strip, which could be considered beneficial in the formation of a well-dispersed center segregation.

Mathematical Analysis of the Coating Process Over a Porous Web Lubricated with Upper Convected Maxwell Fluid

Present study offers mathematical calculations of the roll-coating procedure lubricated with upper Convected Maxwell Fluid. An incompressible isothermal viscoelastic fluid is considered with roll and the porous web having uniform velocities. By employing Lubrication Approximation Theory, the desired equations of motion for the fluid concerned over porous web are modelled and analyzed. The suction rate on the web and injection rate at the roll surface are anticipated proportionate. Results for velocity profile and pressure gradient are obtained analytically. Fluid parameters of industrial significance i.e. detachment point, pressure, sheet /roll separating force, power contribution and coating thickness are also calculated numerically. Substantial and monotonic increase is witnessed in these quantities with the increase of flow parameters.

Calendering of non-isothermal Rabinowitsch fluid

A non-isothermal analysis of calendering by using the Rabinowitsch fluid model is presented in this article. The flow equations are simplified by utilizing the lubrication approximation theory. The exact expressions of velocity and pressure gradient are obtained. The pressure distribution and engineering quantities are computed numerically by employing the Runge-Kutta algorithm. The temperature distribution is obtained by solving the energy equation numerically using the hybrid numerical method. The influence of the involved parameters on the velocity profile, pressure, pressure gradient and mechanical quantities such as roll-separating force, power function and exiting sheet thickness are shown graphically. The temperature distribution at various axial points is also shown through graphs.

Phosphorus Segregation in Meta-Rapidly Solidified Carbon Steels

Twin-roll strip casters for near-net-shape manufacture of steels have received increased attention in the steel industry. Although negative segregation of phosphorus occurred in twin-roll strip casting (TRSC) steels in our prior work, its mechanism is still unclear. In this work, V-shaped molds were designed and used to simulate a meta-rapid solidification process without roll separating force during twin roll casting of carbon steels. Experimental results show that no obvious phosphorus segregation exist in the V-shaped mold casting (VMC) steels. By comparing TRSC and the VMC, it is proposed that the negative phosphorus segregation during TRSC results from phosphorus redistribution driven by recirculating and vortex flow in the molten pool. Meanwhile, solute atoms near the advancing interface are overtaken and incorporated into the solid because of the high solidification speed. The high rolling force could promote the negative segregation of alloying elements in TRSC.