Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study
Background: The roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several rol...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-11-01
|
| Series: | Case Studies in Thermal Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214157X23008092 |
| _version_ | 1797672706573860864 |
|---|---|
| author | Fateh ali Yanren Hou Xinlong Feng M. Zahid M.A. Rana Basma Souayeh |
| author_facet | Fateh ali Yanren Hou Xinlong Feng M. Zahid M.A. Rana Basma Souayeh |
| author_sort | Fateh ali |
| collection | DOAJ |
| description | Background: The roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several roll-to-roll coating methods, including forward and roll over web. However, the reverse roll coating study of the non-Newtonian fluid model is presented in this paper. The constitutive equation for the viscoelastic Carreau fluid model as the non-Newtonian fluid is derived using the momentum and energy equations. To simplify the nonlinear systems of partial differential equations, appropriate non-dimensional parameters are employed to convert them into systems of ordinary differential equations. Method: By taking the Weissenberg number as a small parameter, a series solution is obtained for considerable quantities like pressure gradient, axial velocity, flow rate, pressure distribution, and temperature distribution using the perturbation method. In contrast, the numeric outcome of some quantities of engineering interest, like flow rate, coating thickness, share stresses, and separation points, are calculated. Streamlines in 2D and 3D are also drawn to observe the flow pattern. To validate the solution, the problem is also solved numerically with the BVP Midrich method. The analysis of the results demonstrates a satisfactory agreement between the analytical and numerical solutions. Results: The graphical investigation examines the influence of different fluid parameters on velocity profile, shear stress, pressure profile, temperature profile, and pressure gradient. A comprehensive mechanism behind these outcomes is deliberated. It has been observed that velocity rises on increasing the Weissenberg number; however, velocity decreases in the case of the velocities ratio. Further, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Moreover, the separation point and coating thickness decrease with the velocities ratio increase. The results accuracy is checked against papers that have already been published. The comparison reveals good agreement; therefore, the resultant analytical model gives new ways to forecast film thickness and explain influence parameters. Hence, these factors may help in an efficient coating process and improve the substrate life. |
| first_indexed | 2024-03-11T21:35:05Z |
| format | Article |
| id | doaj.art-aea31928863b430c849b2002c096e2a1 |
| institution | Directory Open Access Journal |
| issn | 2214-157X |
| language | English |
| last_indexed | 2024-03-11T21:35:05Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Case Studies in Thermal Engineering |
| spelling | doaj.art-aea31928863b430c849b2002c096e2a12023-09-27T04:43:01ZengElsevierCase Studies in Thermal Engineering2214-157X2023-11-0151103503Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative studyFateh ali0Yanren Hou1Xinlong Feng2M. Zahid3M.A. Rana4Basma Souayeh5College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China; Corresponding author.College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China; School of Mathematics & Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaDepartment of Mathematics, COMSATS University Islamabad, Abbottabad Campus, 22060, Abbottabad, PakistanDepartment of Mathematics and Statistics, Riphah International University, 44000, Islamabad, PakistanDepartment of Physics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa, 31982, Saudi Arabia; Laboratory of Fluid Mechanics, Physics Department, University of Tunis El Manar, Tunis, 2092, Tunisia; Corresponding author. Department of Physics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa 31982, Saudi Arabia.Background: The roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several roll-to-roll coating methods, including forward and roll over web. However, the reverse roll coating study of the non-Newtonian fluid model is presented in this paper. The constitutive equation for the viscoelastic Carreau fluid model as the non-Newtonian fluid is derived using the momentum and energy equations. To simplify the nonlinear systems of partial differential equations, appropriate non-dimensional parameters are employed to convert them into systems of ordinary differential equations. Method: By taking the Weissenberg number as a small parameter, a series solution is obtained for considerable quantities like pressure gradient, axial velocity, flow rate, pressure distribution, and temperature distribution using the perturbation method. In contrast, the numeric outcome of some quantities of engineering interest, like flow rate, coating thickness, share stresses, and separation points, are calculated. Streamlines in 2D and 3D are also drawn to observe the flow pattern. To validate the solution, the problem is also solved numerically with the BVP Midrich method. The analysis of the results demonstrates a satisfactory agreement between the analytical and numerical solutions. Results: The graphical investigation examines the influence of different fluid parameters on velocity profile, shear stress, pressure profile, temperature profile, and pressure gradient. A comprehensive mechanism behind these outcomes is deliberated. It has been observed that velocity rises on increasing the Weissenberg number; however, velocity decreases in the case of the velocities ratio. Further, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Moreover, the separation point and coating thickness decrease with the velocities ratio increase. The results accuracy is checked against papers that have already been published. The comparison reveals good agreement; therefore, the resultant analytical model gives new ways to forecast film thickness and explain influence parameters. Hence, these factors may help in an efficient coating process and improve the substrate life.http://www.sciencedirect.com/science/article/pii/S2214157X23008092Reverse roll coatingCarreau fluid modelTemperature distributionAnalytic solutionsLubrication approximation theoryEngineering quantities |
| spellingShingle | Fateh ali Yanren Hou Xinlong Feng M. Zahid M.A. Rana Basma Souayeh Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study Case Studies in Thermal Engineering Reverse roll coating Carreau fluid model Temperature distribution Analytic solutions Lubrication approximation theory Engineering quantities |
| title | Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study |
| title_full | Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study |
| title_fullStr | Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study |
| title_full_unstemmed | Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study |
| title_short | Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study |
| title_sort | theoretical and numerical investigation of the carreau fluid model during a non isothermal roll coating process a comparative study |
| topic | Reverse roll coating Carreau fluid model Temperature distribution Analytic solutions Lubrication approximation theory Engineering quantities |
| url | http://www.sciencedirect.com/science/article/pii/S2214157X23008092 |
| work_keys_str_mv | AT fatehali theoreticalandnumericalinvestigationofthecarreaufluidmodelduringanonisothermalrollcoatingprocessacomparativestudy AT yanrenhou theoreticalandnumericalinvestigationofthecarreaufluidmodelduringanonisothermalrollcoatingprocessacomparativestudy AT xinlongfeng theoreticalandnumericalinvestigationofthecarreaufluidmodelduringanonisothermalrollcoatingprocessacomparativestudy AT mzahid theoreticalandnumericalinvestigationofthecarreaufluidmodelduringanonisothermalrollcoatingprocessacomparativestudy AT marana theoreticalandnumericalinvestigationofthecarreaufluidmodelduringanonisothermalrollcoatingprocessacomparativestudy AT basmasouayeh theoreticalandnumericalinvestigationofthecarreaufluidmodelduringanonisothermalrollcoatingprocessacomparativestudy |