### Effect of Temperature-Dependent Viscosity on the Final Sheet Thickness in the Calendering of Newtonian Sheets of Finite Thickness

#### Abstract

In this work, a non-isothermal simplified model for the calendering process of a Newtonian

liquid with exponential dependence of viscosity on temperature is theoretically treated. The effects of non-isothermal conditions on the exiting sheet thickness in calendering process are investigated. The mass, momentum and energy balance equations, based on the lubrication theory, were nondimensionalized and solved for the velocity, pressure and temperature fields by using perturbation and numerical techniques, where the leave-off distance of the calendered material is unknown and represents an eigen-value of the mathematical problem. With the knowledgement of the above variables, the exiting sheet thickness in the calendering process was determined. The mentioned governing equations contain basically two dimensionless parameters: the well-known Graetz number, Gz; and a parameter that takes into account the effect of the variable viscosity as a function of the temperature, defined as the ratio of the Nahme-Griffith number, Na, to the Graetz number, Gz. For values of this parameter much less than unity, the dimensionless exiting sheet thickness of the calendering process has been obtained as a function of the involved dimensionless parameters. The numerical results show that the inclusion of temperature-dependent viscosity effect reduces about 6 % the dimensionless exiting sheet thickness, or 20 % in the leave-off distance in comparison with the case of temperature independent viscosity.

liquid with exponential dependence of viscosity on temperature is theoretically treated. The effects of non-isothermal conditions on the exiting sheet thickness in calendering process are investigated. The mass, momentum and energy balance equations, based on the lubrication theory, were nondimensionalized and solved for the velocity, pressure and temperature fields by using perturbation and numerical techniques, where the leave-off distance of the calendered material is unknown and represents an eigen-value of the mathematical problem. With the knowledgement of the above variables, the exiting sheet thickness in the calendering process was determined. The mentioned governing equations contain basically two dimensionless parameters: the well-known Graetz number, Gz; and a parameter that takes into account the effect of the variable viscosity as a function of the temperature, defined as the ratio of the Nahme-Griffith number, Na, to the Graetz number, Gz. For values of this parameter much less than unity, the dimensionless exiting sheet thickness of the calendering process has been obtained as a function of the involved dimensionless parameters. The numerical results show that the inclusion of temperature-dependent viscosity effect reduces about 6 % the dimensionless exiting sheet thickness, or 20 % in the leave-off distance in comparison with the case of temperature independent viscosity.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**