Question: Viscous heating in a ball-point pen, you are asked to decide whether the apparent decrease in viscosity in ball-point pen inks during writing results from

Viscous heating in a ball-point pen, you are asked to decide whether the apparent decrease in viscosity in ball-point pen inks during writing results from "shear thinning" (decrease in viscosity because of non-Newtonian effects) or "temperature thinning" (decrease in viscosity because of temperature rise caused by viscous heating). If the temperature rise is less than 1K, then "temperature thinning" will not be important. Estimate the temperature rise using Eq. 10.4-9 and the following estimated data:

Clearance between ball and holding cavity 5 x 10^–5 in

Diameter of ball 1 mm

Viscosity of ink 10⁴ cp

Speed of writing 100 in/min

Thermal conductivity of ink (rough guess) 5 x 10^-4 cal/s ∙ cm ∙ C

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