The science behind the phenomenon of a tongue sticking to a metal pole on a winter day is that the cold pole will freeze the water in saliva, causing it to turn to ice and freeze to the pole. Metal poles have a very high thermal conductivity, meaning the heat traveling in from a tongue will spread across the pole quickly and not heat up the metal pole locally where the tongue is touching. This causes the pole to stay cold where the tongue is touching and applies a fixed temperature boundary condition at the tip of the tongue, potentially causing it to freeze. Since both a metal pole in the ground and a tongue sticking out of a mouth act like 1D fins (remember that fins have convection perpendicular to conduction along their x-direction), we can use fin analysis to better study this phenomenon and analyze this particular movie scene. Use the following properties throughout the next set of questions regarding the pole and the stuck tongue: Property Meaning kp Dp Lp kt W₁ Tt Lt Thermal conductivity of the metal pole Diameter of the metal pole Length of the metal pole Approximate thermal conductivity. of a human tongue Approximate average width of a human tongue Approximate thickness of a human tongue Approximate length of a human tongue Value Unit 45 W m-K 0.15 m 18 m 0.65 W m-K 0.050 m 0.015 m 0.090 m

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.39P

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Question

b) How much heat (in W) is dissipated by the pole based on your answer to the previous question?

c) What is the temperature at the tip of the pole ( in ∘C)?

d) assume Flick sticks his tongue to the pole in the movie at a height of 1.1m from the ground. What is the temperature of the pole at this location ( in ∘C)?

The science behind the phenomenon of a tongue sticking to a metal pole on a winter day is
that the cold pole will freeze the water in saliva, causing it to turn to ice and freeze to the
pole. Metal poles have a very high thermal conductivity, meaning the heat traveling in from a
tongue will spread across the pole quickly and not heat up the metal pole locally where the
tongue is touching. This causes the pole to stay cold where the tongue is touching and applies
a fixed temperature boundary condition at the tip of the tongue, potentially causing it to
freeze.
Since both a metal pole in the ground and a tongue sticking out of a mouth act like 1D fins
(remember that fins have convection perpendicular to conduction along their x-direction), we
can use fin analysis to better study this phenomenon and analyze this particular movie scene.
Use the following properties throughout the next set of questions regarding the pole and the
stuck tongue:
Property Meaning
kp
Dp
Lp
kt
Wt
Tt
Lt
Thermal conductivity of the metal
pole
Diameter of the metal pole
Length of the metal pole
Approximate thermal conductivity.
of a human tongue
Approximate average width of a
human tongue
Approximate thickness of a
human tongue
Approximate length of a human
tongue
Value Unit
45
W
m.K
0.15 m
18
0.65
m
W
m.K
0.050 m
0.015 m
0.090 m

m² K
Start by analyzing the pole and assume that the air surrounding the pole is at T = -10°C
on a cold day, with h = 10 W. The ground in which the pole sits (which is typically warmer
than the air on winter days due to the effects of thermal radiation and the ground's insulative
properties) is at 5°C. The base of the pole is assumed to be the same temperature as the
ground in steady state. Treating the pole as a cylindrical fin with constant cross-section, first
find the value of m for the pole. Enter your numeric answer below (in units of 1) to at
least two decimal places. Don't forget to decipher this given geometry into a drawing in your
written work!
meter

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