Finite
body is heated by a fluid with contact resistance: In this case, the unsteady state solution to
the problem involves three parameters
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Finite
body is heated by a fluid with contact resistance: In this case, the unsteady state solution to
the problem involves three parameters
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The
dimensionless temperature Y is given as a function of these parameters for
different types of geometries by Gurnie-Lurie.
Example
5.22:
A steel circular rod having diameter 8 in, length 12 ft, is initially at a
temperature of 400 °F. It is immersed in a bath having a constant
temperature of 200 °F. What is the
temperature 2 in below the surface after 15 minutes if the following data
apply.
Free
convection coefficient from oil, h = 50 Btu/(h·ft2·°F).
Thermal
conductivity, k = 25 Btu/(h·ft·°F);
Thermal
diffusivity, α = 0.425 ft2/h.
Solution: This is a situation where unsteady state
heat transfer occurs through a cylindrical object with a contact resistance.
Characteristic
length of the cylinder is the diameter of the cylinder, L = 8 in = 0.667
ft
Time
lapsed, θ = 15 min = 0.25 h. And
the parameter values can be calculated as
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We
can find the dimensionless temperature for cylindrical object from Gurney-Lurie
Chart, Fig 18.13 as Y = 0.31.
The
initial temperature, To of the body is 200 °F, and the
surface temperature, Ts of the body is 400 °F. Plugging these values, we can find the
temperature at the center of the cylinder as
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