Analysis for heat transfer coefficients across polymer-steel interfaces

Figure 3: Single layer structure

Figure 4: Three layer sandwich structure

 

For a single specimen between plates, Figure 3, the thermal resistance R₁is given as the sum of thermal resistances of the two interfaces and the sandwiched layer plus a contribution due to the instrument construction itself r_inst:

Equation 8

where is the thermal resistance of the interface (denoted by the superscript _h) between the metal and polymer (denoted by the subscript _m-p) and  is the thermal resistance of the polymer specimen (denoted by the subscript _p1) due to its thermal conductivity and thickness (denoted by the superscript΢΢). The term r_inst is a factor for the thermal resistance of the instrument due to the interfaces and layers within the instrument itself.

Similarly for a polymer specimen of a different thickness, indicated by the use of the subscript _p2:

Equation 9

For the three-layer system, Figure 4, the total thermal resistance is similarly given by:

Equation 10

where is the resistance of the metal layer. In order to express the thermal resistances of the component layers and interfaces in terms of measurable or determinable quantities, taking the difference of Equations 8 and 9 yields:

Equation 11

or, using Equation 4:

Equation 12

Assuming equal thermal conductivities of the two specimens, i.e. _p = _p1 = _p2, as they were made of the same material, then:

Equation 13

Thus the thermal resistances of the polymer layers are given by:

Equation 14

and:

Equation 15

Similarly, the thermal resistance of the metal layers is given by:

Equation 16

Rearranging equation 10 yields:

Equation 17

The thermal resistance of the instrument, r_inst, without specimen and without the plate-plate interface, can be determined from measurements of the metal plate specimen. For no specimen:

Equation 18

For the metal plate specimen:

Equation 19

Thus from the difference in equations 18 and 19 the thermal resistance of the metal-metal interface is given by:

Equation 20

and can be determined, given values for the thickness and thermal conductivity of the metal plate. Thus using Equations 18 and 20 the thermal resistance correction factor r_instcan be determined:

Equation 21

Thus by substituting using the above, Equation 17 becomes:

Equation 22 

thereby enabling the heat transfer coefficient of the polymer-metal interface to be determined.

For more information, please contact Angela Dawson