Apparatus and method for simultaneously determining thermal conductivity and thermal contact resistance

Apparatus for simultaneously determining the thermal conductivity and thermal contact resistance of a sample, wherein said sample defines a first and second surface, and said apparatus comprises:

• a) a first block comprising an upper surface, a lower surface, and a periphery, wherein said first block comprises a melting point greater than the melting point of said sample;
• b) a second block comprising an upper surface, a lower surface, and a periphery, wherein said second block comprises a melting point greater than the melting point of said sample;
• c) a sample chamber for holding said sample, wherein said chamber is defined by said lower surface of second block and said upper surface of said first block, such that a first interface is formed between said first surface of said sample and said lower surface of said second block, and a second interface is formed between said second surface of said sample and said upper surface of said first block;
• d) a heat source connected to said upper surface of said second block;
• e) a heat sink connected to said lower surface of said first block, wherein said heat sink has a temperature less than that of said heat source, wherein said heat source and said heat sink modulate the temperature of said sample;
• f) temperature sensing means connected to said blocks;
• g) a temperature calculating means connected to said temperature sensing means, wherein said temperature calculating means converts a signal from said temperature sensing means into a numerical temperature value;
• and
• h) a computing means interfaced with said temperature calculating means, wherein said computing means simultaneously determines the thermal conductivity of said sample and the thermal contact resistance of said sample at said first and second interfaces with the temperatures of said first block and said second block as a function of time, wherein said computing means utilizes the function:
• .beta..sub.k+1 =.beta..sub.k +[X.sup.T WX+V].sup.-1 [X.sup.T W(T-.eta.(.beta..sub.k))+V(.nu.-.beta..sub.k)]
• where:
• C is heat capacity (j/m.sup.3 -K),
• k is thermal conductivity (W/m-K),
• R.sub.c is thermal contact resistance (m.sup.2 -K/W),
• n,m are number of points at which k and R.sub.c are defined, respectively,
• t is time (seconds),
• T is Temperature, vector of measured temperature (C.),
• V is variance matrix,
• W is weighting matrix,
• X is axial distance (m),
• x is sensitivity matrix=[.differential..eta..sub.i /.differential..beta..sub.j ],
• .beta. is parameter vector=[k.sub.t=1,n R.sub.c1 .vertline..sub.t=1,n R.sub.c2 .vertline..sub.t=1,n ].sup.T,
• .eta. is Temperature, vector of temperatures from physical model of apparatus (.degree.C.),
• .nu. is initial value of .beta.,
• R.sub.S is the thermal resistance of the sample=t/kA(m.sup.2 -K/W),
• t.sub.h is sample thickness (m),
• A is surface area (m.sup.2),
• subscripts
• 1,2 are upper and lower interfaces between plastic specimen and steel blocks, respectively.

A method for simultaneously determining the thermal conductivity and thermal contact resistance of a sample, wherein the sample defines a first and second surface, wherein the method comprises the steps of:

• a) providing a first block comprising an upper surface, a lower surface and a periphery, and a second block comprising an upper surface, a lower surface, and a periphery, wherein the first and second blocks comprise melting points greater than the melting point of the sample;
• b) forming a sample chamber for holding the sample by positioning the first and second blocks such that the upper surface of the first block is parallel to the lower surface of the second block;
• c) placing the sample in the sample chamber so that a first interface is formed between the first surface of the sample and the lower surface of the second block, and a second interface is formed between the second surface of the sample and the upper surface of the first block;
• d) modulating the temperature of the sample;
• e) measuring the temperature of the first and second blocks at specific nodes relative to the first and second interfaces as a function of time during the modulating of the temperature of the sample;
• and
• f) determining simultaneously the thermal conductivity of the sample, and the thermal contact resistance of the sample at the first and second interfaces, using the function:
• .beta..sub.k+1 =.beta..sub.k +[X.sup.T WX+V].sup.-1 [X.sup.T W(T-.eta.(.beta..sub.k))+V(.nu.-.beta..sub.k)],
• where:
• C is heat capacity (j/m.sup.3 -K),
• k is thermal conductivity (W/m-K),
• R.sub.c is thermal contact resistance (m.sup.2 -K/W),
• n,m are number of points at which k and R.sub.c are defined, respectively,
• t is time (seconds),
• T is Temperature, vector of measured temperature (C.),
• V is variance matrix,
• W is weighting matrix,
• x is axial distance (m),
• X is sensitivity matrix=[.differential..eta..sub.i /.differential..beta..sub.j ],
• .beta. is parameter vector=[k.sub.t=1,n R.sub.c1 .vertline..sub.t=1,n R.sub.c2 .vertline..sub.t=1,n ].sup.T,
• .eta. is Temperature, vector of temperatures from physical model of apparatus (.degree.C.),
• .nu. is initial value of .beta.,
• R.sub.S is the thermal resistance of the sample=t/kA(m.sup.2 -K/W),
• t.sub.h is sample thickness (m),
• A is surface area (m.sup.2),
• subscripts
• 1,2 are upper and lower interfaces between plastic specimen and steel blocks, respectively.