----------------------------------- Summary -----------------------------------
Similar to klog 14740, here is the thermal conductivity estimation using the heating curve of the high power beam dump. Again, the heat occurred at the dump is conducted from the dump to the copper flange through 10 copper heat sinks. The fitted thermal conductivity is 1400 W/m/K, where as the thermal conductivity of copper (heat sink) is 400 W/m/K around 30-60 deg C. This is consistent with the cooling measurement (klog 14740).
----------------------------- The fitting function T(t) ----------------------
Heating is done by 10W laser continuously hitting the beam dump. In this case, the differential equation of the heat can be written as
M*C0 * dT(t)/dt = lambda * A / dx * (Tb - T(t)) + Pin
where lambda is a thermal conductivity of the path, A is the area of the path, dx is the length of that path, and Tb is an albtrary parameter of temperature, respectively. Again solving this equation, we get
Tt = Tb + Pin/K + (T0 - Tb - Pin/K) * exp (-K/C *t);
where K = lambda * A/x, C = M * C0 with the dump weight M and specific heat of heat sink C0. The equilibrium temperature after a long time is thus Tb + Pin/K.
Heating is done by 10W laser continuously hitting the beam dump. In this case, the differential equation of the heat can be written as
M*C0 * dT(t)/dt = lambda * A / dx * (Tb - T(t)) + Pin
where lambda is a thermal conductivity of the path, A is the area of the path, dx is the length of that path, and Tb is an albtrary parameter of temperature, respectively. Again solving this equation, we get
Tt = Tb + Pin/K + (T0 - Tb - Pin/K) * exp (-K/C *t);
where K = lambda * A/x, C = M * C0 with the dump weight M and specific heat of heat sink C0. The equilibrium temperature after a long time is thus Tb + Pin/K.
Heating is done with a 10W laser continuously hitting the beam dump. In this case, the differential equation of the heat can be written as
M*C0 * dT(t)/dt = lambda * A / dx * (Tb - T(t)) + Pin
where lambda is a thermal conductivity of the path, A is the area of the path, dx is the length of that path, C0 is a specific heat of the heat sink (ignoring the temperature dependency), M is a weight of the dump, and Tb is an arbitrary parameter of temperature, respectively. Again solving this equation, we get
Tt = Tb + Pin/K + (T0 - Tb - Pin/K) * exp (-K/C *t);
where K = lambda * A/dx, C = M * C0 for simplicity. The equilibrium temperature after a long time is thus Tb + Pin/K.
