The thermal diffusivities and thermal conductivities of powders, especially PMMA-coated
silicon carbide, at various temperatures, have been tested by two different dynamic methods, the
water-bath method and the laser-heated method. The thermal conductivity data found by these two
techniques are found to be consistent with each other.Mechanical Engineerin

Barlow, Joel W.

Sih, Samuel S.

English

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MEASUREMENT OF THE THERMAL CONDUCTIVITYOF POWDERS TWO DIFFERENT .METHODSSamuel S. Sih and Joel W. BarlowChemical Engineering DepartmentUniversity of Texas at AustinAbstractThe thermal diffusivities and thermal conductivities of powders, especially PMMA-coatedsilicon carbide, at various temperatures, have been tested by two different dynamic methods, thewater-bath method and the laser-heated method. The thermal conductivity data found by these twotechniques are found to be consistent with each other.A Review of the Two TechniquesA Differential scanning calorimeter (DSC), DSC-7 made by the Perkin-Elmer Company, hasbeen used [l] to measure the heat capacities at various temperatures for all of the powders used.The heat capacities of the powders were found to be functions of temperature. The specific heatsof all the powders are found to be the same as those of the corresponding solids.The thermal conductivities of powders are measured by an unsteady state method with twowater baths of small temperature differences[1,2,3]. The range of the temperatures investigated,limited by the boiling point of water in the water-bath method, was mainly from 30-90°C, i.e.below the sintering temperatures of the powders. During the process of raising the temperature,sometimes bubbles of air were seen to adhere to the outside surface of the sample tube whichobviously decreases the rate of the transfer of heat. The authors found that the formation of airbubbles may be avoided by the addition of some soap solution into the water baths to decrease thesurface tension of the water used. Only small changes in temperature, typically 10°C, are used.This is necessary to account for the temperature dependent thermal properties at the powder beds.As the temperatures used during the SLS process are not limited to the ambient temperatures, alaser-heated method [5,6,7] was adopted to study thermal conductivity at the higher temperatures.This technique uses a laser to heat the surface of a sample powder bed while a thermocouple at acertain depth inside the powder bed records the rise of temperature against time.Figure 1 shows the basic experiment. The powder bed is contained in a 1 inch diameter by 5inch long glass tube. The bed temperature is maintained at the desired temperature by a 675 wattTempco Co. coil heater (MHS1255BL02). That is controlled by a pulsed DC output temperaturecontroller (Omega CN76120). The pulsed output is used to switch a solid state relay connected athe heater AC power line. The powder samples completely fill the sample tube. The centertemperature, 1 cm below the bed surface, is measured with a thermocouple. The tube is wrappedwith thin aluminum foil and placed inside the coil heater.370Thermal coupleleadingto the data acquisitionsystemSample powderAluminum foilBeam expanderThermal~__- couple for thecoil heater(inside the coilheater, fortemp.controlling)i ++ 10Figure 1. The laser and the powder sampleOne might have the worry whether the heat energy supplied through the coil heater mightinterfere with the energy supplied by the laser power. But actually, with the short incidence of thelaser light (from 1 min. to about 4 min.) and with the small change in temperature caused by thelaser, the coil heater generally sends in little energy, if any.Experimental ResultsThe PMIvl.A-eoated SiC., prepared by Neal Vail, has 19.3 vol% of the polymer. The soliddensity for PMMA is 1.2 glee, the solid density of SiC is 3.217 glee. So the solid density of thePMMA-eoated SiC is 2.827 glee.The bulk density of the powder sample we used for the waterbath method was 1.328 glee. Consequently, the porosity of the powder sample was 0.530. Thetemperature range for the water bath method was 30-90°C. One of the temperature vs. time curveof water bath runs is shown below. (See Figure 2.)371SiCIPMMA, 50-60°C0.000015 .....--[-....•+..~.Yl vs.time graph for PMMA-coated SiC powder0.00003 j"TT....-j""T""""'-rrr-r-t""""""'''''''''''''''''''''''''''"T"T"","","T"T""f1000800400 600t(sec)200: i. ,.~ *...g,-~.cE1;F.. iii i5 ~ L : : : ..! : : :5 -/- , + , , .t(sec)Figure 2. PMMA-coated SiC powdertemperature rising curve, SO-60°CFigure 3. Yl vs time graph for the samepowder and same heating cycleThe analysis of the water bath data is done according to the procedure discussed before. [1]The Yl vs time graph for the PMMA-coated SiC powder, from 50-60°C is shown in Figure 3.(See Figure 3.)The heat capacity of the PMMA-coated SiC powder vs. temperature is shown in Figure 4.(See Figure 4.) The resulting thermal conductivity of the PMMA-coated SiC powder vstemperature is shown in Figure S.k, SiC/PMMA powder,water bath method0.2 rr-r..,...,....t"T""T..,..,-t"T""T...,...,..1'""'r""...,...,..1'""'r""---r-T"-r-r--~· ,· ,· .. ,"no no':'.""'hV1(Wiiii:K)1' .........+.......... ;..........; 0 k(high) ; ; ;i0 kO~w) ! ! !, . i : 8. , .··········1············r··········· ······--···r···········-r··········! 6 i !!· ,... "., . . ,·······T·········T·······.·T···....··T...·· ..····,··...·....Cp of SiCIPMMA, , . . , ,.t=t::t=IL:ili2 i;: i ; ; ,~ :']:;:111[17 •••••••• : ········[·········T·········T·········T········+······..+ .: : : : : ;60 70 80 90 100T("C)0.1i2 0.1is~~ 0.10.120')0 40 50 60 70 so 90T("C)Figure 4. The heat capacity vs. temperature Figure 5. The thermal conductivity vs.curve ofPMMA-coated SiC powder temperature curve ofPMMA-coated SiC powderThe porosity of the powder of the PMMA-coated SiC which we tested through the laser-heatedmethod was also 0.530. The temperature rise vs. time curve of one of the runs of the laser-heatedmethod is shown in Figure 6.372131.130...-. 129.~[:::128.127.k for PMMA-coated SiC powder, laser-heated method132.00r-----,,----...,..----,------:------,. .. .It;[~limt~tIilj:mri~~~~mlmmm. j{"liji•••W( ( l}.O.u .. __ .• __ ._ } i u .~o: . ::; :t(sec)Figure 6. The temperature rise vs. time curve of PMMA-coated SiC powder in the laser-heatedmethod.The data are analyzed by the ratio method as discussed before [5]. For the run of Figure 6, thereading of the temperature at 90 sec. was 127.82°C, and the reading of the temperature at 180 sec.was 131.15°C. (The reading of the numbers were obtained not through the graph, but through theoutput of the data acquisition system.) As the initial temperature of the run was 126.05°C, theratio, R, of the two temperature differences at the two time periods isR = 131.15 -126.05 =2.88 (1)127.82 -126.05The mathematical solution for this semi-infinite I-D heat conduction problem [5] is~T(z, t) = 2Elo -f(ii ieife[ ~ ]k 2vat-Ii ieife[ L ]R = ~T(L, 2tl) = T2 - To = 2-1fii;~T(L, tl) TI - To ieife[_L_]2..fiit.1-Ii ieife[ ]=__--=2-:...,-li:=--JFO~F:...:::o:.._ieife[ ~]2vFo(2)In the above equation, the Fourier number, Fo =aqlL2, and L is the depth of the pointbeneath the surface at which the thermocouple is placed.The authors wrote a Fortran program for the above relationship and got a table to find out thevalue of Fo for every definite R value, in Equation (2). For the value of R =2.88, we found Fo =0.322. Therefore,373

Measurement of the Thermal Conductivity of Powders by Two Different Methods

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Measurement of the Thermal Conductivity of Powders by Two Different Methods

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