HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text Free Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Knight, J. H. Articles by Kluitenberg, G. J. Search for Related Content PubMed Articles by Knight, J. H. Articles by Kluitenberg, G. J. GeoRef GeoRef Citation Agricola Articles by Knight, J. H. Articles by Kluitenberg, G. J. Related Collections Soil Methods/Instrumentation Soil Thermal Properties Heat Transport

Sensitivity of the Dual-Probe Heat-Pulse Method to Spatial Variations in Heat Capacity and Water Content

^a CSIRO Land and Water, 120 Meiers Rd., Indooroopilly, QLD 4068, and Dep. of Environmental Engineering, Griffith Univ., Nathan, QLD 4111, Australia
^b Dep. of Agronomy, Kansas State Univ., Manhattan, KS 66506. Contribution no. 07-97-J from the Kansas Agric. Exp. Stn., Manhattan

View larger version (13K): [in this window] [in a new window]   FIG. 1. Diagram of a dual-probe heat-pulse (DPHP) sensor with heater probe and temperature probe. The plane passing through the heater and temperature probes corresponds to the x–y plane in Fig. 2 and defines the area in which the spatial sensitivity of the DPHP method is characterized. The plane is oriented normal to the probes and passes through the temperature probe as the location where temperature is measured with a thermistor or thermocouple. See Heitman et al. (2003) for a more detailed schematic diagram that includes cutaway views of the probes and sensor body.

View larger version (9K): [in this window] [in a new window]   FIG. 2. Geometrical configuration of the heater probe and temperature probe of a dual-probe heat-pulse sensor. The arbitrary point (x,y) represents the point at which the Fréchet kernel F(x,y,t) is calculated. The heater and temperature probes are separated by distance a, with the heater probe at (x,y) = (–a/2,0) and the temperature probe at (x,y) = (a/2,0). The scalar quantities r1 = [(x + a/2)2 + y2] and r2 = [(x – a/2)2 + y2] give the distance from the point (x,y) to the heater probe and temperature probe, respectively.

View larger version (17K): [in this window] [in a new window]   FIG. 3. Dimensionless Fréchet kernel F*(X,0,) for a dual-probe heat-pulse sensor with heater probe at (X,Y) = (–,0) and temperature probe at (X,Y) = (,0). Results are from Eq. [32] with Y = 0 for dimensionless times = 0.21, 0.23, 0.25 0.27, and 0.29. The curve for = 0.25 is the special case of Eq. [34] for which there are no singularities at the heater probe or temperature sensor.

View larger version (8K): [in this window] [in a new window]   FIG. 4. Dimensionless integral I*() as defined by Eq. [40]. It is the spatial integral of the Fréchet kernel F*(X,Y,) across a small region of radius R2 = b centered at (X,Y) = (,0), the location of the temperature probe. Results are from Eq. [A5] with b = 1/12. Note that I*() varies smoothly near = 0.25, despite the fact that the kernel F*(X,Y,) has a negative singularity at (X,Y) = (,0) for < 0.25 and a positive singularity at (X,Y) = (,0) for > 0.25.

View larger version (25K): [in this window] [in a new window]   FIG. 5. Surface representing the Fréchet kernel F*(X,Y,) as a function of X and Y for X 0 at dimensionless time = 0.25. The kernel F*(X,Y,) is for a dual-probe-heat-pulse sensor with heater probe at (X,Y) = (–,0) and temperature probe at (X,Y) = (,0). The vertical line shows the location of the temperature probe at (X,Y) = (,0). Results are from Eq. [34]. The dimensionless kernel is negative everywhere, and there is no singularity at (X,Y) = (,0).

View larger version (34K): [in this window] [in a new window]   FIG. 6. Contour lines representing selected values (numbers on curves) of the dimensionless heat capacity kernel F*(X,Y,) for a dual-probe heat-pulse sensor with heater probe at (X,Y) = (–,0) and temperature probe at (X,Y) = (,0). The dots show the location of the probes. The two contours for F*(X,Y,) = –0.054051 (unlabeled) intersect to form two saddle points. The kernel has a local maximum of F*(X,Y,) = –0.044986 at (X,Y) = (0,0) and global minima of F*(X,Y,) = –0.082842 near (X,Y) = (–,0) and (X,Y) = (,0) (cross symbols). Results are from Eq. [34]. The dimensionless heat capacity kernel is negative everywhere, and has no singularities at (X,Y) = (–,0) and (X,Y) = (,0).

View larger version (28K): [in this window] [in a new window]   FIG. 7. Contour lines representing selected values (numbers on curves) of the dimensionless heat capacity kernel F*(X,Y,) for a dual-probe heat-pulse sensor with heater probe at (X,Y) = (–,0) and temperature probe at (X,Y) = (,0). The dots show the location of the probes. The exact values (solid lines) are from Eq. [34] and are identical to the contours for F*(X,Y,) = –0.0001, –0.001, –0.005, –0.02, and –0.04 in Fig. 6. The dashed lines are ellipses, which are approximations of the exact contours.

View larger version (32K): [in this window] [in a new window]   FIG. 8. Contour lines representing selected values of the dimensionless heat capacity kernel F*(X,Y,) for a dual-probe heat-pulse sensor with heater probe at (X,Y) = (–,0) and temperature probe at (X,Y) = (,0). The dots show the location of the probes. The numbers on the contour lines are values of P*(,0,), which indicate the fraction of the total spatial sensitivity for the region contained within a particular contour. The fractional spatial sensitivity for each contour of F*(X,Y,) was obtained from Eq. [43]. Table 1 shows the value of F*(X,Y,) for each contour, as well as the area of the region bounded by each contour.