caa a22 4500 475839684 CHVBK 20180406123858.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1023/A:1004637514734 doi (NATIONALLICENCE)springer-10.1023/A:1004637514734 Bubanja V. New Zealand Institute for Industrial Research and Development, PO Box 31-310, Lower Hutt, New Zealand aut The ac-dc difference of single-junction thermal converters [Elektronische Daten] [V. Bubanja] A nonlinear parabolic partial differential equation of heat conduction subject to the Robin boundary conditions is considered. The equation describes energy conservation in the heater wire of a single-junction thermal converter for both ac and dc currents. In the audio-frequency range the temperature distribution along the heater is calculated and the ac-dc difference deduced by means of the Picard iterative technique. The previously neglected effects of radiation and the thermal properties of the heater wire are included. An expression for the ac-dc difference is also derived in the low-frequency regime. The thermal conductance of the thermocouple, which has previously been neglected, is taken into account. The calculated increase in the ac-dc difference is consistent with recent measurements. The solution in this limit is found by both an eigenfunction-expansion method and the Laplace-transform method. Comparison of the solutions obtained by the two methods gives some useful formulae for the summation of numerical series. Key words:alternating current standard, single junction thermal converters, heat conduction Kluwer Academic Publishers, 2000 Journal of Engineering Mathematics Kluwer Academic Publishers 38/1(2000-07-01), 33-50 0022-0833 38:1<33 2000 38 10665 https://doi.org/10.1023/A:1004637514734 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004637514734 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bubanja V. New Zealand Institute for Industrial Research and Development, PO Box 31-310, Lower Hutt, New Zealand aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 38/1(2000-07-01), 33-50 0022-0833 38:1<33 2000 38 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer