Characterization of single-blow temperature responses by first moments.
Author:
Gerhard F. Kohlmayr
Journal:
Quart. Appl. Math. 27 (1969), 161-172
MSC:
Primary 80.45; Secondary 35.00
DOI:
https://doi.org/10.1090/qam/250564
MathSciNet review:
250564
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Abstract: Transient temperature response functions, given as analytic solutions of the single-blow problem in transient heat transfer analysis, are characterized by the first moment of the difference between downstream and upstream fluid temperatures. Both the single-blow problem and the corresponding inverse problem are formulated in terms of Volterra integral equations. Monotonicity and boundedness properties of the response functions are derived. It is shown that the first moment of the temperature difference is well suited for an indirect solution of the curve matching problem.
H. Hausen, Über die Theorie des Wärmeaustausches in Regeneratoren (On the theory of heat exchange in regenerators), Z. angew. Math. Mech. (3) 9, 173–200 (1929)
T. E. W. Schumann, Heat transfer: a liquid flowing through a porous prism, J. Franklin Inst. 208, 405 (1929)
G. L. Locke, Heat transfer and flow friction characteristics of porous solids, TR No. 10, Department of Mechanical Engineering, Stanford University, California (June 1950)
M. Jakob, Heat transfer, vol. 2, Wiley, New York, 1957, pp. 261–341
G. F, Kohlmayr, Exact maximum slopes for transient matrix heat-transfer testing, Int. J. Heat Mass Transfer 9, 671 (1966)
P. F. Pucci, C. P. Howard, and C. H. Piersall, Jr., The single-blow transient testing technique for compact heat exchanger surfaces, J. of Engineering for Power, Trans. ASME, Series A (1), 89, 29–40 (1967)
G. F. Kohlmayr, Extension of the maximum slope method to arbitrary upstream temperature changes, J. Heat Transfer, Trans. ASME, Series C (1), 90, 130–134 (1968)
G. F. Kohlmayr, Analytical solution of the single-blow problem by a double Laplace transform method, J. Heat Transfer, Trans. ASME, Series C (1), 90, 176–178 (1968)
G. F. Kohlmayr, Properties of the transient heat transfer (single-blow) temperature response function, AIChE Journal 14, 499–501 (1968)
- J. A. Shohat and J. D. Tamarkin, The Problem of Moments, American Mathematical Society Mathematical surveys, Vol. I, American Mathematical Society, New York, 1943. MR 0008438
- David Vernon Widder, The Laplace Transform, Princeton Mathematical Series, vol. 6, Princeton University Press, Princeton, N. J., 1941. MR 0005923
- Lothar Berg, Introduction to the operational calculus, North-Holland Series in Applied Mathematics and Mechanics, Vol. 2, North-Holland Publishing Co., Amsterdam; Interscience Publishers John Wiley & Sons Inc., New York, 1967. Translation by Veneda Publishing Company, Ltd., Oxford. MR 0220009
G. F. Kohlmayr, An indirect curve matching method for transient matrix heat-transfer testing in the low $N_{tu}^ -$ range, Int. J. Heat Mass Transfer 11, 567 (1968)
H. Hausen, Über die Theorie des Wärmeaustausches in Regeneratoren (On the theory of heat exchange in regenerators), Z. angew. Math. Mech. (3) 9, 173–200 (1929)
T. E. W. Schumann, Heat transfer: a liquid flowing through a porous prism, J. Franklin Inst. 208, 405 (1929)
G. L. Locke, Heat transfer and flow friction characteristics of porous solids, TR No. 10, Department of Mechanical Engineering, Stanford University, California (June 1950)
M. Jakob, Heat transfer, vol. 2, Wiley, New York, 1957, pp. 261–341
G. F, Kohlmayr, Exact maximum slopes for transient matrix heat-transfer testing, Int. J. Heat Mass Transfer 9, 671 (1966)
P. F. Pucci, C. P. Howard, and C. H. Piersall, Jr., The single-blow transient testing technique for compact heat exchanger surfaces, J. of Engineering for Power, Trans. ASME, Series A (1), 89, 29–40 (1967)
G. F. Kohlmayr, Extension of the maximum slope method to arbitrary upstream temperature changes, J. Heat Transfer, Trans. ASME, Series C (1), 90, 130–134 (1968)
G. F. Kohlmayr, Analytical solution of the single-blow problem by a double Laplace transform method, J. Heat Transfer, Trans. ASME, Series C (1), 90, 176–178 (1968)
G. F. Kohlmayr, Properties of the transient heat transfer (single-blow) temperature response function, AIChE Journal 14, 499–501 (1968)
J. A. Shohat and J. D. Tamarkin, The problem of moments, Math. Surveys, no. 1, Amer. Math. Soc., Providence, R. I., 1943
D. V. Widder, The Laplace transform, Princeton University Press, Princeton, N. J., 1941
L. Berg, Introduction to the operational calculus, North Holland, Amsterdam, 1967
G. F. Kohlmayr, An indirect curve matching method for transient matrix heat-transfer testing in the low $N_{tu}^ -$ range, Int. J. Heat Mass Transfer 11, 567 (1968)
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Article copyright:
© Copyright 1969
American Mathematical Society
