Abstract
One of the most popular approximate analytical methods are Thermal balance method [3, 4, 6, 7, 12–19, 22÷25] and the Biot method [1, 2, 9–11, 20]. Also the Gauss’ principle of least constraint, known from the analytical mechanics, can also be applied when approximately solving the differential heat conduction equation [20]. In this chapter, the first of the aforementioned methods will be discussed in greater detail.
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Literature
Barry GW, Goodling JS (1987) A Stefan problem with contact resistance. Transactions of the ASME, J. of Heat Transfer 109: 820–825
Biot MA (1970) Variational Principles in Heat Transfer. Clarendon Press, Oxford
Chung BTF, Hsiao JS (1985) Heat transfer with ablation in a finite slab subjected to time-variant heat fluxes. AIAA Journal 23: 145–150
Goodman TR (1964) Application of Integral Methods to Transient Non-linear Heat Transfer. Advances in Heat Transfer 1: 51–122
Karman T (1921) Über laminare und turbulente Reibung. Zeitschrift für angewandte Mathematik und Mechanik 1: 233–252
Młynarski F, Taler J (1976) The effect of thermal-shock-caused stresses on the durability of radiant tubes of converter waste-heat boilers. Power Engineering Archives 3: 115–127
Młynarski F, Taler J (1982) Temperature and stress field triggered by a thermal shock. Chemical and Process Engineering 3(1): 149–162
Pohlhausen K (1921) Zur näherungsweisen der Differentialg-leichung der laminaren Reibungsschicht. Zeitschrift für angewandte Mathematik und Mechanik 1: 252–268
Prasad A, Agrawal HC (1972) Biot’s variational principle for a Stefan problem. AIAA Journal 10(3): 325–327
Prasad A, Sinha SN (1975) Radiative ablation of melting solids. AIAA Journal 14(10): 1494–1497
Rao VD, Sarma PK, Raju GJVJ (1985) Biot’s variational method to fluidized-bed coating on thin plates. Transactions of the ASME, J. of Heat Transfer 107: p. 258–260
Razelos P (1973) Methods of Obtaining Approximate Solution. Section 4 In: Handbook of Heat Transfer, Ed. by WM Rohsenow, JP Hartnett, McGraw-Hill, New York
Rup K, Taler J (1977) Defining transient temperature field in a flat wall with a variable heat conduction coefficient. Theoretical and Applied Mechancis 15(1): 21–28
Rup K, Taler J (1979) Approximate analysis of transient temperature field in simple fins. Engineers’ Thesis 1: 145–153
Taler J, Rup K (1976) Applying heat balance method when determining transient temperature and stress field in a flat wall. Chemical Engineering 6(3): 657–672
Taler J (1978) Approximation of transient temperature field in cylindrical and spherical bodies. Theoretical and Applied Mechanics 16(2): 247–263
Taler J (1979) Approximation of transient temperature fields by one-dimensional polynomials. Chemical Engineering 9(1): 243–258
Taler J, Rup K (1997) Calculating fins by means of ‘averaging functional corrections’ method. Machinery Construction Archives 26(1): 143–153
Taler J (1980) ‘Averaging functional corrections’ method and its relation to heat balance method. Chemical and Process Engineering 3(1): 609–626
Taler J (1977) Application of Gauss method to an approximate solving of heat conduction differential equations. Engineers’ Thesis 25 (2): 349–368
Taler J (1980) Weighted residuums method and its application to the calculation of temperature fields in boilers’ elements. Monography (14) Pub. Krakow University of Technology, Kraków
Venkateshan SP, Solaiappan O (1988) Approximate solution of non-linear transient heat conduction in one dimension. Wärme-und Stoffübertragung 23:229–233
Venkateshan SP, Rao VR (1991) Approximate solution of non-linear transient heat conduction in cylindrical geometry. Wärme-und Stoffübertragung 26: 97–102
Yang JW, Bankoff SG (1987) Solidification effects on the fragmentation of molten metal drops behind a pressure shock wave. Transactions of the ASME, J. of Heat Transfer 109: 226–231
Yang KT, Szewczyk A (1959) An approximate treatment of unsteady heat conduction in semi-infinite solids with variable thermal properties. Transactions of the ASME, J. of Heat Transfer 81: 251–252
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(2006). Approximate Analytical Methods for Solving Transient Heat Conduction Problems. In: Solving Direct and Inverse Heat Conduction Problems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33471-2_20
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DOI: https://doi.org/10.1007/978-3-540-33471-2_20
Publisher Name: Springer, Berlin, Heidelberg
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