Condition-convection from a cylindrical source with increasing radius

Author:
H. R. Bailey

Journal:
Quart. Appl. Math. **18** (1961), 325-333

MSC:
Primary 80.00

DOI:
https://doi.org/10.1090/qam/121075

MathSciNet review:
121075

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Abstract: The problem of heat flow by conduction and convection from a cylindrical source with increasing radius is solved. A quasi stationary state solution is obtained for the case of a finite convection coefficient and with the radius increasing at a constant velocity. A transient solution is obtained for the case of an infinite convection coefficient and with the radius increasing at a rate proportional to the square root of time.

**[1]**H. R. Bailey,*Heat conduction from a cylindrical source with increasing radius*, Quart. Appl. Math.**17**(1959), 255–261. MR**0106694**, https://doi.org/10.1090/S0033-569X-1959-0106694-3**[2]**H. R. Bailey, and B. K. Larkin,*Heat conduction in underground combustion*, Trans. Am. Inst. Mining, Met. and Pet. Engrs.**216**, 123-129 (1959)**[3]**H. R. Bailey, and B. K. Larkin,*Conduction-convection in under-ground combustion*, AIChE SPE Joint Symposium on Oil Recovery Methods, Dee. 1959**[4]**D. R. Bland,*Mathematical theory of the flow of a gas in a porous solid and of the associated temperature distributions*, Proc. Roy. Soc. London. Ser. A.**221**(1954), 1–28. MR**0060968**, https://doi.org/10.1098/rspa.1954.0001**[5]**J. Crank,*The mathematics of diffusion*, Oxford, at the Clarendon Press, 1956. MR**0082827****[6]**A. Erdélyi,*Tables of integral transforms*, vol. 2, Bateman Manuscript Project, McGraw-Hill, New York, 1954, p. 51**[7]**Max. Jacob,*Heat transfer*, vol. I, Wiley, New York, 1949, pp. 343-52.**[8]**K. Pearson,*Tables of incomplete gamma functions*, University College, 1934**[9]**H. J. Ramey,*Transient heat conduction during radial movement of a cylindrical source-applications to the thermal recovery process*, Trans. Am. Inst. Mining, Met. and Pet. Engrs.**216**(1959).**[10]**Ian N. Sneddon,*Fourier Transforms*, McGraw-Hill Book Co., Inc., New York, Toronto, London, 1951. MR**0041963****[11]**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR**1349110**

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DOI:
https://doi.org/10.1090/qam/121075

Article copyright:
© Copyright 1961
American Mathematical Society