Analysis of heat transfer, including axial conduction, for laminar tube flow with arbitrary circumferential wall heat flux Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8k71nm94k

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  • This thesis is concerned with the analysis of heat transfer in a tube with forced flow under conditions of an arbitrary variation of wall heat flux both axially and circumferentially. This total study is separated into two distinct problems which are presented separately. The first is the case of a Newtonian fluid in laminar flow with allowance made for the inclusion of axial heat conduction, viscous heat dissipation and heat generation. Secondly, the problem of laminar flow of a non-Newtonian fluid is considered. Axial conduction is not included in this problem since it is likely negligible in those cases where non-Newtonian effects are significant. Heretofore, no general method has been available for obtaining solutions to these problems. Analytical results are given in such generality and completeness that many of the previously reported work in the heat transfer literature in laminar tube flow are limiting cases of the present work. In the first problem, the solution is expanded in a power series form that accounts for any arbitrary variation of wall heat flux around the circumference that can be expressed in terms of a Fourier series expansion. Substitution of this series into the energy equation leads to an eigenvalue problem. The first 12 eigenvalues and eigenfunctions have been obtained numerically. The resulting eigenfunctions are not orthogonal and therefore the power series expansion coefficients cannot be obtained by the usual analytical schemes. A least squares method was used to determine these coefficients. For the limiting problem of uniform wall heat flux around the circumference with the inclusion of axial conduction, the eigenfunctions and eigenvalues are in excellent agreement with previously reported work; however, two additional considerations were made to correct errors made in the heat transfer literature. The first was the determination of coefficients of the non-orthogonal power series expansion and, second was the inclusion of the nonvanishing axial conduction term at the tube entrance which was not included in earlier asymptotic expressions for the temperature. Both of these considerations are included in the numerical procedures in this work. The problem where wall heat flux varies circumferentially but axial fluid conduction is neglected is another limiting case of the present work. For the special case of uniform wall heat flux, the eigenfunctions, eigenvalues, and expansion coefficients agree well with those in the existing literature. The same analytical techniques were employed for the second problem. The resulting eigenfunctions for this problem are orthogonal, therefore the power series expansion coefficients were determined by utilizing the orthogonality property of the eigenfunctions. For the special case of power-law pseudo-plastic fluids with uniform wall heat flux the eigenfunctions, eigenvalues, and the expansion coefficients are in excellent agreement with previously reported values. Finally, by an illustrative example, it was concluded that circumferential wall heat flux variation has a pronounced effect in both Newtonian and non-Newtonian heat transfer results.
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  • File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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  • description.provenance : Made available in DSpace on 2014-01-08T16:38:07Z (GMT). No. of bitstreams: 1 FaghriMohammad1974.pdf: 4146585 bytes, checksum: 039385fd0dda436fc39c33fa35c18763 (MD5) Previous issue date: 1973-12-11
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