In the early 1960s Hall, Jackson and Price published a paper in the Journal of Mechanical Engineering Science in which they obtained the fundamental solution of the fully developed energy equation in steady flow. Some attention in the same research group is now turned to the measurement and calculation of transient convective heat transfer and it is shown here that the analysis of Hall et. al. may be extended to such time-dependent flows. The analysis is restricted to forced convection conditions but applies equally to laminar and turbulent flows.
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References
1.
HallW. B.PriceP. H.The effect of a longitudinally varying wall heat flux on the heat transfer coefficient for turbulent flow in a pipe. Proceedings of International Heat Transfer Conference International developments in heat transfer, Boulder, 1961, pp. 607–613.
2.
HallW. B.JacksonJ. D.PriceP. H.Note on forced convection in a pipe having a heat flux which varies exponentially along its length. J. Mech. Engng Sci., 1963, 5, 48–52.
3.
SparrowE. M.HallmanT. M.SiegelR.Turbulent heat transfer in the thermal entrance region of a pipe with uniform heat flux. Appl. Sci. Res., 1958, A7, 37–52.
4.
DuryT.The development of a smooth circular tube test section with variable heat flux distribution for experiments on the forced convection cooling of supercritical pressure carbon dioxide. MSc thesis, 1970, University of Manchester.
5.
AxcellB. P.Forced convection heat transfer with an exponential wall heat flux. MSc thesis, 1973, University of Manchester.
6.
CottonM. A.JacksonJ. D.The effect of heat conduction in a tube wall upon forced convection heat transfer in the thermal entry region. In Numerical methods in thermal problems (LewisR. W.MorganK.), Vol. IV, 1985, pp. 504–515 (Pineridge Press).
7.
CottonM. A.Analysis and calculation of coupled convection and conduction for laminar flow in a tube. The Nuclear Engr, 1985, 26, 170–173.
8.
CottonM. A.Calculation of turbulent forced convection in a pipe with exponentially-distributed wall heat flux using a mixing length model of turbulence. Department of Engineering report, University of Manchester, 1985.
9.
JacksonJ. D.HallW. B.CottonM. A.AxcellB. P.Experimental and theoretical studies of turbulent forced convection in a pipe with exponentially-distributed wall heat flux. Proceedings of Eighth International Conference on Heat Transfer, San Franciso, 1986, pp. 931–936.
10.
CottonM. A.Theoretical studies of mixed convection in vertical tubes. PhD thesis, 1987, University of Manchester.
11.
AxcellB. P.TongeD. A.JemssonT.Turbulent forced convection in a pipe with an exponential wall heat flux In Experimental heat transfer, fluid mechanics and thermodynamics (ShahR. K.GanicE. N.YangK. T.), 1988, pp. 808–815 (Elsevier).
12.
HasegawaS.FujitaY.Turbulent heat transfer in a tube with prescribed heat flux. Int. J. Heat Mass Transfer, 1968, 11, 943–962.
13.
WalkerV.RishehriS. A.Forced convection in parallel and tapered passages: the importance of the heat flux boundary condition. Int. J. Heat Mass Transfer, 1972, 15, 781–788.
14.
SparrowE. M.PatankarS. V.Relationships among boundary conditions and Nusselt numbers for thermally developed duct flows. J. Heat Transfer, 1977, 99, 483–485.
15.
RouaiN. M.Influences of buoyancy and imposed flow transients on turbulent convective heat transfer in a tube. PhD thesis, 1987, University of Manchester.
16.
TuS. W.RamaprianB. R.Fully developed periodic turbulent pipe flow. Part 1. Main experimental results and comparison with predictions. J. Fluid Meek, 1983, 137, 31–58.
17.
RamaprianB. R.TuS. W.Fully developed periodic turbulent pipe flow. Part 2. The detailed structure of the flow. J. Fluid Meek, 1983, 137, 59–81.
18.
CottonM. A.JacksonJ. D.Comparison between theory and experiment for turbulent flow of air in a vertical tube with interaction between free and forced convection. In Mixed convection heat transfer (PrasadV.CattonI.ChengP.), American Society of Mechanical Engineers publication HTD-84, 1987, 43–50.
