Abstract
In this paper the two-dimensional steady-state problem of laminar forced convective heat transfer from an isothermal cylinder, elliptic in cross section, inclined to a uniform stream is investigated. Numerical solutions of the Navier-Stokes and energy equations have been obtained for Reynolds numbers, Re, 5 and 20 for various values of the Prandtl number, Pr, and inclination angle, α. Particular attention is focussed on a solution process utilizing the asymptotic properties of the Navier-Stokes and energy equations. The average rate of heat transfer, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGobGaamyDaaaaaaa!36B5!\[\overline {Nu} \], was found to behave closely to the theoretical result % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGobGaamyDaaaacqWI8iIocaWGqbGaamyzamaaCaaaleqabaWaaSGb% aeaacaaIXaaabaGaaG4maaaaaaaaaa!3B58!\[\overline {Nu} \sim Pe^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \] for large Pe where Pe=RePr is the Peclet number.
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D'Alessio, S.J.D., Dennis, S.C.R. Steady laminar forced convection from an elliptic cylinder. J Eng Math 29, 181–193 (1995). https://doi.org/10.1007/BF00051742
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DOI: https://doi.org/10.1007/BF00051742