Journal of Engineering Mathematics

, Volume 27, Issue 3, pp 265–292

The effects of blowing and suction on free convection boundary layers on vertical surfaces with prescribed heat flux

  • M. A. Chaudhary
  • J. H. Merkin
Article

DOI: 10.1007/BF00128967

Cite this article as:
Chaudhary, M.A. & Merkin, J.H. J Eng Math (1993) 27: 265. doi:10.1007/BF00128967

Abstract

The effects that blowing and suction have on the free convection boundary layer on a vertical surface with a given surface heat flux are considered. Similarity equations are derived first, their solution being dependent on the wall flux exponentn and a dimensionless transpiration parameter γ, (as well as on the Prandtl number). The range of existence of solutions is considered, with it being shown that solutions exist only forn > −1 for blowing,whereas they exist for alln >n0 for suction, wheren0 < −1 and depends on γ. The solutions for strong suction and blowing are derived. In the latter case the asymptotic structure is found to be different forn in the three ranges −1 <n < − % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% aIXaaabaGaaGinaaaaaaa!3775!\[\frac{1}{4}\], −% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% aIXaaabaGaaGinaaaaaaa!3775!\[\frac{1}{4}\] <n < % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabgkHiTmaaleaaleaacaaIXaaabaGaaGinaaaaaaa!3EB1!\[ - \tfrac{1}{4}\], % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabgkHiTmaaleaaleaacaaIXaaabaGaaGinaaaaaaa!3EB1!\[ - \tfrac{1}{4}\] <n < % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaaleaaleaacaaI3aaabaGaaGOmaaaaaaa!3DC8!\[\tfrac{7}{2}\],n % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaaleaaleaacaaI3aaabaGaaGOmaaaaaaa!3DC8!\[\tfrac{7}{2}\]. Results are then obtained for the non-similarity problem of constant heat flux with a constant transpiration velocity. Solutions valid for large distances from the leading edge for both suction and blowing are derived.

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • M. A. Chaudhary
    • 1
  • J. H. Merkin
    • 1
  1. 1.Department of Applied MathematicsUniversity of LeedsLeedsU.K.

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