Local Nonsimilarity Solution for Vertical Free Convection Boundary Layers

Abstract

Suatu analisis dalam mengkaji ciri-ciri aliran dan pemindahan haba bagi masalah lapisan sempadan olakan bebas berlamina terhadap plat menegak di dalam bendalir likat dibincangkan dengan menggunakan kaedah ketakserupaan setempat. Kes apabila suhu permukaan berubah secara eksponen dipertimbangkan dalam mengilustrasikan kaedah tersebut. Dalam kaedah ini, sebutan ketakserupaan yang wujud pada persamaan momentum dan tenaga dikekalkan dan pemansuhan sebutan hanya dilakukan pada persamaan bantu yang diterbitkan. Sistem persaman yang diperolehi diselesaikan secara berangka menggunakan kaedah Keller-box. Kadar pemindahan haba dan tegasan ricih dinding yang diperolehi menunjukkan keputusan yang memuaskan. Kesan parameter $\xi$ dan nombor Prandtl terhadap taburan halaju dan suhu juga ditunjukkan. Katakunci: Olakan bebas; lapisan sempadan; kaedah ketakserupaan setempat; kaedah Keller-box. Laminar free convection boundary layer over a vertical flat plate with an exponential variation of surface temperature in viscous fluids is analyzed using the local nonsimilarity method. The present approach takes into consideration the nonsimilarity terms appearing in the momentum and energy equations, which have been unaccounted for previously, in for example, the similarity and the local similarity methods. The governing equations are solved numerically using the Keller-box method, an efficient implicit finite difference scheme. Numerical results are presented in the form of heat transfer rates, local wall shear stress, velocity and temperature profiles. The heat transfer rates and local wall shear stress obtained show good agreement with available nonsimilar solutions. The effects of various values of transformed stream-wise coordinate $\xi$ and Prandtl numbers on velocity and temperature profiles are also presented. Keywords: Free convection heat transfer; boundary layers; local nonsimilarity method; Keller-box