Free Convection Boundary Layer Over a Nonisothermal Vertical Flat Plate

Abstract

Penyelesaian berangka bagi masalah lapisan sempadan olakan bebas terhadap plat menegak dengan taburan suhu atau fluks haba yang ditetapkan akan dibincangkan. Perbincangan tertumpu kepada dua jenis syarat sempadan iaitu, variasi sinusoid suhu dinding dan variasi eksponen fluks haba. Dalam kajian ini, pengiraan berangka dilakukan menggunakan suatu skema beza terhingga tersirat yang efisien, yang dinamakan kaedah kotak Keller. Ilustrasi pengiraan dijalankan dan keputusan baru yang diperolehi dibandingkan dengan keputusan-keputusan lepas yang diperolehi menggunakan kaedah-kaedah penyelesaian yang lain, dan didapati bahawa hasil perbandingan adalah baik. Perbandingan melibatkan kecerunan suhu tak berdimensi bagi variasi sinusoid suhu dinding dan suhu tak berdimensi bagi variasi eksponen fluks haba. Keputusan baru bagi variasi tegasan ricih permukaan dengan pelbagai nombor Prandtl juga dibincangkan. Di samping itu, bagi kes variasi sinusoid suhu dinding, profil halaju dan suhu diberikan bagi beberapa nombor Prandtl iaitu 0.7, 1, 10 dan 100, manakala bagi kes variasi eksponen fluks haba, profil halaju dan suhu juga diketengahkan untuk beberapa nilai koordinat mengikut-strim yang terjelmakan ξ iaitu 0, 1, 10 and 100. Kata kunci: Olakan bebas; lapisan sempadan; plat menegak tak isoterma; kaedah berangka Numerical solutions are presented for the free convection boundary layer problems on a vertical flat plate with prescribed temperature or heat flux distributions, namely the sinusoidal wall temperature and the exponential heat flux variations. The numerical computation is carried out using a very efficient implicit finite difference scheme known as the Keller-box method. Illustrative computational examples are carried out and the present results are compared with previously available theoretical results obtained using other methods of solution, and they are found to be in good agreement. Comparisons of nondimensional temperature gradient for sinusoidal wall temperature variation and of nondimensional wall temperature with exponential variation in wall heat flux are made between the present and previous results. New results for the variation of the surface shear stress with various Prandtl numbers are also presented. In addition, for the case of sinusoidal wall temperature variation, representative velocity and temperature profiles are presented for Prandtl numbers 0.7, 1, 10 and 100, while for the case of exponential heat flux distribution, the velocity and temperature profiles for various transformed streamwise coordinate ξ = 0, 1, 10 and 100 are illustrated. Key words: Free convection; boundary layer; nanoisothermal vertical plate; numerical method