Analytic Approximate Solution of the Extended Blasius Equation with Temperature-Dependent Viscosity

• Published in: Journal of nonlinear mathematical physics Vol. 30; no. 1; pp. 287 - 302
• Main Authors: Khanfer, Ammar, Bougoffa, Lazhar, Bougouffa, Smail
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2023; Springer Nature B.V
• Subjects: Algorithms; Approximation; Blasius equation; Boundary conditions; Boundary layers; Boundary value problems; Energy consumption; Fluid dynamics; Friction; Mathematical Physics; Mathematics; Mathematics and Statistics; Research Article; Skin friction; Software; Temperature dependence; Viscosity; Dynamic viscosity; Blasius equation; Approximate solution; Skin friction coefficient
• ISSN: 1776-0852; 1402-9251; 1776-0852
• DOI: 10.1007/s44198-022-00084-3

An explicit approximate solution is obtained for the extended Blasius equation subject to its well-known classical boundary conditions, where the viscosity coefficient is assumed to be positive and temperature-dependent, which arises in several important boundary layer problems in fluid dynamics. This problem extends a previous problem by Cortell (Appl Math Comput 170:706–710, 2005) when the viscosity is constant, in which a numerical solution was obtained. A comparison with other numerical solutions demonstrates that our approximate solution shows an enhancement over some of the existing numerical techniques. Moreover, highly accurate estimates for the skin-friction were calculated and found to be in good agreement with the numerical values obtained by Howarth (Proc R Soc A: Math Phys Eng Sci 164(919):547–579, 1938), Töpfer (Z Math Phys 60:397–398, 1912), and Cortell [ 34 ] when the viscosity is equal to 1, and when it is equal to 2.