Explicit solutions of wall jet flow subject to a convective boundary condition

Boundary value problems

Muhammad Raees-ul-Haq¹  Ammarah Raees²  Hang Xu² 

[1] Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China

关键词: jet flow;    convective heat transfer;    exponential behavior;    nanofluid flow;    convective boundary condition;    explicit solutions;   

DOI  :  10.1186/1687-2770-2014-163

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, an analysis is made on the laminar jet flow and heat transfer of a copper-water nanofluid over an impermeable resting wall. With the homogeneous model (Maïga et al. in Int. J. Heat Fluid Flow 26(4): 530-546, 2005), the Navier-Stokes equations describing this heat fluid flows are reduced to a set of differential equations via similarity transformations. An implicitly analytical solution overlooked in previous publications is discovered for the velocity distribution. We further present the explicit solutions with high precision for both the velocity and the temperature distributions. A mathematical analysis shows that those explicit solutions have exponential behaviors at far field. Besides, the effects of the volumetric fraction parameter ϕ and the dimensionless heat transfer parameter γ on the velocity and temperature profiles, as well as on the reduced local skin friction coefficient and the reduced Nusselt number, are examined in detail.

【 授权许可】

CC BY