Title: Natural convection analysis of water near its density extremum between finite vertical plates: a differential transform approach
Authors: Ryoichi Chiba
Addresses: Department of Mechanical Systems Engineering, National Institute of Technology, Asahikawa College, 2-2-1-6 Shunkodai, Asahikawa 071-8142, Japan
Abstract: Using a two-dimensional differential transform method, we solve the steady natural convection problem of cold water between vertical isothermal plates of finite length. The cold water exhibits a density variation approximated as a quadratic function of temperature. Given the temperature-dependent viscosity, we present approximate analytical solutions in the form of power series for temperature, vertical flow velocity, and pressure defect. Numerical calculations are carried out for two cases of water temperature in which the following occur with respect to increases in temperature: 1) the density decreases monotonously; 2) the density increases and subsequently decreases. The numerical results reveal how the temperature-dependent properties affect the developing temperature and velocity profiles and pressure defect distribution along the streamwise direction.
Keywords: cold water; DTM; differential transform method; semi-analytical method; natural convection; temperature-dependent property; vertical channel; series solution; mathematical modelling; heat transfer; convective flow; density extremum.
International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.4, pp.429 - 448
Received: 28 May 2018
Accepted: 18 Dec 2018
Published online: 23 May 2019 *