Abstract
The two-dimensional differential transform method (DTM) is applied to analyse the transient natural convection of cold water in a vertical channel. The cold water gives rise to a density variation with temperature that may not be linearized. The vertical channel is composed of doubly infinite parallel plates, one of which has a constant prescribed temperature and the other of which is insulated. Considering the temperature-dependent viscosity and thermal conductivity of the water, approximate analytical (series) solutions for the temperature and flow velocity are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical computation is performed for the entire range of water temperature conditions around the temperature at the density extremum point, i.e.\( 4 {}^{\circ} C\) . Numerical results illustrate the effects of the temperature-dependent properties on the transient temperature and flow velocity profiles, volumetric flow rate, and skin friction. The DTM is a powerful tool for solving nonlinear transient problems as well as steady problems.
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