Analytical solution for buoyancy-driven heat transfer in an inclined channel having a wavy wall

An existing analytical solution based on the perturbation method is amended to include the twodimensional buoyancy-driven fluid flow and heattransfer in an inclined, long channel having a wavy wall. The flow inside the channel which is due to the differentially-heated walls is assumed to be viscous, incompressible and laminar. The amplitude of the wavy wall is assumed to be small compared to the wave length; hence, the perturbation technique is applicable. To implement the method, the field variables are expanded in powers of the small parameter ε (a ondimensional amplitude parameter defined as the ratio of the amplitude to the wave length). These expansions are substituted into the Navier-Stokes and energy equations. Equating the coefficients of powers of ε to zero, yield a set of non-linear ordinary differential equations for the main flow and its perturbations. The pressure is then eliminated from these equations by introducing the stream function-vorticity formulation. The resulting set of non-linear ordinary differential equations is then solved analytically yielding the velocity and the temperature distributions in the channel. Using the analytical solution, a parametric study is performed and the effects of pertinent parameters, such as the channel angle and the amplitude parameter on the flow and temperature fields are investigated. The results show that the main flow velocity along the channel axisincreases with increasing the Rayleigh number. Moreover, this velocity component decreases with increasing the channel angle, i.e., as the channel axis turns from the vertical towards the horizontal direction.

کلیدواژه ها:

natural convection ، wavy channel ، perturbation technique ، analytical solution