International Journal of Thermal Sciences 43 (2004) 569–574 www.elsevier.com/locate/ijts Periodic free convection from vertical plate subjected to periodic surface temperature oscillation Nawaf H. Saeid Lecturer, Mechanical Engineering School, University of Science Malaysia, 14300 Nibong Tebal, Pulau Pinang, Malaysia Received 24 March 2003; accepted 29 September 2003 Available online 7 January 2004 Abstract The effect of the periodic oscillation of the surface temperature on the transient free convection from a vertical plate is investigated in the present paper. The problem has been simplified by the laminar boundary layer and Boussinesq approximations. The fully implicit finite- difference scheme is used to solve the dimensionless system of the governing equations. The results for laminar flow of air Pr = 0.72 and water Pr = 7.00 are presented for an isothermal flat plate and for a periodic oscillation of the plate temperature. The results presented to show the steady periodic variation of Nusselt number with the amplitude and frequency of the oscillating surface temperature. It is found that increasing the amplitude and the frequency of the oscillating surface temperature will decrease the free convection heat transfer from the plate to both air and water.  2003 Elsevier SAS. All rights reserved. Keywords: Free convection; Transient convection; Boundary layer; Oscillating temperature; Numerical study 1. Introduction Transient laminar free convection from vertical wall is important in many practical applications, such as furnaces, electronic components, solar collectors, chemical processing equipments and others. The change in the wall temperature causing the free convection flow could be a sudden or a periodic one, leading to a variation in the flow. If the wall surface temperature is suddenly changed from the ambient temperature to a specific value, the steady free convection flow is reached, following a transient flow which occurs for a certain period of time. The literature shows that the transient free convection problem has been investigated by various researchers. Numerical solutions of the governing boundary layer equations have been obtained by Hellums and Churchill [1] with a vertical surface subjected to a step change in the surface temperature. Hellums and Churchill [1] observed an initial undershoot of the local Nusselt number below the steady-state solution and the eventual approach to the steady flow solution. This undershoot phenomenon is observed also by Callahan and Marner [2] in both Nusselt and Sherwood numbers in the transient E-mail address: n_h_saeid@yahoo.com (N.H. Saeid). free convection with mass transfer on an isothermal vertical flat plate. The transient free convection from vertical flat plate is also investigated, by Harris et al. [3], when the plate temperature is suddenly changed from T 1 to T 2 . They obtained an analytical solution for small values of the non- dimensional time, and detailed numerical solution of the full boundary layer equations form transient solution until the steady-state is reached. For a non-isothermal vertical plate, with the surface tem- perature variation given by the power law dependence, the similarity solution introduced by Sparrow and Gregg [4] is usually used. The free convection from non-isothermal ver- tical wall, but with streamwise surface temperature oscilla- tion has received attention by many researchers including Rees [5], and Li et al. [6]. In this class of free convection problems, Rees [5] has studied the effect of the sinusoidal streamwise surface temperature variation on the steady free convective boundary layer flow. He used combined numeri- cal and asymptotic analysis to find that the rate of heat trans- fer will eventually alternate in sign with distance from the leading edge. The steady and unsteady free convection from vertical wall with streamwise surface temperature oscillation has been investigated by Li et al. [6]. For small values of Grashof number they obtained an asymptotic formula for the average Nusselt number using a perturbation method. 1290-0729/$ – see front matter  2003 Elsevier SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2003.09.007