Step response for free convection between parallel walls

This paper analyzes the heat transfer for laminar natural convection of a viscous, incompressible, Newtonian fluid between parallel vertical plates, due to a step change in the temperature of one of the two plates. The momentum conservation and energy conservation equations are analytically solved applying the Laplace transform technique. The temperature profile, which is presented as an original solution, is a fast converging series of sinusoidal and exponential functions. It is very easy to be used and highlights that the transient distribution of the temperature tends to the steady-state one when the numerical value of dimensionless time approaches the Prandtl number. The results, obtained for different fluids (liquid sodium, air, water and lubricating oil), show that the thermal transient is always faster than the dynamic transient