Developing next generation transient heat exchangers is a transformative technology for efficient thermal management of advanced power electronics and electric machines (APEEM) inside hybrid electric, electric, and fuel cell vehicles as well as renewable energies (wind, solar, tidal). Optimal design criteria for such dynamic heat exchangers should be achieved through addressing internal forced convection with arbitrary flow unsteadiness under dynamic time dependent thermal loads. Exact analytical solutions were obtained for laminar forced-convective heat transfer under arbitrary time-dependent heat flux for steady flow inside a tube (Fakoor-Pakdaman et al., 2014). In this study, the energy equation is solved analytically for arbitrary unsteady flow between parallel plates under dynamic time and position dependent heat flux. As such, laminar pulsating flow between two parallel plates is considered under a harmonic wall heat flux. Exact relationships are obtained to find; (i) temperature distribution for the fluid; (ii) fluid bulk temperature; and (iii) the local and time averaged Nusselt number. New compact relationships are proposed to find the thermal entrance length and the cyclic fully-developed Nusselt number. It is shown that the period of the Nusselt number oscillations is the least common multiple of the periods of the imposed harmonic heat flux and the pulsating flow. We obtained a relationship for the 'cut-off' angular frequency of pulsating flow beyond which the heat transfer does not feel the pulsation. This study also shows that for a given harmonic wall heat flux, there is an optimal pulsating flow velocity, with optimum frequency, which enhances the time averaged Nusselt number by up to 27%. (C) 2014 Elsevier Ltd. All rights reserved.