Transient internal forced convection under dynamic thermal loads: in clean-tech and automotive applications

Developing next generation transient heat exchangers is a transformative technology for efficient ther-mal 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 criteriafor such dynamic heat exchangers should be achieved through addressing internal forced convectionwith arbitrary flow unsteadiness under dynamic time dependent thermal loads. Exact analytical solutionswere obtained for laminar forced-convective heat transfer under arbitrary time-dependent heat flux forsteady flow inside a tube (Fakoor-Pakdaman et al., 2014). In this study, the energy equation is solved ana-lytically for arbitrary unsteady flow between parallel plates under dynamic time and position dependentheat flux. As such, laminar pulsating flow between two parallel plates is considered under a harmonicwall heat flux. Exact relationships are obtained to find; (i) temperature distribution for the fluid; (ii) fluidbulk temperature; and (iii) the local and time averaged Nusselt number. New compact relationships areproposed to find the thermal entrance length and the cyclic fully-developed Nusselt number. It is shownthat the period of the Nusselt number oscillations is the least common multiple of the periods of theimposed harmonic heat flux and the pulsating flow. We obtained a relationship for the ‘cut-off’ angularfrequency of pulsating flow beyond which the heat transfer does not feel the pulsation. This study alsoshows that for a given harmonic wall heat flux, there is an optimal pulsating flow velocity, with optimumfrequency, which enhances the time averaged Nusselt number by up to 27%.2014 Elsevier Ltd. All rights reserved.