1 Copyright © 2013 by ASME Proceedings of the ASME 2013 Summer Heat Transfer Conference HT2013 July 14-19, 2013, Minneapolis, MN, USA TRANSIENT INTERNAL FORCED CONVECTION UNDER ARBITRARY TIME- DEPENDENT HEAT FLUX M. Fakoor-Pakdaman PhD Candidate, mfakoorp@sfu.ca M. Andisheh-Tadbir PhD Candidate, mandishe@sfu.ca Majid Bahrami Associate Professor, mbahrami@sfu.ca Laboratory for Alternative Energy Conversion (LAEC) Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, Canada V3T 0A3 ABSTRACT A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%. 1. INTRODUCTION For optimal design and accurate control of heat transfer in emerging sustainable energy applications and next-generation heat exchangers, it is crucial to develop an in depth understanding of thermal transients. Thermal transient may be accidental and random or may be of cyclic nature. Generally, processes such as start-up, shut-down, power surge, and pump/fan failure impose such transients [1–4]. Examples of thermal transient in sustainable energy applications include: i) the variable thermal load from thermal solar panels in Thermal Energy Storage (TES) systems; ii) the variable thermal load on power electronics of solar/wind/tidal energy conversion systems; and iii) the variable load of power electronics and electric motor of Hybrid Electric Vehicles (HEV), Electric Vehicles (EV), and Fuel Cell Vehicles (FCV). The following provides a brief overview on the importance and the trends of the above thermal engineering applications. Solar thermal systems are widely utilized in solar power plants and are being widely commercialized. Solar power plants has seen about 740 MW of generating capacity added between 2007 and the end of 2010 bringing the global total to 1095 MW [4]. Such growth is expected to continue as in the US at least another 6.2 GW capacity is expected to be in operation by the end of 2013 [4]. However, the growth of such technology is hindered by the inherent variability of solar energy subjected to daily variation, seasonal variation, and weather conditions [1–3]. To overcome the issue of the intermittency, TES systems are used to collect thermal energy to smooth out the output and shift its delivery to a later time. Single-phase sensible heating systems or latent heat storage systems utilizing Phase Change Materials (PCM) are used in TES; transient heat exchange occurs to charge or discharge the