Abstract
In the present study, a series of theoretical and experimental investigations on fluid flow and heat transfer characteristics of partially-confined heat sinks in natural and forced convections have been performed. The relevant parameters in the experiments include Grashof number (GrH), top-bypass ratio (Htb / Hch), and side-bypass ratio (Wsb / Wch) in natural convection; and Grashof number (GrH), Reynolds number (Rech), top-bypass ratio (Htb / Hch), and side-bypass ratio (Wsb / Wch) in forced convection. The parametric ranges in natural convection are GrH = 3.0X107 ~ 9.0X107, Wsb / Wch = 0.00 ~ 0.55 and Htb / Hch = 0.28 ~ 0.83; those in forced convection are GrH = 5.5X108 ~ 1.6X109, Rech = 20209 ~ 40073, Wsb / Wch = 0.00 ~ 0.55 and Htb / Hch = 0.28 ~ 0.83. Their effects on fluid flow and heat transfer characteristics have been systematically explored.From the aspect of fluid flow behavior, the ratio of average velocity in the heat sink region to average channel inlet velocity (Vs/Vin) is significantly affected by Rech, Wsb / Wch or Htb / Hch . The ratio of average velocity in the top-bypass or side-bypass region to average channel inlet velocity ( Vtb/Vin or Vsb/Vin ) is significantly affected by Rech, but insignificantly affected by Wsb / Wch or Htb / Hch . New correlations of Vs/Vin, Vsb/Vin and Vtb/Vin in terms of relevant influencing parameters are proposed. The effects of Rech, Wsb / Wch and Htb / Hch on pressured drop and effective friction factor (feff) are explored. New correlations for evaluating the pressure drop and the effective friction factor in terms of relevant influencing parameters are also presented.From the aspect of heat transfer behavior, a uniform distribution of local effective Nusselt number in natural convection is achieved either in the spanwise or in the streamwise direction due to the spreading effect of the heat conduction within the heat sink; while, the distributions of local effective Nusselt number in the spanwise and streamwise directions are uniform and non-uniform, respectively, in forced convection. The local effective Nusselt number (Nueff) in forced convection gradually decreases along the streamwise direction. A similar trend can be found for the distribution of local external thermal conductance. In natural convection, the average effective Nusselt number (Nueff) decreases with increasing GrH or decreasing Wsb / Wch and Htb / Hch ; while, it increases with increasing Rech or decreasing Wsb / Wch and Htb / Hch in forced convection. Two new correlations of Nueff in terms of relevant influencing parameters in natural and forced convections are presented, respectively. As compared with the average Nusselt number on a heating horizontal flat surface confined in a channel, the average heat transfer performances of partially-confined heat sinks in natural and forced convections can be enhanced in the range of 125% -236% and 961%-4453%, respectively.Furthermore, a novel parametric similarity method to effectively link the relationship between the heat sink and the porous medium models has been successfully developed. Both the direct and inverse transformations on the fluid flow friction and thermal performance with relevant influencing parameters in these two models have also been established. The fluid flow friction and thermal performance for partially-confined heat sinks can be directly evaluated in the heat sink model. With the proposed direct and inverse transformations, those can be indirectly and effectively determined in the porous medium model. The effective friction factor in the porous medium model is evaluated from the permeability and the inertial coefficient, and the correlation in terms of Rech and porosity is presented. All the heat transfer coefficients such as hwa, hws and hsa in the porous medium model are significantly affected by Rech and porosity. The hws and hsa increase with increasing Rech or decreasing porosity; hwa increases with increasing Rech, but is almost independent of porosity. Both the average Nusselt number of Nui and average effective Nusselt number of Nueff in the porous medium model increase with increasing Rech or decreasing porosity. Based on the experimental data, two new correlations of Nui and Nueff in terms of Rech and porosity are presented. The maximum heat transfer enhancement defined as can be achieved up to 4581% in the present parametric range studied. Based on both the experimental data and the CFD results, two new correlations of j and j/feff in terms of Rech and porosity in the porous medium model are reported. With the Colburn factor obtained in the porous medium model, the most suitable geometric parameters such as Wsb / Wch and Htb / Hch in the heat sink model can be effectively determined by porosity used in the porous medium model by using the proposed parametric inverse transformations. From the statistical sensitivity analysis, the contributions of GrH, Rech, Wsb / Wch and Htb / Hch on the effective friction factor in the heat sink model are 1.6%, 49.1%, 23.3%, and 26.0%, respectively; and those on the Colburn factor are 2.6%, 51.1%, 13.4%, and 32.9%, respectively. The contributions of GrH, Rech and porosity on the effective friction factor in the porous medium model are 1.5%, 57.7%, and 40.8%, respectively; and those on Colburn factor are 4.3%, 55.1%, and 40.6%, respectively.Finally, in either the heat sink model or the porous medium model, two empirical response formulas with a quadratic RSM model for evaluating the effective friction factor and the Colburn factor are established for each model, respectively. An effective sequential quadratic programming with a multi-start-point method has been successfully employed to automatically and efficiently seek the global thermal optimization in both the heat sink and the porous medium models. Accordingly, three cases of thermal optimization on j or j/feff in a partially-confined heat sink under different bypass ratio constraints have been explored for either the heat sink model or the porous medium model; and a series of optimal thermal evaluations on j and j/feff for partially-confined heat sinks under multi-constraints with the novel heat sink/porous medium similarity method presented in the study have been successfully performed and verified.