Comparative analysis of jet impingement and microchannel cooling for high heat ~ux applications

In this work\ a comparative investigation of jet impingement and microchannel cooling is presented[ The thermal performance of each technology evaluated at the respective optimal condition is compared to each other with the target dimension as a main parameter[ It is revealed that the microchannel cooling is preferable for a target dimension smaller than 9[96 by 9[96 m\ while the jet impingement is comparable or better than the microchannel cooling for a larger target plate if a proper treatment is applied for the spent ~ow after the impingement[ Various pertinent aspects of each technology as well as a detailed comparative analysis of the two technologies are presented[ In selecting a technology from the two\ the economic aspects\ such as manufacturing and maintenance cost\ also have to be taken into account\ since the better performing one may not be necessarily the more suitable one[ Þ 0887 Elsevier Science Ltd[ All rights reserved[ Nomenclature A surface area of the target plate ðmŁ Acorr surrounding area corresponding to a single jet ðmŁ a0\ a1 exponents in equations "40# and "41# CD ori_ce discharge coe.cient c0\ c1 proportional constants in equations "40# and "41# cP isobaric speci_c heat ðJ kg >CŁ d nozzle diameter ðmŁ dh hydrodynamic diameter of microchannel ðmŁ F Reynolds function f friction factor\ f "Dpdh:L#:1ru G geometric function GP function de_ned in equation "15# H height of the microchannel ðmŁ h heat transfer coe.cient ðW m KŁ K jet interaction correction function kf thermal conductivity of the ~uid ðW m >CŁ ks thermal conductivity of the plate material ðW m >CŁ L length of the target plate ðmŁ Corresponding author[ Tel[] 990 503 181 5459^ fax] 990 503 181 2052^ e!mail] vafai[0Ýosu[edu m constant de_ned in equation "44# n constant de_ned in equation "44# Nu Nusselt number\ Nu hd:kf or Nu hdh:kf P nondimensional pressure loss P9 pumping power per unit area of target surface ðW mŁ p pressure ðPaŁ Dp pressure di}erence ðPaŁ p9 pressure in the plenum chamber ðPaŁ Pr Prandtl number Q heat rate ðWŁ q heat ~ux ðW mŁ R radius of the target plate ðmŁ r radial coordinate ðmŁ ReJ Reynolds number for the jet\ ReJ uJd:n ReM Reynolds number for the microchannel\ ReM udh n SNN nozzle!to!nozzle separation distance ðmŁ SNP nozzle!to!plate spacing ðmŁ T temperature ð>CŁ Tf\in ~uid inlet temperature ð>CŁ Tf\out ~uid outlet temperature ð>CŁ DT temperature di}erence between the plate and ~uid ð>CŁ t thickness of the target plate ðmŁ D[!Y[ Lee\ K[ Vafai:Int[ J[ Heat Mass Transfer 31 "0888# 0444Ð0457 0445 u velocity ðm sŁ uc cross~ow velocity ðm sŁ uJ jet velocity ðm sŁ u J arti_cial jet velocity de_ned in equation "01# ðm sŁ Vþ coolant ~ow rate ðm sŁ W width of the target plate ðmŁ w width of the microchannel ðmŁ x nondimensional radial coordinate[ Greek symbols aJ relative nozzle area aM area enlargement factor in microchannel cooling o perturbation parameter in equation "05# g ratio of the _n thickness to the microchannel width h _n e.ciency k thermal conductivity ratio of plate material to the ~uid\ k ks:kf l quantity de_ned in equation "27# n dynamic viscosity ðm sŁ V quantity de_ned in equation "36# u nondimensional thermal resistance r density of the ~uid ðkg mŁ v pseudo aspect ratio of microchannel j pressure loss coe.cient[ Subscripts cap capacitance resistance cond conductive resistance conv convective resistance _n _n in microchannel J jet impingement M microchannel min minimum max maximum opt optimum[