Single ! phase heat transfer enhancement in a curved \ rectangular channel subjected to concave heating

Experiments were performed to ascertain the single!phase heat transfer enhancement provided by streamwise curva! ture[ Curved and straight rectangular ~ow channels were fabricated with identical 4[9×1[4 mm cross!sections and 090[5 mm heated lengths in which heat was applied to a 21[2 mm radius concave wall in the curved channel and a side wall in the straight[ Reynolds number ranged from 8999 to 029 999 and centripetal acceleration for the curved ~ow reached 204 times the earth|s gravitational acceleration[ Nusselt numbers de_ned with hydraulic and thermal diameters were consistently underpredicted by previous correlations developed for full!periphery!heated channels but were accurately predicted when de_ned with heated width[ Convection coe.cients were enhanced due to ~ow curvature for all conditions tested\ and detailed experimental correlations are provided for both the straight and curved con_gurations[ Increasing Reynolds number produced di}erent enhancement trends for di}erent locations along the heated wall\ decreasing the enhancement near the inlet and increasing it elsewhere downstream[ Mechanisms responsible for the curvature enhance! ment are believed to be Dean vortices and a shift in the maximum axial velocity toward the concave wall[ These mechanisms require a _nite distance to develop su.cient strength to in~uence heat transfer\ which explains the di}erent enhancement trends observed for di}erent locations along the heated wall[ Þ 0887 Elsevier Science Ltd[ All rights reserved[ Nomenclature A channel cross!sectional area C0\ C1 constants in eqn "0# C2\ C3 constants in eqn "1# D geometric diameter of tube dc curvature diameter De Dean number Dh hydraulic diameter of channel ð3A:PwŁ Dth thermal diameter of channel ð3A:PhŁ f friction factor ` centripetal acceleration normalized with respect to earth|s gravitational acceleration `e earth|s gravitational acceleration Corresponding author[ Tel[] ¦0 654 383 4694^ fax] ¦0 654 383 9428^ e!mail] mudawarÝecn[purdue[edu 0 Graduate student[ 1 Professor and Director of the Purdue University Boiling and Two!Phase Flow Laboratory[ H channel height h heat transfer coe.cient k ~uid thermal conductivity L0\ L1 Location 0\ Location 1\ [ [ [ \ thermocouple locations in heater Lq length of discrete heater "streamwise direction# Nu Nusselt number Nu Nusselt number averaged over channel perimeter Ph heated perimeter Po pressure at outlet of heated length Pr Prandtl number Pw wetted perimeter qý heat ~ux ReD Reynolds number based on diameter "geometric or hydraulic# r radial coordinate in curved heater R0 inner wall radius of curved channel R1 outer wall radius of curved channel T temperature Tb bulk ~uid temperature Tin ~uid inlet temperature J[C[ Stur`is\ I[ Mudawar:Int[ J[ Heat Mass Transfer 31 "0888# 0144Ð0161 0145 Tw wall temperature U mean velocity uaxial local value of axial velocity in channel W channel width Wq width of discrete heater "perpendicular to ~ow direction# x transverse coordinate in straight heater ðx 9 at ~uidÐsurface interfaceŁ z streamwise coordinate ðz 9 at heater inletŁ[ Greek symbols n kinematic viscosity m dynamic viscosity u turn angle of ~ow\ measured from beginning of cur! vature[ Subscripts cr transition from laminar to turbulent ~ow cur curved channel:heater D geometric or hydraulic diameter H channel height L heated length str straight channel:heater th thermal W heated width w wall[