Final Program EXPRES 2012 - Conferences

Waa5g(a)H64321(b)LFigure 1. Functional scheme of systemThe CPC module consists of a complexcylindrical-parabolic reflection surface and a coppertube with ø15 mm outside diameter used as theabsorber. Cylindrical cooper absorber is surroundedby a glass surrounding layer for lowering convectiveloss from the collector pipe. The area between thepipe absorber and glass surrounding layer isevacuated. Conversion of solar energy into heat isconducted on the pipe collector. Pipe absorber iscolored with selective color of high absorbingproperties and low emissivity (ε r ). The area of thereflector has high reflection ratio (ρ m ). Between thepipe absorber and the reflector there is a gap (hole)which stops heat transfer from the collector pipe tothe reflector. Water is the working fluid, with alaminar flow through the pipe of the collector.Apparatus of the collector is covered by transparentcover layer made of glass (Plexiglass) so the reflectorarea could be saved from wearing and to lower thevalue of heat loss from the assembly pipe absorbersurroundingpipe layer. The collector consists of sixCPC modules which are connected parallel to theflow paths, so flow properties inside them may beconsidered equal.III.A. IntroductionMATHEMATICAL MODELBased on the physical model represented by theCPC collector, through whose absorber pipe a laminarflow of water occurs, and which is subjected to solarradiation, a mathematical model is proposed. Themathematical model consists of the energy balanceequations for four CPC module components: (1)working fluid, (2) collector pipe- absorber, (3)surrounding pipe layer, (4) transparent cover. Duringthe set-up of mathematical model only one module ofCPC collector was analyzed.B. Basic assumption according to which the modelwas basedThe following assumptions were introduced forthe definition of mathematical model:- The sky was treated as an absolute blackobject, which is the source of infraredradiation during an equivalent skytemperature - Reflected radiation from surroundingobjects was considered negligible andwas not taken into account;- Diffusive insulation on the apparatus ofthe cover is isotropic;- CPC collector has permanent Suntracking, thus Sun rays are normal to theplane of transparent cover (apertureplane);- Radiation to the collector is unified;- CPC module is constructed with idealgeometry, thus the concentration ratio isgiven by: [13]: (1)- Heat transport in the transparent cover,surrounding cover layer, collectorsurrounding layer, pipe absorber and thefluid is transient- Transparent cover, transparent coverlayer, collector surrounding layer, andpipe absorber are homogenous andisotropic objects;- Heat transport by conduction in thetransparent cover layer and the glasslayer is negligible due to small heatconductivity of glass;- Thermo-physical properties of the CPCcollector component material (ρ * , c, λ)as well as optic properties (ρ, τ, ε, α) ofthe components of CPC collector are donot depend on coordinates, temperaturenor time;- Fluid flow is steady state and it isconducted only in the axial direction,thus the velocity field is related just tothe speed component w z ;- Fluid flow shape is the same in everyaxial cross sections, thus the tangentialvelocity component w φ does not exist;- Radial velocity component w r isneglected as a value of smaller order andthus the convection in radial direction isalso neglected;- Fluid flow may be consideredincompressible;- Conduction in the axial direction has anegligibly small contribution to theresulting heat transport compared to theconvection.102