Analytical, experimental, and numerical analysis of a microchannel cooling system for high-concentration photovoltaic cells

  • J. A. A. Ortegon
  • R. R. Souza
  • J. B. C. Silva
  • E. M. CardosoEmail author
Technical Paper


In this work, we present the results of an analytical, numerical, and experimental analysis on the performance of a heat sink system designed as a parallel arrangement of microchannels for cooling a high-concentration photovoltaic (HCPV) cell. The analysis considered the worst-case scenario where no electricity is generated, and the solar incidence is maximum on the northwest region of the São Paulo State in Brazil. For the experimental, analytical, and numerical analysis, the considered HCPV cell has a geometrical concentration ratio of 500×, a maximum efficiency of 40% at cell’s operating temperature of 41.0 °C, and a cell base area of 100 mm2. The numerical analysis adopts the finite volume method implemented in ANSYS Fluent v15 to solve flow and energy equations with second-order upwind schemes, and the steady-state, incompressible, and laminar flow. In the experimental apparatus, the copper microchannel heat sink consists of 33 parallel rectangular channels of 10 mm in length, 200 μm in width, and 500 μm in height for each microchannel. A cartridge heater was used to simulate the on-sun test, i.e., it simulates the total heat rate supplied to the microchannel heat sink. The microchannel heat sink is capable of keeping the operating temperature of the cell below the maximum cell’s operating temperature (41.0 °C). In addition, the pressure drops are slightly higher than the predicted models, but not exceeding 34%. Moreover, the energy spent in the pumping in the microchannel represents < 1% of the energy generated by the photovoltaic cell.


Microchannel heat sink Photovoltaic cell Solar applications 

List of symbols


Microchannel effective area (m2)


Parameter in the pressure drop correlations (–)


Specific heat (J/kg)


Hydraulic diameter (m)

\( f_{\text{app,dh}} \)

Apparent friction factor for entrance length region (–)

\( f_{\text{sp,fh}} \)

Friction factor for fully developed region (–)


Mass flux ( kg/m2 s)


Experimental heat transfer coefficient (W/m2 °C)


Single-phase heat transfer coefficient (W/m2 °C)


Channel height (m)

\( \dot{I}_{\text{solar}} \)

Irradiation (W)


Contraction loss coefficient (–)


Thermal conductivity (W/m °C)


Entrance loss coefficient (–)


Channel length (m)

\( L_{\text{sp,dh}} \)

Entrance length region (m)

\( L_{\text{sp,dh}}^{ + } \)

Non-dimensional entrance length region (–)

\( L_{\text{sp,fh}} \)

Fully developed length region (m)


Number of microchannels (–)


Nusselt number (–)

\( Nu_{ \exp } \)

Experimental Nusselt number (–)


Pressure (Pa)


Prandtl number (–)

\( p_{\text{out}} \)

Outlet pressure (Pa)

\( P_{\text{w}} \)

Power dissipated by the electric resistance (W)


Pressure drop (Pa)

\( \Delta P_{\text{c}} \)

Contraction pressure loss (Pa)

\( \Delta P_{\text{e}} \)

Expansion pressure recovery (Pa)

\( \Delta P_{\text{sp,dh}} \)

Pressure drop in entrance length region (Pa)

\( \Delta P_{\text{sp,fh}} \)

Pressure drop in the fully developed region (Pa)

\( \dot{Q}_{\text{cond}} \)

Heat flux dissipated by the heat sink (W)

\( \dot{Q}_{\text{L,conv}} \)

Natural convection loss (W)

\( q_{\text{eff}}^{{\prime \prime }} \)

Effective heat flux (W/m2)

\( \dot{Q}_{\text{L,rad}} \)

Radiation loss (W)

\( Q_{\text{t}} \)

Total volume flow rate (m3/s)


Reynolds number based on local liquid flow rate (–)

\( Re_{\text{in}} \)

Reynolds number based on inlet liquid conditions (–)

\( Re_{\text{sp}} \)

Reynolds number based on properties at mean temperature in single-phase region (–)


Temperature (°C)

\( T_{\text{ch,out}} \)

Microchannel outlet temperature (°C)

\( T_{\text{f, avg}} \)

Average fluid temperature (°C)

\( T_{\text{f,in}} \)

Inlet temperature of the working fluid (°C)

\( T_{\text{f,out}} \)

Outlet temperature of the working fluid (°C)

\( T_{\text{w,avg}} \)

Average wall temperature (°C)


Heat sink width (m)


Channel width (m)

\( \dot{W}_{\text{electric}} \)

Electric generation power in the cell (W)


Channel wall thickness (m)

Greek letters


Microchannel aspect ratio (–)


Fin efficiency (–)

\( \mu_{\text{b}} \)

Viscosity evaluated at coolant mean temperature (Ns/m2)

\( \mu_{\text{w}} \)

Viscosity evaluated at wall temperature (Ns/m2)

\( \rho_{\text{f}} \)

Working fluid density (kg/m3)











Single-phase liquid





The authors are grateful for the financial support from the PPGEM—UNESP/FEIS, from the National Counsil for Technological and Scientific Development of Brazil (CNPq Grant No. 458702/2014-5) and from FAPESP (Grant Nos. 2013/15431-7, 2014/07949-9, 2014/19497-5, and 2016/02034-8). The authors also extend their gratitude to Prof. Dr. Alessandro Roger Rodrigues from Escola de Engenharia de São Carlos/EESC-USP and to Mr. Paulo Arthur Beck from TUM—Technical University of Munich/Department of Mechanical Engineering for their important contribution to this work.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • J. A. A. Ortegon
    • 1
  • R. R. Souza
    • 1
  • J. B. C. Silva
    • 1
  • E. M. Cardoso
    • 1
    Email author
  1. 1.Post-Graduation Program in Mechanical EngineeringUNESP – São Paulo State UniversityIlha SolteiraBrazil

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