MATHEMATICAL MODEL OF A
HYBRID SOLAR PANEL
Robert Collins and
Ernesto Gutierrez-Miravete
Rensselaer at Hartford
Hybrid Solar Panel
• Uses PV cell to convert a fraction of the solar
irradiance into electricity.
• Uses heat exchanger principles to store most
of the solar irradiance NOT converted into
electricity as useful thermal energy inside a
working fluid.
• The use of the heat exchanger reduces heating
of the PV cell and increases its conversion
efficiency.
Hybrid Solar Panel Schematic
Steady 2D Turbulent Flow of a
Non-Isothermal Newtonian Fluid:
Governing Equations
∂vx/∂x + ∂vy/∂y = 0
v · ∇vx = − ∂p/∂x + µ∇2 vx + ρgx
v · ∇vy = − ∂p/∂y + µ∇2 vy + ρgy
k-ε Turbulence Model
ρ Cp v · ∇T = k∇2 T
Boundary Conditions
Model Geometry and Input
Material
PV Cell
Thermal Paste
Copper
Water
Property
Value
ρ
k
𝐶𝑝
ε
ρ
k
𝐶𝑝
ρ
k
𝐶𝑝
ρ
k
𝐶𝑝 = 𝐶𝑣
μ
Reference
2329
130
700
.60
3500
2.87
.7
8700
400
385
997.1
.611
4.184
902 x 10-6
Silicon
[11]
[12]
Copper
Water @ 25°C
Finite Element Model Mesh
Computed Velocity Field
Computed Temperature and
Heat Flux Fields
Hybrid Panel Overall Efficiency
Conclusions
• The greatest overall PV/T module efficiency of 85.7%
occurs with the labyrinth arrangement or the
arrangement with 27 top and 27 bottom fins that are
¾ the height of the flow path. This is an approximate
5.7% increase in efficiency over the arrangement
with no fins.
• When connected as an array, three modules linked in
a head to tail arrangement, heat the water by 16.5
degrees Celsius and collect energy from the
environment in the form of usable electrical and
thermal energy.