Heat and Mass Transfer

, Volume 42, Issue 12, pp 1065–1081 | Cite as

Sensitivity analysis of thermal performances of flat plate solar air heaters

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First Online:
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Abstract

Sensitivity analysis is a mathematical tool, first developed for optimization methods, which aim is to characterize a system response through the variations of its output parameters following modifications imposed on the input parameters of the system. Such an analysis may quickly become laborious when the thermal model under consideration is complex or the number of input parameters is high. In this paper, we develop a mathematical model to analyse the heat exchanges in four different types of solar air collectors. When building this thermal model we show that for each collector, at quasi-steady state, the energy balance equations of the components of the collector cascade into a single first-order non-linear differential equation that is able to predict the thermal behaviour of the collector. Our heat transfer model clearly demonstrates the existence of an important dimensionless parameter, referred to as the thermal performance factor of the collector, that compares the useful thermal energy which can be extracted from the heater to the overall thermal losses of that collector for a given set of input parameters. A sensitivity analysis of our thermal model has been performed for the most significant input parameters such as the incident solar irradiation, the inlet fluid temperature, the air mass flow rate, the depth of the fluid channel, the number and nature of the transparent covers in order to measure the impact of each of these parameters on our model. An important result which can be drawn from this study is that the heat transfer model developed is robust enough to be used for thermal design studies of most known flat plate solar air heaters, but also of flat plate solar water collectors and linear solar concentrators.

Keywords

Solar air heater Quasi-steady state modelling Sensitivity analysis Thermal performance factor 

List of symbols

A

collector area (m2)

Tc

transparent cover temperature (K)

cp

specific heat (J/kg K)

Tf

fluid temperature (K)

Dh

hydraulic diameter (m)

Tp

blackened back plate temperature (K)

e

thickness (m)

Ts

selective absorber temperature (K)

emb

water vapour pressure (Pa)

Ub

bottom loss coefficient (W/m2/K)

Eu

useful energy gain (J)

UL

overall loss coefficient (W/m2/K)

F′

collector effiiciency factor

Va

wind speed (m/s)

G

mass flow rate per unit collector area (kg/s/m2)

x

space coordinate (m)

hc

convection heat transfer coefficient (W/m2/K)

hr

radiation heat transfer coefficient (W/m2/K)

I

incident solar radiation (W/m2)

L

collector length (m)

Lc or Ls

characteristic length (m)

m

mass per unit collector area (kg/m2)

\(\dot{m}_{f}\)

air mass flow rate (kg/s)

Nu

Nusselt number

Pr

Prandtl number

Qu

useful thermal power (W)

Re

Reynolds number

tr

Iistant of sunrise (s)

ts

instant of sunset (s)

Ta

ambient temperature (K)

Greek letters

αp

absorptance of blackened back plate

k

thermal conductivity (W/m/K)

αs

absorptance of selective absorber plate

ℓ

collector width (m)

ɛp

emittance of blackened back plate

ɛs

emittance of selective absorber plate

η

collector thermal efficiency

ρc

transparent cover reflectance

ρf

fluid density (kg/m3)

σ

Stefan–Boltzmann constant (W/m2/K4)

τc

transmittance of cover for short wavelength radiation

τir

transmittance of cover for thermal IR radiation

Ω

thermal performance factor

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Heat Transfer LaboratoryUniversity of Yaounde IYaoundeCameroon
  2. 2.Laboratoire de Thermodynamique et EnergétiqueUniversité de PerpignanPerpignanFrance

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