A Polyethylene Chamber for Use in Physical Modelling of the Heat Exchange on Surfaces Exposed to a Radiation Regime

Abstract

Bodies located in outdoor environments are radiatively heated in the daytime and cooled at night. Convective heat transfer is subsequently activated between the body surface and the surrounding air. To investigate these heat-exchange processes, we developed a new apparatus, referred to as a “polyethylene chamber”, for use in physical model experiments. The chamber is a 1.51-m-long tube with the ends serving as the air inlet and outlet, and is ventilated in the longitudinal direction by using an exhaust fan. The measurement section of the chamber is open but otherwise the device is covered with 0.02-mm-thick polyethylene film. Because such thin polyethylene film transmits approximately 85 % of both shortwave and longwave radiation, the model surface in the chamber is exposed to a radiation level almost equivalent to the outdoor radiation level. For example, at night the surface of the model is cooled by radiation, and subsequently, the air inside the chamber is cooled by the surface. Consequently, the outlet air temperature becomes lower than the inlet air temperature. The use of this temperature difference between the air inlet and outlet, together with other heat balance components, is a unique approach to the chamber technique for evaluating the heat exchange rate at a model’s surface. This report describes the design and heat balance of the chamber, and compares the heat-balance-based approach with another approach based on the radiation–convection balance on the model surface. To demonstrate the performance of the polyethylene chamber, two chambers were exposed to outdoor radiation on a clear night; one contained a leaf model. Air and surface temperatures were measured and the convective heat flux at the surfaces of the model and floor surface were calculated from the heat balance components of the chambers by assuming steady-state heat transfer. The fluxes agreed closely with those obtained from the radiation–convection balance at the model or floor surface. The results also clearly showed that the air flowing in the polyethylene chamber was cooled more efficiently when the model surface was installed in the chamber, even though the model surface temperature was high.

Appendix: Shortwave (Solar) Radiation Balance Inside and Outside the PE Chamber

Net shortwave radiation above and below the PE film, $S_{\mathrm{n{\text{- }}a}}$ and $S_{\mathrm{n{\text{- }}b}}$, can be expressed by defining $S_{\mathrm{p{\text{- }}up}}$ as the shortwave radiation at the outside film surface directed upward and $S_{\mathrm{p{\text{- }}down}}$ as the shortwave radiation at the inside film surface directed downward, hence

$$\begin{aligned} S_{\mathrm{n{\text{- }}a}}&= S-S_{\mathrm{p{\text{- }}up}} , \end{aligned}$$

(29)

$$\begin{aligned} S_{\mathrm{n{\text{- }}b}}&= S_{\mathrm{p{\text{- }}down}} -S_{\mathrm{f{\text{- }}up}} . \end{aligned}$$

(30)

Upward directed shortwave radiation at the floor surface, $S_{\mathrm{f{\text{- }}up}}$, is equal to the radiation reflected by the floor surface, and is given by

$$\begin{aligned} S_{\mathrm{f{\text{- }}up}} =r_\mathrm{f} S_{\mathrm{p{\text{- }}down}} . \end{aligned}$$

(31)

The radiative characteristics of the PE film, in particular its reflectivity, largely depend on the incident angle of radiation. The downward radiation incident on the outside film surface from the sun and the sky consists of direct beams and scattered radiation, whereas the upward radiation incident on the inside film surface from the floor usually consists of scattered radiation, unless the floor surface is shiny. The characteristics are different for different directions of radiation; therefore, we define transmissivity, reflectivity, and absorptivity separately for downward and upward radiation. Two components, $S_{\mathrm{p{\text{- }}up}}$ and $S_{\mathrm{p{\text{- }}down}}$, are given by

$$\begin{aligned} S_{\mathrm{p{\text{- }}up}}&= r_{\mathrm{s{\text{- }}down}} S+t_{\mathrm{s{\text{- }}up}} S_{\mathrm{f{\text{- }}up}} , \end{aligned}$$

(32)

$$\begin{aligned} S_{\mathrm{p{\text{- }}down}}&= t_{\mathrm{s{\text{- }}down}} S+r_{\mathrm{s{\text{- }}up}} S_{\mathrm{f{\text{- }}up}} . \end{aligned}$$

(33)

Substituting Eqs. 32 and 33 into Eqs. 29 and 30, we obtain

$$\begin{aligned} S_{\mathrm{n{\text{- }}a}}&= S-r_{\mathrm{s{\text{- }}down}} S-t_{\mathrm{s{\text{- }}up}} S_{\mathrm{f{\text{- }}up}} , \end{aligned}$$

(34)

$$\begin{aligned} S_{\mathrm{n{\text{- }}b}}&= t_{\mathrm{s{\text{- }}down}} S+r_{\mathrm{s{\text{- }}up}} S_{\mathrm{f{\text{- }}up}} -S_{\mathrm{f{\text{- }}up}} . \end{aligned}$$

(35)

The difference between net shortwave radiation values above and below the PE film is obtained by subtracting Eq. 35 from Eq. 34,

$$\begin{aligned} S_{\mathrm{n{\text{- }}a}}-S_{\mathrm{n{\text{- }}b}}&= \left( {1-r_{\mathrm{s{\text{- }}down}}-t_{\mathrm{s{\text{- }}down}} } \right) S-\left( {1-r_{\mathrm{s{\text{- }}up}} -t_{\mathrm{s{\text{- }}up}} } \right) S_{\mathrm{f{\text{- }}up}} \\&= a_{\mathrm{s{\text{- }}down}} S{\text{- }}a_{\mathrm{s{\text{- }}up}} S_{\mathrm{f{\text{- }}up}}.\nonumber \end{aligned}$$

(36)

Outdoor global shortwave radiation, $S$, is significantly larger than upward shortwave radiation at the floor surface, $S_{\mathrm{f{\text{- }}up}} (S\,\gg \, S_{\mathrm{f{\text{- }}up}})$. Therefore, the net shortwave radiation below the PE film (inside the chamber) is reduced and the extent of the reduction depends on the outdoor shortwave radiation and the absorptivity of the PE film for incoming shortwave radiation. The absorptivity of a transparent PE film is 5 % or less when the film is as thin as 20 $\upmu$m.