辐射热传递的基本原理

以下是辐射热传递的基本原理。我们将随时添加这方面的信息，请密切关注。以下是摘自由潘钟离与格里菲思•格•阿吞咕噜（Griffiths Gregory Atungulu）编著的《红外线加热在食品与农产品加工中的应用》。此书可以在http://www.crcpress.com/product/isbn/9781420090970.网站上购买。

红外线是电磁波谱的一部分，而电磁波谱是由于太阳的热效应产生的，如图1.1所示（modest，1993）。红外线可以分成三种不同的种类：短波红外线，中波红外线以及长波红外线。如图表1.1所示。(图表1.1; Sakai and Hanzawa, 1994)。由于红外线是一种电磁波，分别具有光谱依赖性与定向依赖性。红外线的光谱依赖性值得引起注意，因为辐射源散发出的能量是由不同的波长组成的，而光谱带中的辐射区与许多因素有关，比如辐射源的温度，辐射源的发射率等等。由于投射在物体表面上的红外线不仅具有光谱依赖性而且还具有定向依赖性，因此放射现象变得比较复杂。

根据黑体辐射基本原理，比如普朗克定律、维恩位移定律还有斯蒂芬 - 玻尔兹曼定律，有辐射就有波长，当最高辐射出现时，波长是由加热器的温度决定的。(Sakai and Hanzawa, 1994; Dangerskog and Osterstrom, 1979)

图1.1, 电磁波谱

普朗克定律

根据普朗克定律，在一个给定的温度下，黑体放射出100%的红外线，可以得出其辐射光谱分布图。
红外线辐射源是由处于不同温度的成千上万的点源组成的。通过连接这些点源可以获取某些特定地区的完整光谱分布图。在此概述的理论使用一个近似的光谱分布图，用一个平均表面温度与辐射率来分辨出红外线。然而，实际上，红外线是不可以分辨出来的，因为如同辐射吸收一样，辐射发射也会随着辐射源的温度的改变而改变。
马克斯•普朗克称黑体发射功率光谱分布图，也就是现在著名的普朗克定律的公式为Ebλ(T,λ)= (2πhc 2/0)/(n2λ5[e(hc0⁄nλkT)-1) （1.1），其中 k为玻尔兹曼常数（1.3806 X 10-23J/K），n为与黑色表面绑定的透明介质的折射率。

E^bλ(T,λ)= (2πhc 2/0)/(n²λ⁵[e^{(hc₀⁄nλkT)}-1)                           (1.1)

按照定义，真空的折射率为n=1。大多数气体的折射率差不多相同。λ指波长，单位是μm。T指辐射源的温度，单位是K。c_0指光速，单位是Km/s。h是普朗克常数，为6.626 X 10-34J-s。

图1.2（a）展示了根据方程式1.1的黑体温度曲线图。大体上，辐射源的辐射功率水平随着温度的升高而升高，而最大辐射功率对应的波长却越来越短。谈到波长，在特定温度下特定区域的红外线发射功率的总量可以通过普朗克定律求积分估算出来。
在已知加热系统的具体的表面温度的前提下，辐射器的热负荷总量可以通过普朗克定律估计出来。为了测出红外线辐射源发射出的能量，能量必须按比例平衡地流经传热室。而经过传热室的数量则被称为传热系数。因此，目标材料所吸收的热负荷的实际数量可以通过计算从辐射源到目标材料的总辐射功率与传热系数来测算出。

维恩位移定律

维恩位移定律可以测出波长（暗指峰值波长）。当波长达到峰值时，黑体的辐射光谱分布图达到一个最大发射功率。曲线图1.2的峰值可以测出来。这与方程式1.1不同:

在这些条件下，能量平衡引出著名的关系式：ρ+α+τ= 1 (1.6)。辐射的消失是至关重要的，因为大部分的红外线热转换模型与被输送到食物材料中的热负荷的数量关系紧密，而食物材料与有效肤深有关。

[d/d(nλT)](E_bλ/n³λ⁵)=0 (1.2)

Source temperatures of IR lamps needed for a desired spectral distribution can be estimated by (Modest, 1993)

λ_max=2898/T (1.3)

Where T is the source temperature and λ_max  is the peak wavelength. If the source temperature is known, the peak wavelength can be derived from Equation 1.3. The dotted line in Figure 1.2(a) demonstrates the relationship between the source temperature and the peak wavelength. As an example, the emissive power spectrum of the original IR source with unknown surface temperature can be measured and recorded using the Fourier transform IR (FTIR) spectrometer (Figure 1.2(b)). Based on the plot and Equation 1.3, a peak wavelength of 2.92μm and correspondent IR source temperature of 720⁰C are obtained.

Figure 1.2 (a), Blackbody emissive power spectrum.

Figure 1.2 (b), Measured emissive power spectrum of IR heating elements.

Stefan-Boltzmann’s Law

Stefan – Boltzmann’s law gives the total power radiated at a specific temperature from an IR source. The entire amount of heat flux estimated using this law should be consistent with integration of the spectral amount of heat flux estimated using Planck’s law given in Sakai and Hanzawa (1994):

Where C1 = 2πhc²₀= 3.7419 X10^-16Wm², C2 = hc_olk=14,388μmK and σ is known as the Stefan-Boltzmann constant (5.670 X 10-8 W/m^2 K^4). Stefan-Boltzmann’s law is available for prompt estimation of the total amount of heat flux at a given source temperature.

Extinction of Radiation, Transmission, Absorption and Reflection

The mechanisms to explain the attenuation of electromagnetic radiation as it propagates through a medium are absorption and scattering. Converting the radiation to some other forms of energy (or some spectral distribution) is called absorption phenomena, whereas scattering mechanisms redirect the radiant energy from its original direction of propagation due to the combined effect of reflection, refraction and diffraction. The sum of the mechanisms of attenuation of electromagnetic radiation as it passes through a medium (absorption plus scattering) is generally called extinction of radiation (Sandu, 1986; Modest, 1993).
When the extinguishing material is agglomerated into particles, separated by regions of different transmissivities (such as emulsions and dispersions), or when variations occur in the density of the samples (as in capillary-porous bodies or in bodies subject to a temperature or moisture gradient or in solid bodies that contain a liquid free phase inside), Beer’s law should be formally adjusted for nonhomogeneous systems using

H_λ=H_λ0 exp(-σ_λ*u) (1.5)

Where H_λ is the transmitted spectral irradiance (W⁄(m²μm)),H_λ0 is the incident spectral irradiance (W⁄(m²μm)),u, is the mass of absorbing medium per unit area (kg⁄m² ) and σ_λ* is the spectral extinction coefficient (m²/kg).

Beer’s law states that the amount of light absorbed by a solution varies exponentially with the concentration of the solution and the length of the light path in the solution. The spectral extinction coefficient, σ_λ* (m²/kg) for a nonhomegeneous system is a complex function of the chemical composition of the radiated medium, the physiochemical state of the radiated medium, and the physiochemical parameters defining the radiated medium (density, porosity, diameter of particles, water content, etc.)

In radiative heating, an energy balance can be defined in relation to the extinction of radiation by a physical body. Assuming that this body is an infinite slab of given physicochemical composition and absorbed energy is the total radiation converted into heat inside the body, the entire process of extinction can be defined in terms of reflection, absorption, and transmission of radiation. The three fundamental radiative properties are reflectivity (ρ), absorptivity (α) as the ration of absorbed part of incoming radiation to the total incoming radiation and transmissivity (τ) as the ratio of transmitted part of incoming radiation to the total incoming radiation.

在这些条件下，能量平衡引出著名的关系式

ρ+α+τ= 1 (1.6)

辐射的消失是至关重要的，因为大部分的红外线热转换模型与被输送到食物材料中的热负荷的数量关系紧密，而食物材料与电子的有效肤深有关。

图1.3, 为辐射的消失过程（吸收、传输与反射）

版权（2011）归潘钟离与格里菲思•格•阿吞咕噜（Griffiths Gregory Atungulu）编著的《红外线加热在食品与农产品加工中的应用》所有。经泰勒与弗朗西斯集团有限公司，信息 plc的一个部门的同意有所改动。