Paper No. : 04 Paper Title: Unit Operations in Food Processing Module-07: Heat Transfer 3: Heat Radiation

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1 Paper No. : 04 Paper Title: Unit Operations in Food Processing Module-07: Heat Transfer 3: Heat Radiation 7.1 Introduction Radiation heat transfer is the transfer of heat energy in the form of electromagnetic waves from one surface to another. Unlike conduction and convection, radiation heat transfer does not require a medium to propagate; even it can travel through complete vacuum without any attenuation. The rate of heat transfer is fastest among all modes, almost at the speed of light just like the solar energy reaches to the earth. The radiation we are talking about is the thermal radiation and it occurs at the wavelength range of 10-7 to 10-4 m and it encompasses mainly the infrared radiation (Fig.7.1). The intensity of radiation strongly depends on the temperature of the source. Even though any substance emit radiation above the absolute zero temperature (0 0 K), the kind of emission we are more concerned with is at high temperature just like in baker s oven and radiant dryers. 7.2 Radiative properties Absorptivity, reflectivity and transmissivity Fig. 7.1 Electromagnetic spectrum When incident radiation (q inc ) from a source, strikes on a surface, some portion of radiation energy gets reflected. The ratio of reflected energy to the incident energy is called reflectivity ( ). The other portion that enters the surface, some portion out of it is absorbed by the body. The fraction of incident energy that gets absorbed is called absorptivity ( ). The remaining incident radiation after q inc Surface q ref = ρq inc q abs = α q inc q tran = τ q inc reflection and absorption is Fig.7.2 Demonstration of emissivity, reflectivity and absorptivity transmitted through the body. This portion of incident energy is called transmissivity ( ). and, But, Hence, the relation between absorptivity, reflectivity and transmissivity is derived as follows; (7.1) Most of the solids and liquids have zero or negligible transmission power. So a real solid or liquid

2 (7.2) So, the radiation energy reflected will be q ref = (1-α) q inc (7.3) The value of these three radiative properties varies from zero to unity. The properties vary from object to object. They depend on the molecular structure and surface smoothness of the body. The heat transfer to or from a body solely depends only on the amount of absorbed incident radiation. The difference between the rate of incident radiation emitted and the rate of incident radiation absorbed is the net rate of heat transfer. If the rate of absorption of incident radiation is greater than the rate of emission of incident radiation, the body gains thermal energy. Otherwise, the body is said to be losing thermal energy Emissivity and Kirchhoff s law Emissivity is a material property, ranging from 0 to 1, which measures how much energy a surface can emit with respect to an ideal emitter ( ) at the same temperature. Emissivity is the ratio of the radiant energy flux of a body to that of a perfect black body whose absorptivity is unity. (7.4) Where, E is the radiant heat flux of a real body and E o is the radiant heat flux of a perfect black Fig7.3 Emissivity of some materials ( body. For a perfect black body emissivity is unity. Furthermore, the absorptivity also expressed as (7.5) From equation (7.4) and (7.5) it is evident that the emissivity and absorptivity of any substance are same at thermal equilibrium. This relation is popularly known as Kirchhoff s law. (7.6) 7.3 Types of surfaces Black body A body is said to be perfectly black if it absorbs all the incident radiation to it. A black body emits maximum radiation energy at a given temperature i.e. the emissive power of a black body is maximum. The absorptivity of a black body is unity and hence the transmissivity and reflectivity are zero. A body in real world cannot be perfectly black. The emissive power of a black body is solely dependent on its absolute temperature. (7.7) Or,, i.e. whatever energy is radiated whole energy gets absorbed.

3 7.3.2 Gray body A body is said to be gray if the monochromatic properties are constant at all wavelengths. For a gray body, and The total absorptivity and emissivity are equal (α = ε) for a gray body even though the material is not in equilibrium with its surroundings. Gray body is a conceptual term that does not exist in practice. This is because of the wavelength dependence of absorptivity and emissivity Opaque body A body is said to be opaque if no incident radiation gets transmitted through the body. All most all the materials are bad transmitter. So, they all are opaque bodies. Thus, No energy is transmitted meaning all the energy is absorbed in the body. So, all opaque bodies behave like black body but they do not show perfect blackness. 7.4 Radiation heat flux The law governing the heat transfer by radiation is called Stefan-Boltzmann law. It states that the total emissive power is the total radiation energy per unit area leaving a surface with temperature T over all wavelengths. (7.8) Where, q/a is the heat flux (W/m 2 ), T is the absolute temperature ( 0 K), ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant,. For a perfectly black body the equation (7.8) will be (7.9) From the formula it is evident that, the heat transfer not only depends on temperature but also it depends on the geometry of the surface. 7.5 Radiation between two bodies The heat transfer from one surface to other consists of three distinct phases such as 1) The thermal energy of a hot body of temperature T 1 is converted to electromagnetic waves, 2) These electromagnetic waves travel through a intervening space in straight line at a speed of 1 2 T 1 Fig. 7.4 Radiation heat transfer between two bodies T 2

4 light and strike to a cold surface of temperature T 2 without heating the medium and 3) The electromagnetic waves striking the surface are absorbed on the surface and converted back to thermal energy. The absorbed energy only contributes to the heating process. The radiation energy cannot pass through the body since the radiation heat transfer is a surface phenomenon. The heat thus passes through the body either by conduction or convection. Consider two bodies which are at temperatures T 1 and T 2 such that T 1 > T 2 and emissivity ε 1 and ε 2 at respective temperatures. The net heat transfer from the hot body to cold body will be in the form Where, ( ) (7.10) 7.6 Radiation from the surroundings Many cases in food processing involve radiation heat transfer from the surroundings. Bread loaf gets the radiation heat from the wall of the baking oven which is at much higher temperature. The beef carcass radiates heat to the freezer wall. The equation (7.10) is applied to calculate the heat transfer, where, T 1 is the temperature of the surrounding whereas T 2 is the temperature of heat receiving surface. T 1 is assumed to be uniform temperature of the surrounding. If we critically analyse, a combined convection and radiation mechanism is observed in a baking oven. Unlike conduction and convection heat transfer across a wall, the combined radiation and convection heat transfer cannot be additive. This is because the radiation heat transfer is 4 th power of absolute temperature where as the convection heat transfer is the unit power of temperature. So, the radiation heat transfer equation need to be modified as follows, ( ) (7.11) For black body equation (7.10) is reduced to ( ) (7.12) Combining equation (7.11) and (7.12), we get the expression of h r as, Where, h r is the radiation heat transfer coefficient. So, the total heat transfer to the body is (7.13). (7.14) Problem: In a baking oven, a loaf of bread with rectangular dimensions (33 cm X 11 cm X 11 cm) is baked whose surface temperature is C. If the surrounding air temperature and wall temperature is C, calculate the total heat transfer to the loaf if the emissivity of loaf is assumed to be Solution: The radiation heat transfer ( )

5 , ( ) ( )-*( ) ( ) + Note: This solution holds good if convection heat transfer is neglected. However, in real situation a combined convection and radiation mode of heat transfer occur. In that case you need to calculate heat transfer coefficient for each horizontal and vertical surfaces taking the help of Grashof and Prandtl number. So, heat transfer by convection in each face is calculated first and then added to get total convection heat transfer. Both the convection and radiation heat transfer will give you total heat transfer to the bread loaf Radiation heat transfer with emitting and absorbing medium So far we have considered the radiation heat transfer from the source to the body without any interference of the medium or complete vacuum or transparent medium. However, there are some gases if present in air with sufficient concentration, the emission and absorption must be considered in radiation heat transfer calculations. The gases contain asymmetric molecules such as H 2 O, CO 2, CO, SO 2 and hydrocarbons. Combustion gases in furnace or in combustion chamber contain sufficient H 2 O and CO 2 and thus emission and absorption in gases must be taken in to account. References 1. Transport Processes and Unit Operations (3 rd Edition), C. J. Geankoplis, Prentice Hall Inc. Publ., Unit operations in food processing, R.L. Earle and M.D. Earl, NZIFST (Inc.) Publ., Fundamentals of food process engineering, Romeo T. Toledo, Springer, 3 rd edn., 2007