Thermal Energy Storage Systems and Applications. Ibrahim Dincer

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Figure 1.14 Representations of heat transfer modes: (a) conduction through a solid, (b) convection from a surface to a moving fluid, and (c) radiation between two surfaces.

      1.6.1 Conduction Heat Transfer

      Conduction is a mode of transfer of heat from one part of a material to another part of the same material, or from one material to another in physical contact with it, without appreciable displacement of the molecules forming the substance. For example, the heat transfer in a solid object, subject to cooling in a medium, is by conduction. In solid objects, the conduction of heat is partly due to the impact of adjacent molecules vibrating about their mean positions and partly due to internal radiation. When the solid object is a metal, there are also large numbers of mobile electrons that can easily move through the matter, passing from one atom to another, and they contribute to the redistribution of energy in the metal object. The contribution of the mobile electrons predominates in metals, which explains the relation that is observed between the thermal and electrical conductivities of such materials.

      (a) Fourier's Law of Heat Conduction

      Fourier's law states that the instantaneous rate of heat flow through a homogeneous solid object is directly proportional to the cross‐sectional area A (i.e. the area at right angles to the direction of heat flow) and to the temperature difference driving force across the object with respect to the length of the path of the heat flow, dT/dx. This is an empirical law based on observation.

Figure 1.15 presents an illustration of Fourier's law of heat conduction. Here, a thin slab object of thickness dx and surface area F has one face at a temperature T and the other at a lower temperature (T − dT). Heat flows from the high‐temperature side to the low‐temperature side, with a temperature change dT in the direction of the heat flow. Therefore, under Fourier's law we obtain the heat transfer as

(1.83)

Figure 1.15 Conduction in a slab (a) and in a thin slice of the slab (b).

      Here, we have a term thermal conductivity, k, of the object, which can be defined as the heat flow per unit area per unit time when the temperature decreases by one degree over a unit distance.

      The SI units of thermal conductivity are usually W/m°C or W/m K.

Integrating Eq. (1.83) from T₁ to T₂ for dT and 0 to L for dx yields

(1.84)

Equation (1.84) can be solved when the variation of thermal conductivity with temperature is known. For most solids, thermal conductivity values are approximately constant over a broad range of temperatures, and can be taken as constants.

      1.6.2 Convection Heat Transfer

      Convection is the heat transfer mode that occurs within a fluid by mixing one portion of the fluid with another. Convection heat transfer may be classified according to the nature of the flow. When the flow is caused by some mechanical or external means such as a fan, a pump, or atmospheric wind, it is called forced convection. On the other hand, for natural (free) convection, the flow is induced by buoyancy forces in the fluid that arise from density variations caused by temperature variations in the fluid. For example, when a hot object is exposed to the atmosphere, natural convection occurs, whereas in a cold place with a fan‐driven air flow, forced‐convection heat transfer takes place between air flow and the object subject to this flow. The transfer of heat through solid objects is by conduction alone, whereas the heat transfer from a solid surface to a liquid or gas takes place partly by conduction and partly by convection. Whenever there is an appreciable movement of the gas or liquid, the heat transfer by conduction in the gas or liquid becomes negligibly small when compared with the heat transfer by convection. However, there is always a thin boundary layer of fluid on a surface, and through this thin film the heat is transferred by conduction. The convection heat transfer occurring within a fluid is due to the combined effects of conduction and bulk fluid motion. In general, the heat that is transferred is the sensible or internal thermal heat of the fluid. However, there are convection processes for which there is also latent heat exchange, which is generally associated with a phase change between the liquid and vapor states of the fluid.

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