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Figure 2.10: Shell and tube heat exchanger [49]. in industry is the shell and tube HX, shown in figure 2.10. Other common types of HXs are plate HXs and Tube-in-Tube HXs. Thermal conduction is the primary mechanism by which the heat transfer in a heat exchanger, from one fluid to the other, occurs. In general, thermal energy is transfered through the material by disorganized microscopic collisions of particles and movements of electrons within the material. In solids, conduction is mediated by the combinations of the vibrations, propagation and diffusion of molecules, phonons and electrons. Metals are therefore good thermal conductors, and often used in heat exchangers, due to their metallic bonds which allow for the free movement of electrons within the material. Fourier’s law describes the rate of heat transfer as proportional to the negative temperature gradient across the surface. It is given as q ̇ = −k∇T (2.32) where ∇ is the nabla operator ( ∂ , ∂ , ∂ ) and k is the conductivity of the material which may be ∂x ∂y ∂z seen as constant in certain temperature ranges, depending on the material. Differentiating across the entire surface, S, of a material the heat transfer is found as the closed surface integral ∂Q ∂t =−k ∇T·dS (2.33) where the dS represents the differential surface element. In the one-dimensional case, e.g. through a plane surface, the equation [2.33] simplifies to Q ̇ =−kdT (2.34) dx 32PDF Image | Analysis of Organic Rankine Cycles for a Boiler Station
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