Plane walls multilayer

Thermal flesislance Concept 133 Thermal Resistance Network 135 Multilayer Plane Walls 137... 

We stait this chapter with one-dimensional steady heat conduction in a plane wall, a cylinder, and a sphere, and develop relations for thennal resistances in these geometries. We also develop thermal resistance relations for convection and radiation conditions at the boundaries. Wc apply this concept to heat conduction problems in multilayer plane wails, cylinders, and spheres and generalize it to systems that involve heat transfer in two or three dimensions. We also discuss the thermal contact resislance and the overall heat transfer coefficient and develop relations for the critical radius of insulation for a cylinder and a sphere. Finally, we discuss steady heat transfer from finned surfaces and some complex geometries commonly encountered in practice through the use of conduction shape factors. 

Steady heat transfer through multilayered cylindrical or spherical shells can be handled just like multUayered plane walls discussed earlier by simply add ing an additional resistance in series for each additional layer. For example, the steady heat transfer rale through the three-layered composite cylinder of length L shown in Fig. 3-26 with convection on both sides can be expressed as... 

The individual conducting planes in double-sided and multilayer substrates are usually interconnected by holes, the walls of which are plated with copper, as illustrated in Fig. 9.4. These are usually referred to as plated through holes. 

Clearly, from Equation 9.45, depending on the character of decay of the surface forces field, which affects the extent of the boundary phase, the influence of the second term is revealed at different pore sizes. Thus, if the surface forces field fades into the bulk phase very sharply, and the thickness of boundary phase is restricted within the height of one monolayer, then (/ Y i(lw)) (fsw Ylw) the factor r/h the curvature term, 2(Ysw —Ylw)> will sensibly increase the shift of triple point only for pores with r of the same order as h, whereas for wider pores A will be dose to that at plane interfaces. In contrast, when the interaction of a confined substance with pore walls is strong enough to induce the multilayer boundary phase (such as takes place for water in hydroxylated mesoporous silica [64, 69]), then y l(Lw)) ( I sw Ylw) small k, and the shift of the triple point for... 

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