Plane walls thermal resistance

The thermal-resistance concept may be used for multiple-layer cylindrical walls just at it was used for plane walls. For the three-layer system shown in Fig. 2-4 the solution is... 

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. 

Note that the heat transfer area A is constant tor a plane wall, and the rate of heat transfer through a wall separating two mediums is equal to the temperature difference divided by the total thermal resistance between the mediums. Also note that (he thermal resistances are in series, and the equivalent thermal resistance is determined by simply adding the individual resistances, just like the electrical resistances connected in series. Thus, the electrical analogy still applies. We summarize this as the rate of steady heat transfer between two surfaces is equal to the temperature difference divided by the total thermal resistance behveen those Uvo surfaces. 

In practice we often encounter plane walls that consist of several layers of different materials. The tbermal resistance concept can still be used to detennine the rate of steady heat transfer through such composite walls. As you may have already guessed, this is done by simply notiifg that the conduction resistance of each wall i.s IJkA connected in series, and using the electrical analogy. That is, by dividing the temperature difference between two surfaces at known temperatures by the total thermal resistance between them. 

FIGURE 3-9 The thermal resistance network for heat tran.sfer through a two-layer plane wall subjected to convection on botir sides. 

Discussion This is the same result obtained earlier. Note that heat conduction through a plane wall with specified surface temperatures can be determined directly and easily without utilizing the thermal resistance concept. However, the thermal resistance concept serves as a valuable tool in more complex heat transfec problems, as you will see in the following examples. Also, the units W/m "f and W/m K for thermal conductivity are equivalent, and thus inter changeable. This is also the case for °C and K for temperature differences. 

Now consider steady one-dimensional heat transfer through a cylindrical or spherical layer that is exposed to convection on boili sides to fluids at temperatures and T 2 with heat transfer coefftcients /t, and h, respectively, as shown in Fig. 3-25. The thermal resistance network in this case consists of one conduction and two convection resistances in series, just like the one for the plane wall, and the rate of heat transfer under steady conditions can be expressed as... 

The / -value of a wall or roof structure that involves layers of uniform thickness is determined easily by simply adding up the unit thermal resistances of the layers that are in series. But when a structure involves components such as wood studs and metal connectors, then the thermal resistance network involves parallel connections and possible two-dimensional etfects. The overall / -value in this case can be dctcimined by assuming (1) parallel heal flow paths through areas of different construction or (2) isothermal planes normal to the direction of heal transfer. The first approach usually overpredicts the overall thermal resistance, whereas the second approach usually underpredicts it. The parallel heat flow path approach is more suitable for wood frame walls and roofs, whereas the isothermal planes approach is more suitable for inasoiuy or metal frame walls. 

This relation can be extended to plane walls that consist of two or more layers by adding an additional resistance for each additional layer, Tire elementary thermal resistance relations can be expressed as follows ... 

C How does the thermal resistance network associated with a single-layer plane wall differ from the one associated with a five-layer composite wall ... 

Overall conductance (overall heat-transfer coefficient) n. In heat-transfer engineering, the reciprocal of the total thermal resistance, for heat flow through plane walls or tube walls. It is defined by the equation U = q/AAT, where q is the rate of heat flow through (and normal to) the surface of area A, and AT is the fall in temperature through the layer in the direction of q. This is a modification of Fomier s law, invented to deal conveniently with heat flow through stagnant fluid films adjacent... 

The coke formation process can be simplified as a transient heat transport process between two plane walls (brick wall and coking chamber with width Wc). Two thermal resistances have to be considered, the coal/coke charge and the brick wall. Solution of Fourier s second law with the Fourier number Fo and Biot number 6/h parameters shows that the coking time of industrial coking chambers is proportional to about Wq, which favors a small width. 

Overall Conductance n (overall heat-transfer coefficient) In heat-transfer engineering, the reciprocal of the total Thermal Resistance, for heat flow through plane walls or tube walls. It is defined by the equation ... 

COMI QpND RESISTANCES IN SERIES. Consider a flat wall constructed of a series pflayers, as shown in Fig. 10.2. Let the thicknesses of the layers be B,i, B, and Bq and e average conductivities of the materials of which the layers are made be /c, kj, and respectively. Also, let the area of the compound wail, at right angles to the plane of the illustration, be A. Let A7, ATb, and ATc be the temperature drops across layers A, B, and C, respectively. Assume, further, that the layers are in excellent thermal contact, so that no temperature difference exists across the interfaces between the layers. Then, if AT is the total temperature drop across the entire wall,... 

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