Heat transfer through composite walls

SOLUTION The composition of a composite wall is given. The rate of heat transfer through the wall is to be determined. 

Suppose one would like to evaluate a furnace combustion space bounded with refractory material. The composite walls have several layers of different refractory material and thickness. To estimate the losses through the furnace walls, one can obtain an analytical solution for temperature change in each layer of the refractory separately (if needed) and in the wall as a whole. If the heat transfer through the wall is considered to be one dimensional, the solution for the energy loss through the furnace wall can be obtained as... 

Figure 9.1. Heat transfer through a composite wall...

Flfl. 2-1 One-dimensional heat transfer through a composite wall and electrical analog. 

Conduction with Resistances in Series A steady-state temperature profile in a planar composite wall, with three constant thermal conductivities and no source terms, is shown in Fig. 5-3a. The corresponding thermal circuit is given in Fig. 5-3b. The rate of heat transfer through each of the layers is the same. The total resistance is the sum of the individual resistances shown in Fig. 5-3b ... 

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. 

Consider a plane wail that consists of two layers (such as a brick wall with a layer of insulation). The rate of steady heat transfer through this two-layer composite wall can be expressed as (Fig. 3-9)... 

Consider the composite wall shown in Fig. 3-19, which consists of two parallel layers. The thermal resistance network, which consists of two parallel resistances, can be represented as shown in the figure. Noting that the total heat transfer is the sum of the heat transfers through each layer, we have... 

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... 

As a result, the overall heat transfer through the composite refractory wall is known. The hot face and cold face heat transfer coefficients can be calculated from known expressions for forced and free convection near a flat plate. These expressions have the same structure but different empirical constants and can be found in, for example, Reference 20. 

The properties which determine heat transfer through a deposit layer of given thickness are thermal conductivity, emissivity, and absorptivity. These properties vary with deposit temperature, thermal history, and chemical composition. Parametric studies and calculations for existing boilers were carried out to show the sensitivity of overall furnace performance, local temperature, and heat flux distributions to these properties in large p.f. fired furnaces. The property values used cover the range of recent experimental studies. Calculations for actual boilers were carried out with a comprehensive 3-D Monte Carlo type heat transfer model. Some predictions are compared to full-scale boiler measurements. The calculations show that the effective conduction coefficient (k/As)eff of wall deposits strongly influences furnace exit temperatures. 

When a fluid is present in contact with each solid wall, there will be an additional resistance to heat transfer in each fluid boundary layer or film . The combined mechanism of heat transfer from a hot fluid through a dividing wall to a cold fluid has many similarities to conduction through a composite slab reviewed earlier. 

Equation (20) may be compared to Equation (4) for the heat flux through a composite plate. As we have seen, (6w/fcw) is the thermal resistance of the wall to heat transfer by conduction. Similarly, (1//+) and (1 /Ac) are the resistances to heat transfer offered by the hot and cold films, respectively. 

Find the heat transfer per unit area through the composite wall sketched. Assume one-dimensional heat flow. 

Related Calculations. The method described for calculating the overall heat-transfer coefficient is also used to calculate the overall resistance to conduction of heat through a composite wall containing materials in series that have different thicknesses and thermal conductivities. For this case, each individual heat-transfer coefficient is equal to the thermal conductivity of a particular material divided by its thickness. The amount of heat transferred by conduction can then be determined from the formula... 

It will be supposed that the kinetics of all the reactions that are going on and the thermodynamical and molecular transport properties of all the substances present are known, and that it is desired to find out how the composition of the effluent from a reactor depends on the conditions that are imposed. The conditions that must be fixed are the composition, pressure, temperature, and flow rate of the reactant mixture, the dimensions of the reactor and of the catalyst pellets, and enough properties of the heat-transfer medium to determine a relation between the temperature of the tube wall and the heat flux through it. 

Consider a composite wall made of three parallel slabs of cross-sectional area A (Fig. 2.3), The thickness and thermal conductivity of these slabs are 13 and k, respectively. Heat is transferred from a hot fluid at temperature 7 through this composite wall to a cold fluid at temperature To- Coefficients of heat transfer on the hot and cold sides are hi and ho, respectively. 

We will now consider the problem of calculating the heat transfer from a hot fluid to a composite plane of refractory wall and through an outer steel shell. 

From these we can also define the thermal conductance through the composite wall as [7 = 1 /RA, that is, the rate of heat transfer per degree of temperature drop per square meter, from which follows the heat transfer as... 

Table 10 summarizes the thermal performance of various blast furnace hearth wall carbonaceous lining material concepts, utilizing a heat-transfer analysis of each hearth wall composition (Case 1 through Case 5). 

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