Optimum insulation thickness

An example in support of the first point is the case of optimum insulation thickness. A tank, optimally insulated when first installed, can fall below optimal if the value of heat is quadmpled. This change can justify twice the old iasulation thickness on a new tank. However, the old tank may have to function with its old iasulation. The reason is that there are large costs associated with preparation to iasulate. This means that the cost of an added increment of iasulation is much greater than assumed ia the optimum iasulation thickness formulas (Fig. 15). 

In Example 3.3 we developed an objective function for determining the optimal thickness of insulation. In that example the effect of the time value of money was introduced as an arbitrary constant value of r, the repayment multiplier. In this example, we treat the same problem, but in more detail. We want to determine the optimum insulation thickness for a 20-cm pipe carrying a hot fluid at 260°C. Assume that curvature of the pipe can be ignored and a constant ambient temperature of 27°C exists. The following information applies ... 

A Case of a Composite Wall Optimum Insulation Thickness for a Steam Line... 

An example illustrating the principles of an optimum economic design is presented in Fig. 11-1. In this simple case, the problem is to determine the optimum thickness of insulation for a given steam-pipe installation. As the insulation thickness is increased, the annual fixed costs increase, the cost of heat loss decreases, and all other costs remain constant. Therefore, as shown in Fig. 11-1, the sum of the costs must go through a minimum at the optimum insulation thickness. 

The graphical method for determining the optimum insulation thickness is shown in Fig. 11-1. The optimum thickness of insulation is found at the minimum point on the curve obtained by plotting total variable cost versus insulation thickness. 

The slope of the total-variable-cost curve is zero at the point of optimum insulation thickness. Therefore, if Eq. (3) applies, the optimum value can be found analytically by merely setting the derivative of CT with respect to x equal to zero and solving for x. 

Example 3. Find the optimum insulation thickness on the vertical pipe given in Example 2. The following data are available Cost of heat loss, Ch = 2.0/million Btu cost of installation, Ci = 4 depreciation fraction, f = 0.1 operating time, t = 8,000 hrs./year. 

An optimization model could be carried out to calculate the optimum insulation thickness for the storage tank. This could lead to a substantial savings when choosing a small insulation thickness. 

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