Heat sources point

The point of zero heat flow in the grand composite curve in Fig. 6.24 is the pinch. The open jaws at the top and bottom represent Hmin and Qcmin, respectively. Thus the heat sink above the pinch and heat source below the pinch can be identified as shown in Fig. 

In this context, the points correspond to process and utility streams and the lines to heat exchange matches between the heat sources and heat sinks. 

The point at which enough heat has been added to start combustion is known as the ignition point. Once initiated, external heating sources are typically not required to maintain the combustion process, because most fuels release sufficient heat during the combustion process. 

Thermal plumes above point (Fig. 7.60) and line (Fig. 7.61) sources have been studied for many years. Among the earliest publications are those from Zeldovich and Schmidt. Analytical equations to calculate velocities, temperatures, and airflow rates in thermal plumes over point and line heat sources with given heat loads were derived based on the momentum and energy conservation equations, assuming Gaussian velocity and excessive temperature distribution in... 

In reality, heat sources are seldom a point, a line, or a plane vertical surface. The most common approach to account for the real source dimensions is ro use a virtual source from which the airflow rates are calcu-lared " " see Fig. 7.64. The virtual origin is located along the plume axis at a distance on the other side of the real source surface. The adjustment of the point source model to the realistic sources using the virtual stmrce method gives a reasonable estimate of the airflow rate in thermal plumes. The weakness of this method is in estimating the location ol the virtual point source. 

Mundt calculates the thickness of the boundary layer (see Table 7.20) at the top of a vertical extended heat source and adds this to the source radii, and then calculates the position of the virtual source as = 2.1(D + 26) before using the point source equation. 

The coating material, usually in the form of powder, is metered into a compressed-gas stream and fed into the heat source where it is heated to its melting point and proj ected onto the substrate. In the case of refractory metals and compounds which have high melting points, spraying is carried out in an inert atmosphere to avoid detrimental chemical reactions such as oxidation. 

A typical method for thermal analysis is to solve the energy equation in hydrodynamic films and the heat conduction equation in solids, simultaneously, along with the other governing equations. To apply this method to mixed lubrication, however, one has to deal with several problems. In addition to the great computational work required, the discontinuity of the hydrodynamic films due to asperity contacts presents a major difficulty to the application. As an alternative, the method of moving point heat source integration has been introduced to conduct thermal analysis in mixed lubrication. 

If the heat flux from friction or viscous shear is properly estimated, the surface temperature, which is of interest in most engineering problems, can be determined through integrating an analytical solution of temperature rise caused by a moving point heat source, without having to solve the energy equation. For two solid bodies with velocity u j and Ui in dry contacts, the temperature rises at the surfaces can be predicted by the formula presented in Ref. [22],... 

Before stating the main results, it will be sensible to clarify a physical sense of the function u(x), which solves problem (1) subject to the conditions [u] = 0 and [kii ] = — Qq (/ — x) kg = g at the point x =. Here q stands for the capacity of a point heat source (sink) at the point X =. Being dependent on x, the quantity q varies very widely. Specifically, q —+ 00 as X — 5 0. Thus, the physical reason for the convergence of scheme (2) is that the heat balance (the conservation law of heat) is... 

In what follows we share our practical experience of the design of difference schemes for problems with lumped parameters by means of the IIM. Suppose, for instance, that a single heat source of capacity Q is located at a point x — so that a solution of problem (l)-(2) satisfies the conditions... 

Adopting those ideas to problem (1), (2), (14) concerning a point heat source, an excellent start in this direction is to replace the function f x) involved in formula (40) by f x) + 6 x — where 6 x - ) is Dirac s... 

An one-point heat source. Of special interest is the nonstationary heat conduction problem in the situation when a heat source is located only at a single point x = under the agreement that at this point the solution of problem (l)-(3) satisfies the condition of conjugation... 

By means of the integro-interpolation method it is possible to construct a homogeneous difference scheme, whose design reproduces the availability of the heat source Q of this sort at the point x = /. This can be done using an equidistant grid u)j and accepting / = x -f Oh, 0 <0 < 0.5. Under such an approach the difference equation takes the standard form at all the nodes x [i n). In this line we write down the balance equation on the segment x,j. 

The accurate account of the error z can be done as in Section 4, leading to the same rate of convergence. No progress is achieved for a = a in line with approved rules, because the choice of the coefficient should not cause the emergence of a higher-order accuracy. From the formula = 9 Q+0 h) it is easily seen that i]n+i — 0(h) and, hence, z = 0(h +T" ) if = 0, meaning that the heat source is located at one of the nodal points. 

Yokoi (1960) [3], singly produced a small book as a report, which carefully investigated point, line and finite heat sources with eventual applications to the hazard from house fire and window flame plumes. 

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