Cooling of a plate

An approximate solution for the convective cooling of a plate of finite thickness is given by Agassant etal. [1],... 

The three bodies — plate, very long cylinder and sphere — shall have a constant initial temperature d0 at time t = 0. For t > 0 the surface of the body is brought into contact with a fluid whose temperature ds d0 is constant with time. Heat is then transferred between the body and the fluid. If s < i90, the body is cooled and if i9s > -i90 it is heated. This transient heat conduction process runs until the body assumes the temperature i9s of the fluid. This is the steady end-state. The heat transfer coefficient a is assumed to be equal on both sides of the plate, and for the cylinder or sphere it is constant over the whole of the surface in contact with the fluid. It is independent of time for all three cases. If only half of the plate is considered, the heat conduction problem corresponds to the unidirectional heating or cooling of a plate whose other surface is insulated (adiabatic). 

Fig. 2.27 Diagram explaining the initial and boundary conditions for the cooling of a plate of thickness 2R, a long cylinder and a sphere, each of radius R...

For the heating or cooling of a plate dealt with in section 2.3.4.3 and written in dimensionless variables according to (2.158) and (2.159), we obtain... 

Fig. 11.3. Microstructures during the slow cooling of a eutectoid steel from the hot working temperature. As a point of detail, when peorlite is cooled to room temperature, the concentration of carbon in the a decreases slightly, following the a/a + FejC boundary. The excess carbon reacts with iron at the or-FejC interfaces to form more FejC. This "plates out" on the surfaces of the existing FejC plates which become very slightly thicker. The composition of Fe3C is independent of temperature, of course.

Figure 2.23. Evolution of the spatial distribution of the degree of crystallinity on cooling of a polycaproamide plate at Tsur = 140°C. Figures on the curves show time from the beginning of the process.

Figure 2.28. Comparison of the results obtained by solving the inverse problem (solid lines) with experimental data (points) for cooling of a polycaproamide plate with constant rate 4 K/min (curve 1) and 16 K/min (curve 2).

Example Calculation, Large Bi Case Cooling of a Perspex Plate in Water... 

Example 2.6 A steel plate with the material properties A = 15.0 W/Km and a = 3.75 10-6 m2/s is 28 = 270mm thick and has a constant initial temperature o At time to the plate is brought into contact with a fluid which has a temperature s < o that is constant with respect to time. The heat transfer coefficient at both surfaces of the plate is a = 75W/m2K. The temperatures during the cooling of the plate are to be numerically determined. Simple initial and boundary conditions were intentionally chosen, so that the accuracy of the finite difference method could be checked when compared to the explicit solution of the case dealt with in section 2.3.3. 

Table 2.9 Temperatures in the cooling of a steel plate, calculated with the explicit difference method.

T. Ochi, S. Nakanishi, M. Kaji, and S. Ishigai, Cooling of a Hot Plate with an Impinging Circular Water Jet, in Multi-Phase Flow and Heat Transfer III. Part A Fundamentals, T. N. Veziroglu and A. E. Bergles (eds.), pp. 671-681, Elsevier, Amsterdam, 1984. 

A number of different methods for the determination of bacteria in market milk have been devised. The oldest and most widely practiced is tire plate method of Koch. This method is carried out by adding a known amount of milk to a medium which solidifies upon cooling on a plate. When this solidified medium is incubated each bacterium or clump of bacteria multiplies and becomes a colony visible to the naked eye. These colonies are counted and constitute the plate count when proper consideration is made for the amount of milk plated. 

Mouldings are usually designed so that the melt flows from thicker into thinner sections, to ensure that the extremities are fed properly. A two-dimensional heat flow calculation illustrates a problem that can arise during solidification. Figure 6.12a shows isotherms for the cooling of a rib, with a heat transfer coefficient of 1000Wm K at the mould interface, calculated by finite element analysis. The thinner rib solidifies first, and an isolated island of melt, cut off from the melt supply, is left at the intersection of the rib and the plate. Contraction of this melt either causes sink marks in... 

In reality, an instantaneous cooling rate cannot be obtained for a sample of finite size. If we consider the case of a plate cooled at a constant rate, in K s , we will still generate a parabolic thermal gradient through the thickness of the plate. If the material has a thermal... 

Robidou, H., H. Auracher, P. Gardin, and M. Lebonche (2002). Controlled cooling of a hot plate with a water jet. Experimental Thermal and Fluid Science 26(2) 123-129. 

The Cooling of Steel Plates In an annealing process—a process wherein materials such as glass and metal are heated to hi temperatures and then cooled slowly to toughen them—thin steel plates k = thermal conductivity = 40 W/m K, p = density = 7800 kg/m and c = specific heat - 400 J/kg IQ are heated to temperatures of900°C and then cooled in an enviroiunent with temperature of 35°C and a heat transfer coefficient of A = 25 W/m K. Eadi plate has a thickness of = 5 cm. We are interested in determining what die temperature of the plate is after one hour. 

In this secdon, we will discuss logadthmic fimcdons. In order to show the importance of logadthmic fimcdons, we will revisit the cooling of steel plates example, and ask a dififerent quesdon. 

Spinneret Spi-no- ret (1826) n. (1) An extrusion die consisting of a plate with many tiny holes, through which a plastic melt or solution is forced, to make fine fibers and filaments. Early spirmeret holes were round and thus produced fibers of circular cross-section. Today, spinneret holes have many different shapes, even annular ones, to produce fibers of corresponding cross-sections. One purpose is to decrease the fiber-bundle density, giving added warmth, moisture permeability, and enhanced dye receptivity to the textile fabric. An important application of hollow fibers is in artificial kidneys for dialysis. Filaments emerging from the spinneret may be hardened by cooling in air or water, or by chemical action of solutions. (2) A spinneret hole. 

The plate of a power tube resembles a copper cup with the upper-half of a plate contact ring welded to the mouth and cooling fins silver soldered or welded to the outside of the assembly. The lower-half of the anode contact ring is bonded to a base ceramic spacer. At the time of assembly, the two halves of the ring are welded together to form a complete unit, as shown in Fig. 5.34. 

The basic components of a plate distillation column include a feed line, feed tray, rectifying or enriching section, stripping section, downcomer, reflux line, energy-balance system, overhead cooling system, condenser, preheater, reboiler, accumulator, feed tank, product tanks, bottom line, top line, side stream, and an advanced instrument control system. Plate columns hold trays that may be bubble-cap, valve, or sieve. Figure 6-19 shows the basic components of a plate distillation column. 

---