Temperature mixing cup

The dependence of the measured rise in fluid mixed-cup temperature on Reynolds number is illustrated in Fig. 3.12. The difference between outlet and inlet temperatures increases monotonically with increasing Re at laminar and turbulent flows. Under conditions of the given experiments, the temperature rise due to energy dissipation is very significant AT = 15—35 K at L/ i = 900—1,470 and Re = 2,500. The data on rising temperature in long micro-tubes can be presented in the form of the dependence of dimensionless viscous heating parameter Re/[Ec(L/(i)] on Reynolds number (Fig. 3.13). 

The heat balance for the slit geometry in terms of gas mixing-cup temperature... 

The bulk temperature is, of course, equal to the temperature that would be attained if the fluid at the particular section of the duct being considered was discharged into a container and, without any heat transfer occurring, was mixed until a uniform temperature was obtained. For this reason it is sometimes referred to as the mixing cup temperature . 

Unless specifically indicated, all fluid properties are evaluated at the mixing-cup temperature of the fluid ... 

In any case, the fluid temperature at the wall is different from that at the centerline of the flow. When the fluid is being heated, the wall temperature is higher than the centerline temperature, and vice versa for cooling the fluid. The bulk or mixing cup temperature of the fluid, T, is the temperature that would be measured if the total flow through a cross section were collected over a given period and perfectly mixed. The bulk temperature is intermediate between the wall temperature and the centerline temperature (but usually close to the latter) and is the temperature that... 

This general analysis of the chlorine-toluene system based upon first order reacticxi was developed in parallel with a series of experimental measurements (9), in which chlorine was absorbed in toluene in a laminar jet. This absorption device provides remarkable control of surface area and with a flat velocity profile the penetration time is reasonably well defined so that the penetration theory can be directly applied without any uncertainty concerning the complications of convective transport. Experimental mixing cup temperatures for Cl -toluene ranged from i C to 6°C. These can be interpreted as the amount of heat accumulated per unit of Jet surface as the jet plunges into the receiver via the equation... 

A number of experiments have been performed absorbing sulphur trioxide into a laminar Jet of liquid toluene (16). In these experiments, an estimate of the temperature achieved on the surface of the jet on entry into the Jet receiver can be obtained by interpreting the mixing cup temperature of the Jet as it becomes fully mixed in the receiver take-off line. The form of the heat transfer profile is as shown in Fig. 16. The depth of heat penetration into the Jet is assumed to be given by... 

The temperature Tq appearing here is the C-space mean temperature, and not the mixed-cup temperature. 

A significant consideration is the thermal-hydraulic criterion for limiting power for the FI phase of the accident. Initially, a "no bulk boiling" criterion was assumed to apply to the individual annular coolant channels within the fuel assemblies. Locally, subchannels could produce steam prior to the channel mixing cup temperature reaching the saturation temperature. 

All channel elements had an emissivity Sj = e = 0.6, j = 1, N, while examples of the calculated factors Fk-j are presented in Fig. 8.2 for two channel wall elements and the inlet channel enclosure. The inlet and outlet planes of the enclosure had emissivities equal to those of the channel wall surfaces, jj,j = squt — — 0.6, while the inlet and outlet exchange temperatures were set equal to the inlet mixture and outlet mixing cup temperatures, respectively. This arrangement mimics the tight space in microreactor systems, wherein the entry and outlet sections cannot usually be of large enough size to allow for a black body enclosure treatment. The outer horizontal wall of the microreactor channel was treated as adiabatic (see Fig. 8.1) nevertheless, the reactor itself was non-adiabatic due to radiation heat losses, primarily from the channel wall inner surface as well as from the vertical front solid wall face towards the colder inlet enclosure. 

First let us give some further consideration to the bulk-temperature concept which is important in all heat-transfer problems involving flow inside closed channels. In Chap. 5 we noted that the bulk temperature represents energy average or mixing cup conditions. Thus, for the tube flow depicted in Fig. 6-1 the total energy added can be expressed in terms of a bulk-temperature difference by... 

Follow this procedure Mix cup of water with 1 teaspoonful of sucrose. Mix cup of water with 1 teaspoonful of sodium chloride. Mix cup of warm water with 1 teaspoonful of copper sulfate crystals. Note the color of the third solution. Now pour all three solutions into the pyrex flask. Arrange the apparatus as the diagram shows. You will have to bend the glass tubing in two places. Put some ice cubes into the pot or bowl and add some water. This will keep the temperature at a more constant level. Then put the pint jar into the bowl. Place the alcohol burner under the flask, and bring the mixture to a slow boil. 

The fact that T varies with radial position causes a dilemma. If T varies in the radial direction, so must Us, and the assumption of a uniform velocity profile is violated. However, the radial variation in density depends on the ratio of wall and centerline temperatures, T si z)/T 0, z), and will typically be reasonably small. A suggested approximation is to use the mixing-cup average temperature in Equation... 

The most useful parameters for heat transfer are the fluid bulk mean temperature and the heat transfer coefficient. The fluid bulk mean temperature Tm, also known as the mixing cup or flow average temperature, is defined as... 

On mixing the temperature rose to 27.90 °C. Determine the enthalpy of neutralisation and state whether the reaction is exothermic or endothermic. You may assume that the polystyrene cup has a negligible heat capacity, the solution has a density of 1.00 g cm" and that the final solution has a specific heat capacity of 4.18 J g °C. ... 

Lev que s problem was extracted from the rescaled mass balance in Equation 8.28. As can be seen, this equation is the basis of a perturbation problem and can be decomposed into several subproblems of order 0(5 ). The concentration profile, the flux at the wall, and consequently the mixing-cup concentration (or conversion) can all be written as perturbation series on powers of the dimensionless boundary layer thickness. This series is often called as the extended Leveque solution or Lev jue s series. Worsoe-Schmidt [71] and Newman [72] presented several terms of these series for Dirichlet and Neumann boundary conditions. Gottifredi and Flores [73] and Shih and Tsou [84] considered the same problem for heat transfer in non-Newtonian fluid flow with constant wall temperature boundary condition. Lopes et al. [40] presented approximations to the leading-order problem for all values of Da and calculated higher-order corrections for large and small values of this parameter. 

In steady-state and negligible axial diffusion in the monolith channel, the governing equations can be written in terms of four dependent variables, namely, the mixing-cup and surface concentrations ((c) and Cj ,y) and the equivalent quantities for temperature ((T) and T urj). The mixing-cup concentration is given by Equation 8.22, which can be defined similarly for fluid temperature as... 

In order to obtain the (mixing-cup and surface) concentration and temperature profiles, the solution of Equations 8.52 and 8.55 requires the calculation of the dimensionless transfer coefficients Sh and Nw, which are in general functions of the Graetz parameters and of the Damkohler number. Correlations for these dimensionless numbers are available in the literature (e.g., Shah and London [39]), for several conditions regarding the degree of profile development, degree of hydrodynamic flow development, and boundary condition at the wall. These features are briefly discussed in the following. 

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