Temperature mean fluid

For some fluids, such as oils, the viscosity is temperature dependent. Here the correction factor pp/is used, where r)p is the viscosity at the mean fluid temperature and is the viscosity at the wall temperature. 

In each case the physical properties of the fluid are measured at the mean film temperature T f, taken as the average of the surface temperature Tw and the mean fluid temperature... 

Estimation of adiabatic increase in the liquid temperature in circular micro-tubes with diameter ranging from 15 to 150 pm, under the experimental conditions reported by Judy et al. (2002), are presented in Table 3.7. The calculations were carried out for water, isopropanol and methanol flows, respectively, at initial temperature Tin = 298 K and v = 8.7 x 10" m /s, 2.5 x 10 m /s, 1.63 x 10 m /s, and Cp = 4,178 J/kgK, 2,606J/kgK, 2,531 J/kgK, respectively. The lower and higher values of AT/Tm correspond to limiting values of micro-channel length and Reynolds numbers. Table 3.7 shows adiabatic heating of liquid in micro-tubes can reach ten degrees the increase in mean fluid temperature (Tin -F Tout)/2 is about 9 °C, 121 °C, 38 °C for the water d = 20 pm), isopropanol d = 20 pm) and methanol d = 30 pm) flows, respectively. 

In a situation such as that described in Fig. 4, there is no difficulty in establishing the value for AT. However, when fluid is flowing through a pipe surrounded by a medium at another temperature, the fluid s temperature changes as it travels down the pipe and, consequently, the temperature difference varies with position along the pipe. In such cases, it can be shown that the correct value of AT to use in eqn. (74) is the logarithmic mean temperature difference, ATy which is given by... 

In addition to simply solving the differential equation, we seek to use the solution to understand and quantify the heat transfer between the fluid and the duct walls. The heat flux q" (W/m2) can be described in terms of a heat-transfer coefficient h (W/m2 K), with the thermal driving potential being the difference between the wall temperature and the mean fluid temperature ... 

Although supercritical extraction (SFE) has been known for some time, it is still a relatively new technique to the analytical chemist. Before developing an SFE method, the chemist must understand the composition of the matrix and the analyte properties. The key instrumental parameters affecting the extraction of analytes from the matrix include fluid density, temperature, and fluid composition. Both the make-up of the matrix and the analytes must be considered when selecting the extraction conditions. Consideration of the extraction parameters must be given with respect to their affect on the analytes of interest and on the compounds present in the matrix that may either coextract with the analytes or inhibit their extraction by physical or chemical means. 

The rate of heat transfer per unit area of heat exchanger (heat flux), q, will be a function of the temperature driving force AT, tube diameter d, the mean fluid flow velocity u, fluid flow properties density p and viscosity p - and fluid thermal properties - specific heat capacity cp and thermal conductivity k. 

The mean fluid temperature (or bulk fluid temperature) across the tube, Tm(z), is given by Tlt,(z)-Tw(z)... 

When viscous dissipation effects are important it is to be expected therefore, that fluid property variations could be accounted for by evaluating these properties at a mean fluid temperature that is given by an equation of the form [9],[12],[15] ... 

Now, in fully developed flow it is usually convenient to utilize the mean fluid temperature, Tmt rather than the center line temperature in defining the Nusselt number. This mean or bulk temperature is given, its explained in Chapter 1, by ... 

Consider fully developed laminar flow fluid through a circular pipe with a uniform wall heat flux. If heat is generated uniformly in the fluid, perhaps as the result of a chemical reaction, at a rate of q per unit volume, determine the value of the Nusselt number based on the difference between the wall temperature and the mean fluid temperature in the pipe. 

Because the mean fluid temperatures in the two flows will be different, the fluid properties in the two flows will be somewhat different. This will, however, be neglected here, i.e., it will be assumed that ... 

Now in duct flow, the Nusselt number is defined in terms of the difference between the wall temperature and the mean fluid temperature, this mean temperature being defined by ... 

The methods presented above are applicable only for conditions in which the heat transferred is a straight-line function of temperature. For systems that do not meet this condition, the total heat-release curve can be treated in sections, each section of which closely approximates the straight-line requirement. A log mean temperature difference can then be calculated for each section. Common examples in which this approach is encountered include (1) total condensers in which the condensate is subcooled after condensation, and (2) vaporizers in which the fluid enters as a subcooled liquid, the liquid is heated to the saturation temperature, the fluid is vaporized, and the vapor is heated and leaves in a superheated state. 

The nomenclature of the equations above is tj and t2 - temperature of fluid 1 and fluid 2 respectively, wj and W2 - mean velocities for hot and cold fluid, pj and p2 - fluid densities, Cpj and Cp2 - fluid sensible heats, d and D - specific diameters of the basic pipe and mantle of the heat exchanger, Uj and U2 - partial heat transfer coefficients around the basic pipe, 5p and Sp - thickness of the basic pipe and the mantle, Xp and Xp - thermal conductivities of the basic pipe and mantle walls, k and kg - total heat transfer coefficients, tg - external temperature of the heat exchanger. 

Then the mean fluid temperature at tlic lube exit becomes... 

Note that lhc mean fluid temperature increases linearly m the flow direction in the case. bf constant surface heat flux, since the surface area increases linearly in the flow direction (Aj is equal to the perimeter, which is constant, times the tube length). ... 

Variation of the tube swface and the mean fluid temperatures along the tube for the case of constant surface heat flux. 

The slope of the mean fluid temperature T , on a T-x diagram can be determined by applying the steady-flow energy balance to a tube slice of thickness dx shown in Fig. 8-12. It gives... 

Note that the arithmetic mean temperature difference AT,j, is simply the average of the temperature differences between the surface and the fluid at the inlet and the exit of the tube. Inherent in this definition is the assumption that the mean fluid temperature varies linearly along the tube, which is hardly ever... 

Tilts relatioh can also be used to determine the mean fluid temperature 7 (.v) at any x by rcplacing — pL by px. 

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