Temperature bulk fluid

The equations presented herein do not include any viscosity correction to reflect the difference between the viscosity at the wall temperature and the bulk fluid temperature. This effect is generally negligible, except at low temperatures for organic fluids having viscosities that are strongly temperature dependent. For such conditions, the values tabulated in Table 2 should be appropriately modified. 

K Factor, ratio of temperature difference across retaining waU to overaU mean temperature difference between bulk fluids Dimensionless Dimensionless... 

The definition of the heat-transfer coefficient is arbitrary, depending on whether bulk-fluid temperature, centerline temperature, or some other reference temperature is used for ti or t-. Equation (5-24) is an expression of Newtons law of cooling and incorporates all the complexities involved in the solution of Eq. (5-23). The temperature gradients in both the fluid and the adjacent solid at the fluid-solid interface may also be related to the heat-transfer coefficient ... 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

Dg = Mean or centerline diameter of internal coil helix, mm (ft) hj = heat transfer coefficient on inside surface of jacket = viscosity at bulk fluid temperature, [(N s)/m ][kg/(m sec)] = viscosity at die wall temperature, [(N s)/m ][kg/(m sec)]... 

Djj. The Grashof number Nq, = Dj pgpAto/p" were is equivalent diameter, g is acceleration due to gravity, p is coefficient of volumetric expansion, p is viscosity, p is density, and Atg is the difference between the temperature at the wall and that in the bulk fluid. Nq, must be calculated from fluid properties at the bulk temperature. 

AIq = difference between the temperature at the wall and that in the bulk fluid... 

The bulk fluid temperature at which the fluid properties are obtained should be the average temperature between the fluid inlet and outlet temperatures. The viscosity at the tube wall should be the fluid viscosity at the arithmetic average temperature between the inside fluid bulk temper-... 

When heat flows into or out of a fluid through a containing wall, the wall surface reaches a temperature which differs from that of the bulk of the fluid. The wall s corrosion resistance at this temperature may be significantly different from its resistance at the bulk-fluid temperature. Tubes or tank walls heated by steam or direct flame have failed in service in which similar materials, not so heated, performed acceptably. 

In general, the temperature 0S at the axis is not known, and the heat transfer coefficient is related to the temperature difference between the walls and the bulk fluid. The bulk temperature of the fluid is defined as the ratio of the heat content to the heat capacity of the fluid flowing at any section. Thus the bulk temperature 9S is given by ... 

In fully developed flow, equations 12.102 and 12.117 can be used, but it is preferable to work in terms of the mean velocity of flow and the ordinary pipe Reynolds number Re. Furthermore, the heat transfer coefficient is generally expressed in terms of a driving force equal to the difference between the bulk fluid temperature and the wall temperature. If the fluid is highly turbulent, however, the bulk temperature will be quite close to the temperature 6S at the axis. 

Reynolds number. It should be stressed that the heat transfer coefficient depends on the character of the wall temperature and the bulk fluid temperature variation along the heated tube wall. It is well known that under certain conditions the use of mean wall and fluid temperatures to calculate the heat transfer coefficient may lead to peculiar behavior of the Nusselt number (see Eckert and Weise 1941 Petukhov 1967 Kays and Crawford 1993). The experimental results of Hetsroni et al. (2004) showed that the use of the heat transfer model based on the assumption of constant heat flux, and linear variation of the bulk temperature of the fluid at low Reynolds number, yield an apparent growth of the Nusselt number with an increase in the Reynolds number, as well as underestimation of this number. 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

This section is concerned with the UA xtiT — Text) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then A xt refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T - Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is... 

Diffusivities. Our results for the dlffuslvltles of both systems are summarized In Table I. The pore average transverse dlffuslvlty for the bulk fluid at equilibrium agrees very well with experimental and simulation values for the dlffuslvlty of Argon at the same density and temperature (18.12.5). 

In it the pressure P is found in terms of temperature T and volume per particle v. The interactions enter through two parameters uq, the excluded volume per particle, and a, the binding energy per particle at unity density in a bulk fluid. The equation of state arose as an extension of the ideal gas law,... 

Gt = mass velocity, mass flow per unit area, kg/m2s, fj, = fluid viscosity at the bulk fluid temperature, Ns/m2,... 

Cp = fluid heat capacity p = fluid viscosity at the bulk fluid temperature F] = inside(tube-side)volumetric flowrate do = outside(shell-side)diameter... 

AT = mean temperature difference between the heat transfer surface and the bulk fluid (K)... 

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