Heat transfer formulation

Roemer, R.B., Conditions for equivalency of countercurrent vessel heat transfer formulations. /. Biomech. Eng., 1999,121 514-520. 

SCDAP/RELAP5/M0D3 uses a one-dimensional, two-fluid, nonequilibrium, six-equation hydrodynamic model with a simplified capability to treat multidimensional flows. This model provides continuity, momentum, and energy equations for both the liquid and vapor phases within a control volume. The energy equation contains source terms that couple the hydrodynamic model to the heat structure conduction model by a convective heat transfer formulation. The code contains special process models for critical flow, abrupt area changes, branching, crossflow junctions, pumps, accumulators, valves, core neutronics, and control systems. A flooding model can be applied at vertical junctions. 

Aqueous solutions of propylene glycol display excellent antifree2e properties and are therefore valuable as low temperature heat-transfer fluids. For apphcations involving indirect food contact, heat-transfer fluids formulated with the USP grade product are preferred, since there could be inadvertent contact with a food product. These fluids are commonly used in the brewing and dairy industries as well as in refrigerated display cases in retail grocery stores. 

The mathematical formulation of forced convection heat transfer from fuel rods is well described in the Hterature. Notable are the Dittus-Boelter correlation (26,31) for pressurized water reactors (PWRs) and gases, and the Jens-Lottes correlation (32) for boiling water reactors (BWRs) in nucleate boiling. 

Sodium nitrate is also used in formulations of heat-transfer salts for he at-treatment baths for alloys and metals, mbber vulcanization, and petrochemical industries. A mixture of sodium nitrate and potassium nitrate is used to capture solar energy (qv) to transform it into electrical energy. The potential of sodium nitrate in the field of solar salts depends on the commercial development of this process. Other uses of sodium nitrate include water (qv) treatment, ice melting, adhesives (qv), cleaning compounds, pyrotechnics, curing bacons and meats (see Food additives), organics nitration, certain types of pharmaceutical production, refining of some alloys, recovery of lead, and production of uranium. 

Heat Exchangers Since most cryogens, with the exception of helium 11 behave as classical fluids, weU-estabhshed principles of mechanics and thermodynamics at ambient temperature also apply for ctyogens. Thus, similar conventional heat transfer correlations have been formulated for simple low-temperature heat exchangers. These correlations are described in terms of well-known dimensionless quantities such as the Nusselt, Reynolds, Prandtl, and Grashof numbers. 

Stoved phenolics have outstanding acid resistance (up to 200 C in dry conditions and up to 100°C in wet conditions), except to strong oxidizing acids. They are unsuitable for use with alkaline solutions above pH 10, wet chlorine or hypochlorite solutions. Phenolics/silicon formulations can be used for steam up to 180°C without a significant effect on heat transfer rates. 

The preceding discussion has attempted to formulate the situation for laminar boundary layer flow as accurately as possible and to obtain precise correlation between the heat transfer and mass transfer factors. 

In low-hardness FW hardness boilers, where very clean waterside surfaces are needed to maximize heat transfer. Here the formulation may be essentially a straight chelant with minimal additional ingredients, or it may be a balanced chelant-polymer program. 

The final physical properties of thermoset polymers depend primarily on the network structure that is developed during cure. Development of improved thermosets has been hampered by the lack of quantitative relationships between polymer variables and final physical properties. The development of a mathematical relationship between formulation and final cure properties is a formidable task requiring detailed characterization of the polymer components, an understanding of the cure chemistry and a model of the cure kinetics, determination of cure process variables (air temperature, heat transfer etc.), a relationship between cure chemistry and network structure, and the existence of a network structure parameter that correlates with physical properties. The lack of availability of easy-to-use network structure models which are applicable to the complex crosslinking systems typical of "real-world" thermosets makes it difficult to develop such correlations. 

This paper will discuss the formulation of the simulator for the filament winding process which describes the temperature and extent of cure in a cross-section of a composite part. The model consists of two parts the kinetic model to predict the curing kinetics of the polymeric system and the heat transfer model which incorporates the kinetic model. A Galerkin finite element code was written to solve the specially and time dependent system. The program was implemented on a microcomputer to minimize computer costs. 

Zhang, H., Zheng, L. L, Prasad, V., Hou, T. Y., A curvilinear level set formulation for highly deformable free surface problems with application to solidification, Numer. Heat Transfer 34 (1998) 1-20. 

Here a steady-state formulation of heat transfer is considered (Pollard, 1978). A hot fluid flows with linear velocity v, through a tube of length L, and diameter D, such that heat is lost via the tube wall to the surrounding atmosphere. It is required to find the steady-state temperature profile along the tube length. 

A boiling heat transfer model incorporating nucleate boiling, natural convection, and microlayer evaporation was formulated as... 

To predict the heat transfer effects, the engineer must have an adequate quantitative description of heat transfer between the tube wall and the fluid phases, heat transfer between the tube wall and the fluid phases, heat transfer between the two phases, the rate of phase change within the system, and the rate of heat transfer resulting from phase change. Unfortunately, present design procedures only provide estimates of the system performance. Many procedures have not been formulated in a systematic manner, and therefore it is difficult to pinpoint areas where the present understanding of the design process is weakest. 

Two-phase mass transfer and heat transfer without phase change are analogous, and the results of mass-transfer studies can be used to help clarify the heat-transfer problems. Cichy et al. (C5) have formulated basic design equations for isothermal gas-liquid tubular reactors. The authors arranged the common visually defined flow patterns into five basic flow regimes, each... 

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