Heat transfer mixed boundary conditions

Now let us consider the mixing time, t. This will be estimated by an order of magnitude estimate for diffusion to occur across the boundary layer thickness, <5Bl- If we have turbulent natural conditions, it is common to represent the heat transfer in terms of the Nusselt number for a vertical plate of height, , as... 

For known values of the parameters in the kinetic equation for a specific reactive mix, it is easy to calculate the dimensionless factors y and v. Then the flow pattern in the mold filling process is completely determined by the dimensionless Da and Gz Numbers and the boundary conditions. The Damkohler Number characterizes the ratio of the rates of chemical reaction and convective heat transfer and the Graetz Number is a measure of the ratio of the convective heat flux due to a moving liquid to the heat flux due to the conductivity of the liquid. 

Figure 11-8. A schematic representation of the local surface conditions for heat transfer from a solid body with surface temperature T0 to a gas stream when there is a condensed liquid film on the body surface. As explained in the text, this leads to an approximate boundary condition on the surface S of mixed type (11 -98).

Uniform Heat Flux. For laminar flow in a horizontal tube where uniform heat flux is applied at the outer boundary of the tube, the bulk temperature Tb, increases linearly in the axial direction. To maintain the heat flow to the fluid, the wall temperature must remain higher than the fluid temperature, and under these conditions a fully developed natural convection motion becomes established in which velocity and temperature gradients become independent of the axial location. Because the fully developed Nusselt number for laminar pure forced convection is small (Nuf —> 4.36), the buoyancy-induced mixing motion can greatly enhance the heat transfer. 

Physical properties for all flows are inputted. The user must specify certain parameters such as mixing models, kinetic rates, turbulence, and others as required. The CFD model is generally full-scale with complete similitude. The governing differential equations that solve all aspects of mixing, heat transfer, chemistry, turbulence, fluid mechanics, species, and continuity are iterated across the entire model until a converged solution is obtained for all cells and boundary conditions. 

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. 

Whenever flowing streams are joined, heat transfer is governed by mixing. iVIost heat transfer operations, however, are limited by the necessity of maintaining isolation between the flowing streams in these cases, the boundary conditions at the heat transfer surfaces control its flow. Radiation is important where temperatures are sufficiently high to promote incandescence, typically in the combustion of a fuel. Each of these situations will be examined individually. 

At fuel manifold inlets, gaseous species concentrations are specified as equilibrium compositions of the town gas reformate at 650°C. Steam-to-carbon ratio is kept as 3.06 for this particular steady-state analysis. Both fuel and air gas manifold inlet conditions are summarized in Table 9.5. Mixed convective and radiative heat transfer boundary conditions are applied to the side surfaces of the stack to accurately model the heat exchange with the balance of plant components. Top and bottom surfaces, on the other hand, are assigned with... 

As mentioned previously, the driver for undertaking this type of modeling is to optimize the mixing within the melter, to supply temperature boundary conditions to the melter walls for stress simulations, and to explore the relative importance of the different heat transfer mechanisms. 

It is of interest to consider whether impairment of heat transfer would be encountered under the conditions likely to be achieved in a buoyancy-driven flow system of the kind which has been proposed for passively cooling a nuclear reactor containment vessel. In this connection, a further matter needs to be considered. Most of the experimental studies of mixed convection reported to date have been carried out with a thermal boundary condition of uniform wall heat flux. However, in the case of a severe accident in a pressurised water reactor, where steam is released from the core into a steel containment vessel and is condensing on its inside surface, the vessel will take up a uniform temperature. Since the nature of the thermal boundary condition could certainly affect the process of heat transfer to the air, there is a need to consider whether the behaviour with uniform wall temperature will be similar to that with uniform wall heat flux. 

An advanced computer code CONVERT, developed and validated earlier at the University of Manchester for buoyancy-influenced flow in uniformly heated vertical tubes, was used to perform simulations of the present experiments. This code uses a buoyancy influenced, variable property, developing wall shear flow formulation for turbulent flow and heat transfer in a vertical tube in conjunction with the Launder-Sharma low Reynolds number k-8 turbulence model [9], The conditions covered in the simulations ranged from forced flow with negligible influence of buoyancy to buoyancy-dominated mixed convection. In each case, simulations were made for thermal boundary conditions of both uniform wall temperature and uniform heat flux. These show that the computational formulation used does enable observed heat transfer behaviour in the mixed convection region to be reproduced. Buoyancy-induced impairment of... 

JACKSON, J.D., LI, J. and AN, P., The Influence of thermal boundary conditions on mixed convection heat transfer in vertical tubes , Invited Lecture, Proceedings of the 3" Baltic Heat Transfer Conference, Sopot, Poland, Progress in Engineering Heat... 

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