Wall, thermal resistance

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

The overall heat transfer coefficient U in Eqn. (3) is based on the measured temperature difference between the central axis of the bed and the coolant. It is derived by asymptotic matching of thermal fluxes between the one-dimensional (U) and two-dimensional (kr,eff kw,eff) continuum models of heat transfer. Existing correlations are employed to describe the underlying heat transfer processes with the exception of Eqn. (7), which is a new result for the apparent solid phase conductivity (k g), including the effect of the tube wall. Its derivation is based on an analysis of stagnant bed conductivity data (8, 9), accounting for "central-core" and wall thermal resistances. 

From Eqs. (9) and (11), and neglecting the tube-wall thermal resistance, the expression for the overall heat-transfer coefficient for the bundle is ... 

Heat Transfer on Convection Duct Walls. For this boundary condition, denoted as , the wall temperature is considered to be constant in the axial direction, and the duct has convection with the environment. An external heat transfer coefficient is incorporated to represent this case. The dimensionless Biot number, defined as Bi = heDhlkw, reflects the effect of the wall thermal resistance, induced by external convection. 

The wall thermal resistance is evaluated separately during the hot-gas and cold-gas flow periods, since there is no continuous heat flow from the hot gas to the cold gas in the regenerator. Based on the unit area, it is given by [29]... 

Also calculate the wall thermal resistance R , = 8IA kw. Finally, compute overall thermal conductance UA from Eq. 17.6, knowing the individual convective film resistances, wall thermal resistances, and fouling resistances, if any. 

Note that the wall thermal resistance in Eq. 17.137 is ignored in the first iteration. In the second and subsequent iterations, compute U from... 

This boundary condition allows the analysis of micro-condensers and micro-evaporators with finite wall thermal resistance. It is evident that when Uy, tends to infinity, the T3 boundary condition reduces to the T boundary condition. 

In this case, the wall thermal resistance is considered negligible. This kind of thermal boundary condition can be used, for example, for micro-radiators working in space and manufactured with materials having a large value of thermal conductivity. 

Micro-condensers, micro-evaporators with negligible wall thermal resistance... 

Microchanneis heated electrically by taking into account a finite normal wall thermal resistance and a negligible peripheral wall heat conduction... 

Convective Heat Transfer in Microchanneis, Tabie 2 Nusselt numbers for laminar fully developed flow as a function of the dimensionless wall thermal resistance for the T3 boundary condition... 

Dfl —> 0 and Da— oo, are of importance, corresponding to Neumann (uniform surface flux) and Dirichlet (uniform surface concentration) boundary conditions, respectively. For the heat transfer problem. Equation 8.20 expresses finite wall thermal resistance [39] R aii)> where the same limiting forms are found for R aii —> 00 and R aii 0. The well-known solution [49, 50] to this problem has the following separable form ... 

For the T3 boundary condition the average Nusselt number for fuUy developed laminar flow with negligible external volume forces (fent = 0), axial heat conduction (Pe —> oo), viscous dissipation (Br = 0), flow work (p = 0) and thermal energy sources (Sg = 0) within the fluid is a function of the dimensionless wall thermal resistance / the values of Nut3 as a function of / w are quoted in Tab. 2. When Rw tends to zero the Nusselt number tends to the value taken under T boundary conditions. On the contrary, for Rv, oo the Nusselt number tends to the value of the H boundary condition (48/11). In Tab. 3 the values of Nut3 are tabulated as a function of the dimensionless wall thermal resistance / w and the Peclet number by taking into account the axial conduction in the fluid. 

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