Discrete heat sources

For the example of methane steam reforming, Eq. (8) yields an acceleration factor of 4. Accordingly, the axial displacement of the reaction zone is a multiple of the axial displacement of thermal fronts. The difference of the axial displacement between the reaction front and the thermal front determines the axial profile of heat demand during the subsequent exothermic semicycle. Efficient heat recovery requires equal heat capacities of the process streams during both semicycles. The initial state can be restored by discrete heat sources distributed at equal distances along the catalytic part of the reactor. Each point source initiates a thermal wave that covers the distance to the next heating point (Fig. 1.13, right). This concept features... 

Kim, S.H., and Anand, N.K., Turbulent Heat Transfer Between a Series of Parallel Plates with Surface-Mounted Discrete Heat Sources , J. Heat Transfer, Vol. 116, pp. 577-587, 1994. 

Choi, C.Y and Ortega, A., Mixed Convection in an Inclined Channel with a Discrete Heat Source , Int. J. Heat and Mass Transfer, Vol. 36, pp. 3119-3134, 1993. 

B. R. Babin and G. P. Peterson, Experimental Investigation of a Flexible Bellows Heat Pipe for Cooling Discrete Heat Sources, ASME Journal of Heat Transfer (112/3) pp. 602-607,1990. 

Cui, C., Huang, X.Y., Liu, C.Y., 2000. Forced convection in a porous channel with discrete heat sources. ASME J. Heat Transf. 123, 404-407. 

The essential point of a heat flow network model is the division of the structure of the collector into discrete parts with temperatures that can approximately be characterized by a single value. In the network model the discrete parts are represented by nodes. The heat capacities and heat sources and the so-called temperature sources modeling the boundary condition reference temperatures are connected to the nodes. In this way the ambient air is also represented in the network by a node. The nodes are connected to a network by heat transfer resistances characterizing the thermal interactions among the discrete parts. 

The subsequent simulations exclusively refer to the caloric materials data of Section 3.1 as well as to geometry, discretization and side-/initial conditions of Section 2.5. In particular, the heat source macro Lasim provided by ANSYS is applied, cf. Figure 6 (right), by using the following source geometry data ... 

For a typical flowsheet, such as the DME (dimethyl ether) PFD in Figure B.1.1 i Appendix B), there are many decision variables. The temperature and pressure of each unit can be varied. The size of each piece of equipment involves decision variables (usually several per unit). The reflux in tower T-201 and the purity of the distillate fromT-202 are decision variables. There are many more. Clearly, the simultaneous optimization of all of these decision variables is a difficult problem However, some subproblems are relatively easy. If Stream 4 (the exit from the methanol preheater) must be at 154°C, for example, the choice of which heat source to use (Ips, mps, or hps) is easy. There is only a sin e decision variable, there are only three discrete choices, and the choice has no direct impact on the rest of the process. The problem becomes more difficult if the temperature of Stream 4 is not constrained. 

Radiative flux, radiative flux on fe-th discrete surface element, heat source term Universal gas constant Channel radius... 

The radiative source term is a discretized formulation of the net radiant absorption for each volume zone which may be incorporated as a source term into numerical approximations for the generalized energy equation. As such, it permits formulation of energy balances on each zone that may include conductive and convective heat transfer. For K—> 0, GS —> 0, and GG —> 0 leading to S —> On. When K 0 and S = 0N, the gas is said to be in a state of radiative equilibrium. In the notation usually associated with the discrete ordinate (DO) and finite volume (FV) methods, see Modest (op. cit., Chap. 16), one would write S /V, = K[G - 4- g] = Here H. = G/4 is the average flux... 

The radiative source term is a discretized formulation of the net radiant absorption for each volume zone which may be incorporated as a source term into numerical approximations for the generalized energy equation. As such, it permits formulation of energy balances on each zone that may include conductive and convective heat transfer. Eor K—> 0, GS —> 0, and GG —> 0 leading to S —> On. When and... 

---