A Temperature Gradients Inside the

Example 3.13.2.A Temperature Gradients inside the Gatalyst Particles in Benzene Hydrogenation... 

Niemyski et al. (31) also synthesized BP using an autoclave furnace under a high pressure of 1.5 Mbar at a temperature of 1200-1300°C. Crystallization occurred with a temperature gradient inside the chamber, and prolongation of the reaction time resulted in the formation of larger crystals. 

The influence of heat losses through the reactor wall have been studied [5,23]. Radial temperature gradients inside the monolith material can often be neglected, because the operation is usually adiabatic. This means that modeling of one single channel is adequate. Any nonuniform flow distribution may be incorporated into a reactor model by integration of the single channel performance over the whole cross section of the reactor. 

The results confirm that TGA experiments are not significantly affected by heat transport phenomena if low initial sample masses as well as the described TGA configuration and experimental procedures are applied. The temperature gradients inside the samples are sufficiently small to allow the fitting of formal kinetic models to the experimental mass loss curves assuming a homogeneous sample temperature. Cellulose samples with initial sample masses of around 5 mg and higher can only be submitted to kinetic analyses under consideration of the enthalpy balance. 

The pellet mass and heat balances are described by second order differential equations of the two point boundary value type. For this case the reaction is neither too fast nor highly exothermic and therefore the concentration and temperature gradients inside the pellet are not very steep. Therefore the orthogonal collocation method with one internal collocation point was found sufficient to transform the differential equation into a set of algebraic equations which were solved numerically using the bisectional method (Rice,... 

Film thidcness S is typically two or three orders of magnitude smaller than the tube diameter it can therefore be found, for flow either inside or outside a tube, from the equation for a flat plate, Eq. (5.77). Since there is a temperature gradient in the film, the properties of the liquid are evaluated at the average film temperature 7., given by Eq. (13.11). For condensation on a vertical surface, for which cos) = 1, Eq. (5.77) becomes... 

The first boundary condition follows from symmetrical reasons. In practice, the effective heat conductivity of the catalyst, Tie, is often so high that the temperature gradients inside the particle are minor. On the other hand, there often emerges a temperature gradient in the fluid film around the catalyst particle, since the thermal conduction of the fluid is limited. The energy balance of the fluid film is reduced to... 

When the resistance to mass and heat transfer inside the catalyst particle is important the rate of reaction is not uniform throughout the particle. The set of Eqs. 11.8.a-l to 11.8.a-4 of Sec. 11.8.a then no longer adequately describes the system. It has to be completed with equations describing the concentration and temperature gradients inside the particle, so that the complete set may be written ... 

When a polymer slab of thickness L is cooled on one side by convection, we need to know if there is a significant temperature gradient inside the plastic... 

This nonuniform dissipation also results in temperature gradients inside the channel. Xuan and Li [10] studied case (1) and Sinton et al. [11] smdied case (2) for a microcapiUary. 

Using two parallel flow streams with different molar concentrations also results in nonuniform Joule heating and hence a temperature gradient in the transverse direction as well as the longitudinal direction. Cetin and Li [12] studied the effect of these two streams on the temperature field inside a microchannel for the potential use of this gradient in cell manipxflation. 

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