Temperature gradient radial

A technique for calculating radial temperature gradients in a packed bed is given by Smith Chemical Engineering Kinetics, McGraw-HiU, New York, 1956). 

An important effect in the design of a tubular flow reactor is the development of a radial temperature gradient in a highly exothermic reaction with wall cooling. The temperatures near the tube axis are... 

Airway surfaces, like skin, are continually exposed to the ambient environment. In contrast to skin submucosal vessels, however, w hich shed excess heat by vasodilating when heated and conserve heat by vasoconstricting when chilled, it is unclear how the airway vasculature responds to temperature extremes. Inspiring cold air poses two challenges to conducting airway tissues the risk of tissue injury should inadequate heat reach the airway surface and excessive body heat loss due to increasing the radial temperature gradient. Vasodilation would protect airway tissue but increase heat loss, while vasoconstriction would produce the opposite effect. 

A steady-state heat balance for a plug flow reactor with no radial temperature gradients is given by ... 

The derivation was based on two assumptions. First, we assumed a linear radial temperature gradient within the solution, Second, we computed "T " at the radius at which there were equal volumes of solutions on either side of it. 

The temperature with large columns may not be homogenous. A mathematical model of the effect of a radial temperature gradient has been developed and validated on octadecyl-packed columns of 11-15 cm diameter... 

Binary liquid metal systems were used in liquid-metal magnetohydrodynamic generators and liquid-metal fuel cell systems for which boiling heat transfer characteristics were required. Mori et al. (1970) studied a binary liquid metal of mercury and the eutectic alloy of bismuth and lead flowing through a vertical, alloy steel tube of 2.54-cm (1-in) O.D., which was heated by radiation in an electric furnace. In their experiments, both axial and radial temperature distributions were measured, and the liquid temperature continued to increase when boiling occurred. A radial temperature gradient also existed even away from the thin layer next to the... 

There may be radial temperature gradients in the reactor that arise from the interaction between the energy released by reaction, heat transfer through the walls of the tube, and convective transport of energy. This factor is the greatest potential source of disparities between the predictions of the model and what is observed for real systems. The deviations are most significant in nonisothermal packed bed reactors. 

Apply the conservation of energy, Equation (3.40). Since the control volume is fixed the pressure work term does not apply. The shear work (v x shear force) is zero because (a) the radius of the control volume was selected so that the velocity and its gradient are zero on the cylindrical face and (b) at the base faces, the velocity is normal to any shear surface force. Similarly, no heat is conducted at the cylindrical surface because the radial temperature gradient is zero, and conduction is ignored at the bases since we assume the axial temperature gradients are small. However, heat is lost by radiation as... 

The reactor shown in Figure E 14.5a, has no radial temperature gradients because its walls and substrate are heated and slow reaction rates imply small heats of reaction. 

Packed capillaries with a larger inner diameter may be useful in preparative separations. These will find an application in proteome research as a part of multidimensional separation systems that will replace 2-D gel electrophoresis. The preparative CEC will require solving of the problems related to heat dissipation since the radial temperature gradient negatively affects the separations, and sample injection. The fabrication of sintered frits in larger bore capillaries is also very difficult. However, in situ polymerized monolithic frits can be fabricated in capillaries of virtually any diameter [190]. 

A thick-walled kettle of mass temperature T, and specific heat Cj, is filled with a perfectly mixed process liquid of mass M, temperature T, and specific heat C. A heating fluid at temperature Tj is circulated in a jacket around the kettle wall. The heat transfer coeffldent between the process fluid and the metal wall is U and between the metal outside wall and the heating fluid is Inside and outside heat transfer areas A are approximately the same. Neglecting any radial temperature gradients through the metal wall, show that the transfer function between T and T, is two first-order lags. 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

---