Heat Transfer by Thermal Radiation and Laminar Forced Convection to an Absorbing Fluid in the Entry Region of a Pipe

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Abstract
The heat transferred to an absorbing fluid by coupled thermal radiation and laminar forced convection is computed for the entrance region of a tube with circular cross section. The tube wall is black and isothermal and the fluid enters with either a fully developed (parabolic) or uniform axial velocity distribution. Both gray and approximately nongray absorption are considered with the nongray absorption specified by the “box model” which approximates the spectral absorption of a vibration-rotation band in a molecular gas by an absorption coefficient which is a constant within an effective bandwidth and zero elsewhere. The box model is applied to carbon monoxide and to carbon dioxide and the calculations additionally include the effects of variable transport properties and variable density. It is shown that for the range of parameters considered in this paper the effect of the absorbed radiation is to increase the heat transfer near the entrance by as much as a factor of four and to decrease the thermal entry length by a factor of ten. The effects of radiation are shown to be more important when the fluid is heated than when it is cooled. By comparing the solutions for a gray fluid with constant properties with those using the box model of the absorption it is demonstrated that the gray approximation is not quantitatively accurate. Approximate solutions are investigated and it is shown that when the radiation-convection interaction is weak the radiation heat flux can be computed approximately by ignoring the interaction and using the known forced convection temperature solution. When the interaction is intense, both the coupling of the radiation and convection and also the spectral absorption must be accounted for in calculating the heat transfer. The box model is shown to be an acceptable method for specifying the approximate spectral absorption coefficient in nonisothermal gases.

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