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

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.

Thermal radiation and laminar forced convection in a gas pipe flow

“…Finally, the results of this work have been compared with the results of other investigators, such as [3,4], wherein more accurate expressions for the radiative heat flux are adopted.…”

“…Einstein [2] reported only the total heat transfer to the gas in a tube having a length of five diameters via the method of zones. Pearce and Emery [3] considered the flow of a gas with parabolic or uniform axial velocity distributions. They solved the descriptive conservation equations employing a numerical scheme.…”

“…Using finite-difference techniques, these authors examined the energy equation with two-dimensional radiative transfer allowing for a propagation upstream from the entrance of the heating section. In [3,4], it was necessary to evolve an iterative solution procedure in which the integral term and the differential terms of the energy equation are solved consecutively and the calculation process is continued until convergence is achieved. Campo et al [5] adopting a four-flux model for the intensity of radiation solved the conjugate problem of [4] via an equivalent system of partial differential equations utilizing the control volume approach.…”

A Conservative Adaptive-Mesh Algorithm for Unsteady, Combined-Mode Heat Transfer Using the Discrete Ordinates Method

“…The third example is an axisymmetric computation of simultaneously developing laminar flow in the entry region of a pipe (see [23].…”

“…The differences may be due to the fact that Pearce and Emery make two approximations which we do not make. Specifically, in [23] the wall is considered to be an infinite tube at T = T w , and axial temperature variations are neglected in the computation of "'V . qrad.…”