Combined Radiation Convection in Thermally Developing Poiseuille Flow with Scattering

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Abstract
The solution for thermally developing Poiseuille flow with scattering is obtained by using the method of collocation. The results show that scattering tends to decrease radiation component without affecting the convective component at low optical thicknesses. For moderate to high values of optical thicknesses, both the convective and radiation components are reduced. The relative effect of scattering both on convective and radiation Nusselt numbers appears to be unaffected by a change in the surface emissivity. A significant feature of combined radiation-convection in thermally developing flows appears to be that the total Nusselt number increases downstream of position of minimum rather than approaching an asymptotic value as is the case with corresponding pure convection. Another departure in the behavior appears to be the lack of existence of similarity in the temperature profiles, particularly at low values of conduction-radiation parameter.

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