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Effects of viscous dissipation on combined free and forced convection through vertical ducts and passages Rokerya, M. Shafi

Abstract

The effects of viscous dissipation on the flow phenomena and heat transfer rate for fully developed laminar flow through vertical ducts and passages has been analysed under the condition of combined free and forced convection. The fluid properties are considered to be constant except for the variation of density in the buoyancy term of the momentum equation. The thermal boundary condition of uniform heat flux per unit length in the flow direction has been considered. The investigation is carried out for two geometries; (a) Circular ducts and (b) Concentric annuli. The governing momentum and non-linear energy equations are solved for the circular duct by three methods; (i) Power Series Method (ii) Galerkin's Method and (iii) Numerical Integration Method. The solutions for the concentric annuli are obtained by Numerical Integration Method. Results for the velocity and temperature distribution in the flow field are obtained, and information of engineering interest like Nusselt numbers have been evaluated. For combined free and forced convection, the momentum and energy equations are coupled, and hence viscous dissipation affects both the velocity and temperature fields. The effect of viscous dissipation on the velocity field is to reduce the flow velocity near the heated wall(s) and thus it counteracts the effect of free convection on the velocity field for the present study of heating in upflow. The effect of viscous dissipation on the temperature field is to act as a heat source in the fluid and reduce the temperature differences in the system. Viscous dissipation opposes the externally impressed heating and reduces the heat transfer rate when the surface transfers heat to the fluid. Consequently, lower Nusselt number values are obtained when viscous dissipation is taken into consideration. The quantitative effect of viscous dissipation on Nusselt number is found to be small for the case of circular ducts. However, for flow through annular passages and for the corresponding values of the same parameters, the effect of viscous dissipation on the heat transfer rate may not be ignored.

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