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The three dimensional mixed convection heat transfer in a electrically heated horizontal pipe conjugated to a thermal conduction through the entire solid thickness is investigated by taking into account the thermal dependence of the physical properties of the fluid and the outer heat losses. The model equations of continuity, momentum and energy are numerically solved by the finite volume method. The pipe thickness, the Prandtl and the Reynolds numbers are fixed while the Grashof number is varied from 104to107. The results obtained show that the dynamic and thermal fields for mixed convection are qualitatively and quantitatively different from those of forced convection, and the local Nusselt number at the interface solid-fluid is not uniform: it has considerable axial and azimuthally variations. The effect of physical variables of the fluid depending on temperature is significant, which justifies its inclusion. The heat transfer is quantified by the local and average Nusselt numbers. We found that the average Nusselt number of solid-fluid interface of the duct increases with the increase of Grashof number. We have equally found out that the heat transfer is improved thanks to the consideration of the thermo dependence of the physical properties. We have tried modelling the average Nusselt number as a function of Richardson number. With the parameters used, the heat transfer is quantified by the correlation: NuA=12.0753 Ri0.15

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In this work, we numerically study the three-dimensional mixed convection heat transfer in a horizontal pipe equipped by longitudinal and transversal attached fins on its internal surface for the solar application such as the water or air heating with solar panel. The pipe and fins are heated by an electrical intensity passing through their small thickness. The longitudinal fins studied number is: 2 vertical, 4 and 8 fins, while the number of transversal fins is 8 fins. The considered heights fin are H=0.12 cm and H=0.18 cm. The convection in the fluid domain is conjugated to thermal conduction in the pipe and fins solid thickness. The physical properties of the fluid are thermal dependant. The heat losses from the external pipe surface to the surrounding ambient are considered. The model equations of continuity, momenta and energy are numerically solved by a finite volume method with a second order spatiotemporal discretization. As expected for the longitudinal fins, the axial Nusselt number increase with increasing of number and height of fins. For Gr= 5.1 10 5 , the average Nusselt number without fins is equal to 13.144. The introduce of longitudinal fins gives an average Nusselt number equal to 16.83, 22.523 and 32.066 for 2 vertical, 4 and 8 fins respectively. The participation of fins located in the lower part of the tube on the improvement of heat transfer is higher than the participation of the upper fins. On the other hand, the longitudinal fins participate directly on increase of the heat transfer; this is justified by the large local Nusselt number along the interface of the fins. This participation is moderate in the case of transverse fins, these latter are used to mix the fluid for increased the local Nusselt number to the interface in the cylindrical axial sections following the transversal fins.