Investigation of conjugated natural convection heat transfer in thick-walled vertical pipes

Conjugate natural convection heat transfer at steady state with internal laminar flow in thick-walled vertical pipes is investigated by considering the wall and axial fluid conduction. The problem is addressed in a vertical and axisymmetric pipe of finite length with a constant external surface temperature boundary condition. Neglecting the viscous dissipation and assuming that all fluid properties are constant except the density in the buoyancy term by the Boussinesq approximation, the problem is solved numerically by the finite difference method and the set of coupled equations; continuity, momentum and energy, are solved simultaneously. For the velocity solution SIMPLE algorithm with a staggered grid system is used and axial and radial velocity and pressure distributions in the pipe are obtained. The energy equations are also simultaneously solved for both the wall and the fluid sides by considering continuity conditions at the interface and the bulk temperature, interfacial heat flux and local Nusselt number distributions are determined. The effects of the dimensionless parameters defining the problem, which are Grashof number, GrL, Prandtl number, Pr, ratio of wall to fluid thermal conductivity, kwf, wall thickness ratio, d' and pipe length to radius ratio, B, on the flow and heat transfer characteristics, are investigated. Solutions were made for different values of these parameters. GrL=105, 106, 107 and 108; Pr=0.7, 4.7, 50 and 100; kwf =1, 10, 100 and 1000; d'=0.02, 0.1 and 0.3; B=16, 24, 32, 40 and 48. The interfacial heat flux reaches high values in regions very close to the entrance, then decreases rapidly and drops to zero in the thermally developed region. As the Grashof and Prandtl numbers increase, the interfacial heat flux values and total heat transfer also increase. Again, for large Grashof and Prandtl numbers, the hydrodynamic and thermal development distances are longer. It is observed that the thermal development distances decrease as the pipe length to radius ratio increases. Again as the pipe length to radius ratio increases, the flow rate and accordingly the interfacial heat flux values decrease.