Analysis of laminar dissipative flow and heat transfer in a porous saturated circular tube with constant wall heat flux

A theoretical study of the thermal development of forced convection was performed using a circular tube filled with a saturated porous medium, with constant wall heat flux, and with the effect of viscous dissipation. The solution was obtained using the method of separation of variables. The Sturm–Liouville system was solved for the eigenvalues. Ordinary differential equations for the eigenfunctions were solved numerically by the fourth-order Runge–Kutta method. Results show that, in the presence of the viscous dissipation, both the level and distribution of temperature are altered remarkably, even for small values of the Brinkman number, Br, which is the ratio of heat generation caused by viscous dissipation to the value of heat flux at the wall. The value of the local Nusselt number, Nu, is demonstrably independent of Br, unlike the situation in which the wall temperature remains constant.