A study of forced-convection laminar flows in pipes subjected to asymmetric external is presented: the case of a fluid entering a duct subjected to uniform temperature on the upper part of its surface, that breaks the symmetry of the problem and means that 3D simulation is necessary. This configuration is typical of current solar thermal collectors among other industrial devices. The physic-mathematical model partly follows the conditions stablished in the Conjugate Extended Graetz Problem, assuming axial-radial heat conduction in the fluid and the pipe wall. 3D cylindrical coordinates are used due to the problem thermal asymmetry. Stationary process and constant properties of the liquid and materials have been considered. The governing equations are discretized following a finite-difference scheme. Network Simulation Method is used as a numerical tool and, consequently, a discretized network model is built in the form of an electric circuit, whose behavior is formally equivalent to the thermohydraulic process, and which yields accurate solutions to the problem. Based on this scheme, an open software platform called HEATT® has been developed and is now publicly available on the Internet as a service. The platform allows the free online calculation of laminar forced convection flows inside pipes under complex thermal conditions. In this work, three fluids of very different nature and properties have been studied: water, a generic thermal oil, and an ionic liquid. The results are presented in the form of 3D graphs of fluid temperature in the transverse plane and longitudinal fluid temperature curves. The temperature maps of the cross sections show a large irregularity in their temperatures, indicating that the assumption of a uniform temperature is far from reality. It also follows that the heat transfer process requires a large distance for the fluid to reach a homogeneous temperature throughout its flow.