Limitations of the lumped model for in-tube laminar forced convection interacting with cross forced convection flows

The short communication addresses forced convection heat transfer of a viscous fluid flowing in a tube with fully developed laminar velocity and uniform entrance temperature that exchanges heat convection with a surrounding fluid. The idea is to implement the lumped model following the footsteps of the potent lumped model within unsteady heat conduction, instead of the differential model. The computed mean bulk temperatures of the viscous fluid expressed by a simple exponential function agrees well with the baseline numerical mean bulk temperatures when the internal fluid is air, water or crude oil and the external fluid is air for small values of the modified Biot numbers and maximum Reynolds numbers are satisfied.