A mathematical model of heat and mass transfer for a fluid flowing in a hollow cylinder with a tubular biofilm is developed. Results in dimensionless form are presented for mass transfer in isothermal laminar and turbulent flow and for heat transfer and combined heat-mass transfer in turbulent flow. For each system, the dominant resistance to the transport of heat and mass is determined. In a typical heat exchanger, the presence of a biofilm is found to decrease heat transfer significantly. For systems of interest, the biofilm thickness is nearly constant over the length of the tube in isothermal turbulent flow. In tubes with combined heat and mass transfer the thickness varies appreciably with the temperature of the fluid.