A procedure is described for rapidly estimating the ¯ow-rate and heat transfer for laminar free and mixed convection in inclined ducts. Solutions are given by closed-form expressions, suitable for routine use at spreadsheet level. The ¯ow-rate is obtained by equating the sum of the pressure dierences which drive the ¯ow with that of those opposing it. Among the former, the contribution of free convection is represented by superposing a pressure dierence equal to that due to buoyancy in a static column of ¯uid of the same height as the duct. In the initial development it is assumed that wall friction and heat transfer may be represented by expressions for forced convection, including entrance eects. The procedure is tested against CFD results for a vertical parallel-plate duct with heat ¯ux at one wall only. Despite the severity of the case, agreement is found to be suciently good to validate the method for routine initial design and optimisation studies for most conditions of free and mixed convection. Discrepancies become noticeable only at high Grashof number, where the buoyancy component is high enough to produce substantial asymmetry in the velocity pro®le.