A mathematical model that describes the dynamics of the heat transfer in an inflatable-tunnel solar collector for air heating is proposed and validated. The model is distributed-parameters, one-dimensional and unsteady-state. It considers the thermal inertia of a pebble bed acting as the absorber surface and is constituted by three equations that describe the temperature distributions of the three system components: polyethylene cover, transfer fluid (air) and absorber surface. To solve the governing equations, a novel numerical scheme that differs from the standard method of finite differences in the form of generating the discretization equations is proposed. In this scheme, the dimensionless versions of the equations are reduced to linear canonical forms of first order and then are solved analytically in small spatial domains to produce discretization equations in an explicit form. To validate the quality of the present model, some experimental tests in a 50 m long inflatable-tunnel solar collector were carried out. Results of the model compare favorably with experimental results. (C) 2003 Elsevier Ltd. All rights reserved.