This paper presents a nonlinear, time-domain model of thermoacoustic devices based on cross-sectional averaged equations. Heat transfer perpendicular to the device axis - which lies at the core of thermoacoustic effects - is modeled in a novel and more realistic way. Heat conduction in the solid surfaces surrounding the fluid medium is included. Contrary to the previous versions of this model [Watanabe et al., J. Acoust. Soc. Am. 102, 3484¿3496 (1997)], the present version does not require artificial damping and is numerically robust. The model performance is illustrated on several examples: a prime mover, an externally driven thermoacoustic refrigerator, and a combined prime mover/refrigerator system.