with X-ray observations and cluster theory of spherical shock accretion and cooling. We use the NFW parametrization [@Navarro:1997] for the total mass distribution and assume hydrostatic equilibrium. We outline our model with reference to pointed SZ observations with the Cosmic Background Imager 2 experiment (CBI2) located at the Chajnantor observatory in the Atacama Desert, Chile. This was an interferometer operating at 26–36GHz, with 10$\times$1GHz channels, and thirteen 1.4m antennas [@Padin:2002 Taylor et al. in prep.]. CBI2 has a 28arcmin field of view and 6arcmin resolution so that at moderate redshifts ($z \sim 0.3$) it can observe out to the largest radii of galaxy clusters. In future work we will present the application of the procedure outlined here to observations of a number of massive galaxy clusters with CBI2.

We adopt a $\Lambda$CDM cosmology with $\Omega_\rmn{M} = 0.3$, $\Omega_\lambda = 0.7$ and $H_0 = 70$kms$^{-1}$Mpc$^{-1}$ throughout this paper unless otherwise stated.

Modelling the Intra-Cluster Medium {#modelling_the_ICM}
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Current Models of the intra-cluster medium
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In the past most of the joint analysis of SZ and X-ray data from observations of galaxy clusters made use of the isothermal $\beta$ model prescription for modelling the ICM [@Cavaliere:1976; @Cavaliere:1978]. This model is typically used 