The junction conditions for a magnetohydrodynamic fluid sphere undergoing dissipative gravitational collapse in the form of a radial heat flux with shear are obtained. These conditions extend particular results of earlier treatments. We demonstrate that the pressure is proportional to the magnitude of the heat flux as is the case in shear-free models. However in our case the gravitational potentials must be solutions of the Einstein-Maxwell system of equations. The mass function m(v) is increased by a factor related to the charge Q of the radiating star. Physical quantities relating to the local conservation of momentum and surface redshift are obtained.

In this work we provide a framework for modelling compact stars in which the interior matter distribution obeys a generalised Chaplygin equation of state. The interior geometry of the stellar object is described by a spherically symmetric line element which is simultaneously co-moving and isotropic with the exterior space–time being vacuum. We are able to integrate the Einstein field equations and present closed form solutions which adequately describe compact strange star candidates such as 4U 1538-52, PSR J1614-2230, Vela X-1 and Cen X-3 (Gangopadhyay $\it{et al, Mon. Not. R. Astron. Soc.} \bf{431}$, 3216 (2013)).