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Mathematical models and numerical simulations are used to analyse and predict the behaviour of porous materials under coupled mechanical and thermal loading conditions in poroelastic thermoelastic studies. This field is crucial in understanding and designing systems involving porous media where mechanical and thermal factors are important. For this reason, this work aims to provide a theoretical study of porous elastic materials surrounded by a magnetic field using the dual phase lag (DPL) model of thermoelasticity. The significance of this study lies in its diverse range of applications across several engineering, and geophysical disciplines, encompassing soil mechanics, geomechanics, petroleum engineering, and civil engineering. An investigation was conducted on an indefinitely long, porous, solid circular cylinder subjected to a constant magnetic field to demonstrate the proposed theoretical framework. The outer surface of the cylinder was thermally shocked and maintained free from any stress or traction. To solve the problem, Laplace transforms and their inverse methods are used. Numerical examples of excess pore water pressure, temperature, displacement, induced magnetic field, and thermal stresses are given at different medium sites. Finally, graphical representations were created to depict the results of field variables across different thermal delays and porosity estimates. [ABSTRACT FROM AUTHOR]