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In this present study, the impacts of magnetic field and thermal radiation on squeezing flow and heat transfer of third grade nanofluid between two disks embedded in a porous medium with temperature jump boundary conditions is analyzed using differential transformation method. The results of the approximate analytical solutions are verified using a fifth-order Runge-Kutta Fehlberg method (Cash-Karp Runge-Kutta) coupled with shooting method. From the analysis, the results of the two methods show excellent agreements. Also, the parametric studies using the approximate analytical solutions show that for a suction parameter greater than zero, the radial velocity of the lower disc increases while that of the upper disc decreases as a result of a corresponding increase in the viscosity of the fluid from the lower squeezing disc to the upper disc. For an increasing magnetic field parameter, the radial velocity of the lower disc decreases while that of the upper disc increases. As the third grade fluid parameter increases, there is a reduction in the fluid viscosity thereby increasing resistance between the fluid molecules. Also, it is found that as the radiation parameter increases, rate of heat transfer to the third grade fluid increases. There is a recorded decrease in the fluid temperature profile as the Prandtl number increases due to decrease in the thermal diffusivity of the third grade fluid. The agreement of the results of the present study and the experimental work shows the validation of the models used in this work to study the flow behaviour of the fluid. It is envisaged that the present work will increase the understanding of the flow behaviour of third grade nanofluid and heat transfer processes as evident in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.