Heat transfer of a radial, nanofluid water-graphene oxide hydromagnetic flow between coaxial pipes with a variable radius ratio

The main objective of the present study is to analyze the heat transfer of a water-graphene oxide nanofluid flow between coaxial pipes, analytically. The radius ratio of pipes is variable, and a radial constant magnetic field applies to the pipes. Moreover, the Robin boundary condition is considered on the pipe's walls. As a novelty, the exact solution is utilized to obtain the velocity distribution; further, the energy equation is solved employing the semi-analytical collocation method. The results reveal that the enhancement of nanoparticle volume fraction and radius ratio increases the dimensionless shear stress on pipes walls by 2% and 100%, respectively; consequently, the friction on walls grows. Though, the magnetic parameter has the contrary effect. Furthermore, it is observed the Eckert number augmentation decuples the bulk temperature and the heat transfer. Moreover, when the outer pipe Biot number and radius ratio increase, the bulk temperature and the heat transfer augment more than 90%. However, the magnetic parameter and nanoparticle volume fraction have a contrary effect. Also, as the inner pipe Biot number rises, we do not observe a constant pattern for the dimensionless temperature and heat transfer rate variation.