Abstract
This investigation deals with the study of heat transfer analysis of fractional Maxwell fluid in a vertical circular cylinder which is initially at rest. Semi-analytical elucidations for velocity as well as temperature fields have been established by using a hybrid technique which has less time cost and mathematical calculations as compared to other techniques existing in the literature. This problem is also solved exactly with the help of integral transform technique which involves Laplace along with finite Hankel transforms Exact solutions that satisfy all prescribed initial and boundary conditions have been particularized to get the similar solutions for Newtonian and ordinary Maxwell fluids. Impact of distinct physical parameters for example fractional parameter, Prandtl number, Grashof number on fluid function and heat transfer is illustrated through graphical and tabular discussion in the end. Moreover, the fractional Maxwell model helps us to choose the non-integer parameter for the validation of results between theoretical and experimental findings.