Numerical and asymptotic solutions of the unsteady mixed convection boundary-layer flow over an expanding/contracting vertical cylinder

Purpose The purpose of this study is to obtain both the numerical and asymptotic solutions of the unsteady mixed convection flow and heat transfer over an expanding or contracting cylinder which is placed vertically. Design/methodology/approach Solutions of the governing ordinary (similarity) differential equations for the fluid flow and temperature field are obtained using the function bvp4c from MATLAB. The problem involves the Prandtl number σ, the mixed convection parameter λ and unsteadiness parameter S that characterize an expanding or contracting cylinder. This solution approach is capable of producing multiple solutions once the necessary assumptions are provided. Findings It is found that solutions exist for all negative values of S, expanding cylinder, and only for small positive values of S, contracting cylinder. Further, more than one solution is observed; numerical computation shows that the critical point of S becomes singular as λ approaching zero. For the case of expanding cylinder, the mixed convection parameter has a significant effect on both the flow and heat transfer characteristics. Asymptotic analysis also shows that when σ is large, dual solutions exist for some values of S and λ. Originality/value The present results are new and original for the study of the unsteady mixed convection flow and heat transfer over an expanding/contracting cylinder where numerical solutions are obtained for representative values of the involved parameters. Asymptotic solutions for large λ and large σ are derived.