Fully developed mixed convection flow in a vertical microtube with time periodic heating boundary condition

Abstract

Purpose The purpose of this paper is to investigate fully developed mixed convection flow in the steady-periodic regime for a Newtonian fluid in a vertical microtube in the presence of velocity slip and temperature jump, which has not been accounted for in the literature. Design/methodology/approach To achieve this objective, the governing equations for the problem are separated into steady and oscillatory components using separation of variable method; this gives a pair of independent boundary value problems. This is then solved along with its boundary conditions and constraint equations using the method of undetermined coefficient. The exact solutions of momentum and energy equations are obtained under the velocity slip and temperature jump conditions. Findings The significant result from the study is that increase in rarefaction parameter as well as fluid–wall interaction parameter decreases the oscillation amplitude of the dimensionless velocity. Furthermore, it was found that the product of dimensionless frequency and Prandtl number initiate a strong convection current inside the microtube. Practical implications Such type of study may be used on the determination of the thermal and tangential momentum accommodation coefficients and be applicable to the designs and fabrications of microheat exchanger. Moreover, it provides the possibility to get a bench mark for numerical solvers with reference to basic flow configuration. Originality/value These solutions generally deserve great attention, since the application of a magnetic field has been found to be effective tool in controlling the convection current. The current work is aimed as an extension of the previous analytical studies to prove some insight into a number of industrial applications, which use similar configurations.