Unsteady thermal convection of a heat-generating liquid having variable viscosity in a vertical cooling cylinder

Purpose The purpose of this study is to numerically examine the time-dependent energy transport during the natural convection of a heat-generating fluid with temperature-dependent viscosity in a vertical cooling cylinder. Design/methodology/approach The thermo-gravitational convection has been assumed to be laminar and two-dimensional, and governed by a set of dimensionless equations based on the Boussinesq approach with non-primitive functions, including vorticity and stream function. The viscosity of the fluid has been defined as a temperature function with the exponential law. The inner volumetric heat generation is a constant. The cylinder surface is cooled with constant temperature. The analysis has been conducted numerically using the finite difference method of the second order of accuracy on a uniform grid. The in-house computational code has been developed and comprehensively verified using numerical data of other authors and mesh sensitivity analysis. Findings As a result of the computations, the time profiles of the average Nusselt number at the walls of the cavity have been obtained for Rayleigh numbers varying from 103 to 106, whereas the Prandtl number is equal to 7.0. The data reveals the steady heat transfer rate at the top of the cylinder is greater than that at the lateral and bottom surfaces owing to the structure of the flow. In addition, the outcomes represent the time dependencies of the fluid flow rate and temperature within the domain at the aforementioned parameters. Next, the research shows the details regarding an influence of the variable viscosity on the Nusselt numbers, maximum dimensionless stream function and temperature. The effect has been evaluated by plotting the time-dependencies of these quantities at constant and variable viscosities. It has been found that a reduction of the viscosity with temperature illustrates a weak change of the average Nusselt number at the lower and side cooling surfaces, whilst the average Nusselt number at the upper surface is reduced due to the flow enhancement with a decrement of internal friction. Finally, the steady distributions of isotherms and streamlines have been depicted within the domain for the considered values of Rayleigh and Prandtl numbers, as well as their time evolution for Ra = 106. Originality/value To the best of the authors’ knowledge, in this paper for the first time, the effect of temperature-dependent viscosity on a natural convection of a thermally producing liquid is studied in a confined region. The previous research studies devoted to the thermally induced flows in cavities have been omitting this circumstance despite a prominent influence of variable properties and practical importance of such flow to nuclear, chemical or biochemical and metallurgical equipment. Moreover, the performed analysis and obtained results are new and illustrate the complex flow structures and heat transfer performance within the vertical cylinder under internal volumetric heat generation and time dependence of the fluid dynamic viscosity.