Stability of mixed convection in a differentially heated vertical fluid layer with internal heat sources

Abstract

The linear stability of mixed convection caused by a constant external pressure gradient, buoyancy force and a uniform internal heating in a vertical incompressible fluid layer whose vertical walls are kept at different constant temperatures is studied. The ensuing eigenvalue problem is solved numerically using the Chebyshev collocation method for two-dimensional motions after ensuring the validity of Squire’s theorem. The presence of internal heating introduces the point of inflection as well as reverse flow and increasing in its strength is found to amplify the back flow. The stability characteristics of the system are discussed for three values of Prandtl number representative of liquid mercury, water and oil. Multiple local minimum wave numbers are observed even in the presence of internal heating which facilitates instability of the system for all the values of Reynolds number and the Prandtl number considered. Additionally, the streamlines and isotherms of the perturbation modes are presented for different values of internal heat source strength, the Reynolds number and the Prandtl number. An energy budget analysis is embarked upon to understand the physical mechanisms involved in the flow transition.