Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

The onset of instability of thermal convection in an inclined layer of viscous, incompressible fluid having internal heat source is studied using linear stability analysis. The heat source consists of a uniform component as well as a temperature-dependent component. The boundaries of the layer are maintained at different constant temperatures. The thermal Rayleigh number \(R_1\) $R_1$ and the dimensionless parameters \(R_2\) $R_2$ and \(R_3\) $R_3$ determining the strength of the internal heat source are used to establish the onset of instability. The collocation method utilising Chebyshev polynomials is adopted to obtain the critical values of various parameters. The Prandtl number of the fluid and the angle of inclination of the layer are also the key factors in determining the onset of instability.