A NEW APPROACH FOR INVESTIGATING THE THERMAL-INSTABILITY OF A FLUID LAYER

A new direct method for solving the several value problems arising in the linear theory of thermal convection in a layer of fluid heated fro m below in the absence or presence of rotation and/or magnetic field i s presented. Necessary and sufficient conditions for the existence of nontrivial solutions of several characteristic value problems are deri ved in the general case, and then the method is favourably applied to study the thermal instability of a layer confined by any type of bound aries. The method is rigorous, simple to apply, applicable to any type of boundaries: free, rigid, mixed, perfectly conducting or non-conduc ting, and moreover, it is easily implemented using the available mathe matical software packages. Some unsolved convection problems with rota tion and magnetic field acting simultaneously are tackled for the firs t time using this method.