Effect of noninertial acceleration on heat transfer by Rayleigh–Bénard magnetoconvection: Exploring nonlinear dynamics

Abstract Buoyancy‐driven Rayleigh–Bénard convection in the presence of a magnetic field, rotation, and temperature‐dependent viscosity has applications in the field of crystal growth, space laboratory experiments, and atmospheric convection. It also has potential applications in heat transfer and magnetohydrodynamics, which can occur in planetary and stellar interiors. The present work aims to study the combined effect of magnetic fields and rotation on the onset of Rayleigh–Bénard convection in temperature‐dependent viscosity Newtonian liquids with internal heat sources/sinks. Both linear and weak nonlinear stability analyses of convection are performed in the problem. The minimal representation of the Fourier series for the stream function and the magnetic potential allows us to derive the analytical expression for the thermal Rayleigh number () and the generalized Lorenz model. In linear theory, the critical Rayleigh number and the wave number are tabulated for different values of the Chandrasekhar number (), the Taylor number (), and the thermorheological parameter (), and the onset of stability is analyzed. It is found that the instability manifests at when for stress‐free and isothermal boundaries. In nonlinear theory, the generalized Lorenz model obtained is not amenable to analytical treatment; therefore, the classical fourth‐order Runge–Kutta method is applied to solve the Lorenz model. It is found that the internal Rayleigh number, the thermorheological parameter, and the Taylor number influence the onset of convection and heat transfer coefficient. It is also demonstrated that the joint increase in rotational force and magnetic field strength stabilizes the system strongly, thereby reducing heat transfer. However, increasing the heat source and the variable viscosity parameter have antagonistic influences.