Effects of temperature-dependent viscosity on Rayleigh-Bénard convection in rectangular enclosures heated locally from below: A lattice Boltzmann study

Rayleigh–Bénard (RB) convection is a canonical model for buoyancy-driven thermal flows and is widely encountered in geophysical and industrial systems such as mantle convection, electronic cooling, solar air heating and heat exchangers. Although asymmetric thermal boundary conditions and temperature-dependent fluid viscosity have been extensively studied, previous works have primarily focused on symmetric configurations or uniform heating. The combined effect of localized bottom-wall heating and temperature-sensitive viscosity remains insufficiently explored, particularly regarding its nonlinear influence on flow structure and heat transfer. This study investigates the influence of the localized heating length L (the portion of the bottom wall subjected to heating) and the viscosity–temperature coupling parameter b on the flow and thermal transport characteristics of RB convection using the lattice Boltzmann method. The viscosity variation follows an exponential model [Formula: see text], where [Formula: see text] is the dimensionless temperature and [Formula: see text] is the reference viscosity. Here, b quantifies how strongly the viscosity depends on temperature: [Formula: see text] represents fluids whose viscosity decreases with temperature (e.g. water), while [Formula: see text] represents fluids whose viscosity increases with temperature (e.g. oils). The wall-averaged Nusselt number [Formula: see text] is used to characterize heat transfer performance, and the Prandtl number [Formula: see text] represents the ratio of momentum diffusivity to thermal diffusivity. Simulations are conducted at a fixed Rayleigh number of [Formula: see text] and for Prandtl numbers in the range [Formula: see text], covering both low-[Formula: see text] (liquid-metal-like) and high-[Formula: see text] (oil-like) fluids. This range ensures a laminar yet convectively active regime that balances numerical stability with physically meaningful dynamics. Results show that [Formula: see text] exhibits a nonmonotonic dependence on b. As b increases from [Formula: see text] to [Formula: see text], [Formula: see text] initially decreases and reaches a minimum near [Formula: see text]. Beyond this point, its behavior strongly depends on [Formula: see text]. For low-[Formula: see text] fluids (e.g. [Formula: see text]) at [Formula: see text], [Formula: see text] increases by up to [Formula: see text] due to enhanced cold-plume activity, whereas high-[Formula: see text] fluids show limited or even reduced heat transfer. Furthermore, when [Formula: see text], the heating length L significantly affects the flow mode. A critical length [Formula: see text] exists, beyond which the flow transitions from central upwelling to sidewall-dominated convection, resulting in a sudden [Formula: see text] increase in [Formula: see text]. Despite this transition, the overall trend indicates that [Formula: see text] decreases as L increases. These findings highlight the intricate interplay between viscosity stratification and geometric asymmetry in thermal convection. They provide valuable insights for the design and optimization of thermal systems involving nonuniform heating and variable-viscosity fluids, as well as for understanding natural convection processes in geophysical contexts.