Investigation of Rayleigh–Bénard Convective Heat Transfer in an L-Shaped Enclosure for Non-Newtonian Fluids

نوع: Type: Thesis

مقطع: Segment: Masters

عنوان: Title: Investigation of Rayleigh–Bénard Convective Heat Transfer in an L-Shaped Enclosure for Non-Newtonian Fluids

ارائه دهنده: Provider: Amirreza Mehrpasand

اساتید راهنما: Supervisors: Dr. Mohammad Saeed Aghighi

اساتید مشاور: Advisory Professors:

اساتید ممتحن یا داور: Examining professors or referees: Dr. Mohsen Goudarzi – Dr. Habibollah Sayehvand

زمان و تاریخ ارائه: Time and date of presentation: 2026

مکان ارائه: Place of presentation: 50

چکیده: Abstract: In this study, Rayleigh–Bénard natural convective heat transfer of a non-Newtonian Casson fluid inside a two-dimensional L-shaped enclosure is investigated numerically. The primary objective is to examine the combined effects of the viscoplastic characteristics of the fluid, buoyancy-force intensity, and enclosure geometry on the flow structure and heat transfer behavior. In the physical model, the lower horizontal wall of the enclosure is maintained at a constant hot temperature, while the upper horizontal walls are maintained at a constant cold temperature, and all remaining walls are assumed to be thermally insulated. The flow is assumed to be laminar, steady, incompressible, and two-dimensional, and density variations in the buoyancy term are accounted for using the Boussinesq approximation. The rheological behavior of the fluid is described using the Casson model, and the Papanastasiou regularization method is employed to eliminate the discontinuity associated with the yield stress. Following nondimensionalization, the governing equations are solved using the Galerkin finite element method implemented in MATLAB. The numerical results are investigated for Rayleigh numbers ranging from ten to the fourth power to ten to the sixth power, Bingham numbers ranging from zero to the maximum Bingham number, and at a constant Prandtl number of 100. To investigate the effect of enclosure geometry, five different configurations are considered by varying the dimensionless ratios a/H and b/L, and the effects of these parameters on the flow field, unyielded regions, and heat transfer characteristics are examined. To analyze the flow behavior under different conditions, streamline contours together with the unyielded regions, isotherms, maximum velocity, and average Nusselt number are extracted, analyzed, and plotted at different Bingham-number increments. These quantities are also employed to evaluate the progressive attenuation of the flow and to determine the maximum Bingham number. The results demonstrate that increasing the Rayleigh number strengthens the buoyancy forces, thereby intensifying fluid circulation and enhancing convective heat transfer within the enclosure. In contrast, as the Bingham number increases and the influence of the yield stress becomes more pronounced, the resistance of the fluid to motion increases, the flow intensity decreases, and unyielded regions gradually form and expand throughout different parts of the enclosure. The continuation of this process weakens the convective vortices and reduces the average Nusselt number. At Bingham numbers approaching the maximum Bingham number, the flow reaches a near-stagnant state, and the heat-transfer mechanism tends toward a conduction-dominated regime. The results further indicate that the enclosure geometry significantly affects the formation and expansion of unyielded regions, the vortex structure, and the overall heat-transfer rate. Variations in the dimensionless ratios a/H and b/L alter the response of the flow to increasing yield-stress effects. Furthermore, as the Rayleigh number increases, stronger buoyancy-driven flow requires larger Bingham numbers to sufficiently suppress fluid motion and drive the system toward a near-stagnant state