## 1 Introduction  
Over the past decade, the study of natural convection has garnered significant attention from researchers across various disciplines. Its ability to transfer heat without external energy sources makes natural convection a promising area of research for numerous natural and industrial applications. From energy-efficient cooling systems to advanced heat exchangers, the potential for natural convection to revolutionize engineering practices is immense. Numerous investigations have explored the natural convection that arises when a solitary heated object is positioned within an enclosure where the walls are maintained at lower temperatures [1; 2; 3; 4; 5; 6]. However, in practical engineering applications, it becomes essential to gain insights into temperature gradients and fluid flow within enclosures that consist of multiple objects arranged in diverse positions. Studying the convective transport driven by buoyancy within enclosures holds significant importance due to its wide range of applications, including energy storage, material processing, cooling systems, and human comfort. [PERSON] [7] conducted a comprehensive examination of heat transfer in natural convective flow, wherein the majority of recent research has concentrated on scenarios featuring either horizontal or vertical temperature gradients. Natural convection through enclosures with partially active walls, such as heated and cooled walls, can be used for cooling electrical gadgets and buildings [8]. Using the asymptotic approach, [PERSON] et al. [9] developed a new heat transfer coefficient correlation for radial plate-fin heat sinks and thermal optimized horizontally oriented ones using natural convection. [PERSON] et al. [10] developed an analytical method for predicting heat transmission via unsteady natural convection. Using an analytical solution, [PERSON] et al. [11] determined the conditions under which free convection occurs in vertically asymmetrically heated shafts at low Rayleigh numbers. [PERSON] et al. [12] and [PERSON] et al. [13] analyzed the onset of Rayleigh-Bernard convection. The focus of the study is the investigation of power law fluid convection in rectangular-shaped cavities. Specifically, the study examines the convection patterns in an enclosure with differentially heated walls, where the lower wall is heated while the side walls are adiabatic. Polymeric fluids with shear-thinning and -thickening properties have practical applications. Their viscosity changes with shear rate, making coupling momentum and thermal fields crucial in measuring heat transfer. These fluids significantly minimize heat loss in various applications, including storage tanks, crude oil production, food reheating, electronic component cooling, and polymeric pallet melting or heating. A mathematical model called the power law model provides a comprehensive approach to understanding these materials. The power law model is a significant tool for predicting the behavior of polymeric materials under both minimum and maximum stresses and accurately describing the deformation rate response. Various studies have extensively investigated the behavior of power law materials within confined geometries accompanied by natural convection. [PERSON] et al. [14] utilized the Boussinesq approximation to demonstrate the characteristics of a power law fluid with variable density in a 2D enclosure subject to different Rayleigh numbers. [PERSON] and [PERSON] [15] investigated the behavior of thermal-dependent density and quiescent power law fluid enclosed in an inclined cavity subjected to laminar flow for different kinematic conditions. In their study, [PERSON] and [PERSON] [16] investigated the laminar convective motion of a power law fluid through a series of horizontally aligned tandem cylinders with differential heating. In their study, [PERSON] et al. [17] discussed entropy generation analysis using a hybrid nanofluid model in a convectively heated moving wedge.