Numerical Analysis of Heat Transfer in Permeable Surfaces with Newtonian and Non-Newtonian Nano Fluids
Abbas I and Ejaz A
Published on: 2023-12-31
Abstract
In this study, both Newtonian and non-Newtonian Nano-fluids are used to look into heat transfer and fluid flow. The objective of this study is to examine the interaction between fluids and permeable surfaces in the presence of a magnetic field. Specifically, the study focuses on the behavior of cassion fluids, the occurrence of chemical reactions, as well as the processes of injection and suction. The research employs the approach of similarity solutions to convert partial differential equations into ordinary differential equations, which are subsequently solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order (RKF45) method. This study investigates the utilization of Cu, CuO, TiO2 and Al2O3 nanoparticles within a sodium carboxymethyl cellulose and water base fluid. The analysis focuses on key parameters such as power-law index, nanoparticle volume percentage, and permeability to assess the influence of these factors on the flow and heat transfer properties of the Nano fluid.
The findings of the study demonstrate that the flow and heat transfer characteristics of non-Newtonian Nano fluids are significantly affected by the presence of suction and injection, leading to discernible patterns of behavior. In the context of injection settings and impermeable plates, it has been observed that non-Newtonian Nano fluids have superior heat transfer capabilities compared to Newtonian Nano fluids. Nevertheless, the alteration in nanoparticle composition has a substantial influence on heat transmission during the process of suction.
Keywords
MHD; Shouting method Heat transfer; Nano fluidsIntroduction
Non-Newtonian Nano fluids, containing solid nanoparticles, are increasingly used in heat transfer applications due to their non-Newtonian properties. These fluids can improve thermal device efficiency, potentially conserving energy, reducing device size, and reducing material and manufacturing costs, making them a priority for industrial unit designers. The advancements achieved in the field of nanotechnology throughout the previous twenty years, in conjunction with the utilization of Nano fluids as an innovative medium for heat transmission, have expanded the potential areas of investigation for scientists and researchers. Traditional heat transfer fluids commonly used in industry, such as water and ethylene glycol, demonstrate comparatively lower thermal conductivity in comparison to solid solids composed of metals [1]. Consequently, the thermal performance of the aforementioned fluids can be improved through the incorporation of metallic nanoparticles [2,3]Metal oxide nanoparticles [4], Carbon-based nanoparticles are a type of nanomaterial composed primarily of carbon atoms [5-9]. The use of Nano fluids has become widespread in several fields, including electronics cooling, heat exchangers, and renewable energy, in recent years [10]. The utilization of Nano fluids may be traced back to the early 1990s, when the notion of Nano fluids was initially presented by Choi and Eastman. The addition of nanoparticles to conventional fluids, even in little quantities, can result in substantial enhancements in their thermal efficiency. Subsequent to then, there has been a significant expansion in the investigation of Nano fluids, resulting in the emergence of non-Newtonian Nano fluids. Non-Newtonian fluids exhibit a departure from the linear relationship between shear stress and shear rate, as dictated by Newton's equation of viscosity. On the other hand, non-Newtonian fluids display changes in viscosity in relation to the rate of deformation, leading to a wide array of complex flow phenomena. The non-Newtonian characteristics of these fluids can be further intensified by including nanoparticles [11-13]. Power law fluids, Non-Newtonian fluids, commonly known as such, demonstrate a non-linear correlation between shear stress and shear rate. The assessment of the flow characteristics of power law fluids in porous media may be accomplished by utilizing the power law index, which measures the extent of non-linearity in the rheological properties of the fluid. The study of the flow characteristics of power law fluids in porous media holds significant importance in a range of applications, including but not limited to oil and gas extraction, groundwater resource management, and environmental remediation. When evaluating phenomena in these domains, mathematical models and simulations can be employed to predict the behavior of power law fluids within porous media across different scenarios. In the study conducted by Sui et al. [14] aims to conduct an experimental investigation of the heat distribution inside the boundary layer of a non-Newtonian fluid that demonstrates power-law behavior. The experiment utilized a mixed convection device designed for the purpose of measuring temperature distribution and flow velocity inside the boundary layer of a fluid. The research focused on investigating the behavior of a dilute aqueous solution of carboxymethyl cellulose (CMC), which exhibited non-Newtonian fluid characteristics following a power-law model. The experimental setup employed by the researchers involved the utilization of an inclined plate and a moving conveyor to investigate the impacts of shear flow, power-law viscosity, and temperature variability. In the study conducted by Jalil et al. [15], the researchers aimed to investigate the characteristics and flow dynamics of a fluid exhibiting shear-thinning qualities over a smooth and permeable surface in a boundary layer. Additionally, the researchers investigate the impact of the fluid's permeability, surface stretching rate, and viscosity on the flow behavior of the shear-thinning fluid. In their study, Ahmed et al. [16] utilized the shooting technique and homotopic analysis as separate mathematical approaches to investigate the heat transport and fluid flow properties of a power-law fluid across a radially stretched sheet. The research done by Meghdad et al. [17] examined the effects of heat radiation, particularly the transfer of thermal energy through electromagnetic waves like infrared radiation. The examination of fluid properties, particularly under high temperatures or in the presence of objects that absorb or emit radiation, necessitates the inclusion of heat radiation as a crucial element. Numerous researchers have undertaken investigations pertaining to the flow characteristics of a power-law fluid across a planar, permeable surface, while considering variables such as thermal flux, suction, and injection. Heat flux is the phenomenon that involves the flow of thermal energy over a surface, whereas suction and injection pertain to the process of removing or adding fluid to the system. The parameters under consideration in the study were examined by the researchers in order to enhance comprehension of the fluid's behavior through the porous plate. The primary objective of their study was to enhance their comprehension of fluid dynamics over porous surfaces, a subject with wide-ranging implications in disciplines such as chemical engineering, geology, and environmental science [18]. The present study investigates the heat transfer characteristics of a power-law fluid when it is subjected to flow across a plate positioned at a right angle to the direction of flow. The investigation takes into account the influences of radiation, a Darcy porous media, and chemical reaction. The study contributes to the field of mixed convection heat transfer and provides valuable insights for the design and optimization of heat transfer processes involving power-law fluids.The Casson fluid, a non-Newtonian fluid model, was initially introduced by O. G. Casson in 1959. The substance in question is a distinct type of viscoelastic fluid that exhibits a yield stress characteristic. This implies that before to reaching a given stress threshold, the substance demonstrates solid-like behavior, transitioning into a liquid-like flow state thereafter. The utilization of Casson fluid is prevalent throughout various domains of research and engineering [19-23]. The study undertaken by Uddin et al. [24] involved a numerical inquiry to analyses the characteristics of power-law non-Newtonian Nano fluid on a linearly growing sheet. The researchers employed the linear hydrodynamic slip boundary condition to simulate the magneto hydrodynamic (MHD) boundary layer in their study. The study conducted by Lin et al. [25] investigated the behavior of a finite film of pseudo-plastic magneto hydrodynamic (MHD) Nano fluid as it flowed across a surface undergoing stretching. The simulation was performed by including indoor heating. The study conducted by Sandeep et al. [26] examined the behavior of non-Newtonian Nano fluids, namely those of the Jeffrey, Maxwell, and Holroyd-B types, when subjected to a permeable stretching sheet. A simulation was conducted to analyses the flow, mass transfer, and heat transfer phenomena in the presence of a transverse magnetic field, as well as injection and suction effects. The simulation also took into account the influence of Brownian motion. The research conducted by Madhu et al. [27] focused on the investigation of non-Newtonian Nano fluids flowing across a nonlinear stretching sheet. Numerous authors have extensively examined the impact of chemical reactions on the behavior of fluid in motion across various dimensions. In their study, Das et al. [28] examined how mass transfer affects the dynamics of an infinite vertical plate flow initiated on the spur of the moment. A constant heat flux and chemical reaction were applied to the plate. By using a chemically reactive molecule, Andersson et al. showed that diffusion may occur from a stretched sheet which is adders by Andersson et al. [29]. In their study in their study, Fan et al. [30] found the similarity solutions for the issue of mixed convection with diffusion and chemical reaction occurring over a horizontal moving plate. The phenomenon of magneto hydrodynamic (MHD) free convective flow and mass transfer occurring over a stretched sheet with chemical reaction was initially investigated and reported by Afify in their study [31]. The study conducted by [32-33] focused on examining the properties of magneto hydrodynamic (MHD) flow and mass transfer in the context of an upper-convicted Maxwell fluid. The passage of fluid through a porous sheet experiencing shrinkage was seen, with the added presence of chemically reactive species. Bhattacharyya and Layek [34] conducted a research to examine the properties of solute distribution in a boundary layer flow using magneto hydrodynamics (MHD) across a permeable stretched sheet, focusing on chemically reactive solutes. In this work, we used the Tiwari and Das model, which brings in new ideas by including the cassion fluid and stagnation flow. The main goal of this study is to look into how heat moves through non-Newtonian Nano fluids with pseudo-plastic behavior as they flow above a transparent flat plate with chemically reactive species. In this study, the results and analyses are carefully shown using MATLAB, which is a well-known tool for numerical simulations and data analysis. The study gives us a much better understanding of how non-Newtonian Nano fluids behave when a magnetic field is present. It also shows us how different factors affect the velocity and temperature ranges.