Bead Size Research Articles

Martini 3 Coarse-Grained Force Field for Cholesterol.

Cholesterol plays a crucial role in biomembranes by regulating various properties, such as fluidity, rigidity, permeability, and organization of lipid bilayers. The latest version of the Martini model, Martini 3, offers significant improvements in interaction balance, molecular packing, and inclusion of new bead types and sizes. However, the release of the new model resulted in the need to reparameterize many core molecules, including cholesterol. Here, we describe the development and validation of a Martini 3 cholesterol model, addressing issues related to its bonded setup, shape, volume, and hydrophobicity. The proposed model mitigates some limitations of its Martini 2 predecessor while maintaining or improving the overall behavior.

Building-Block Size Mediates Microporous Annealed Particle Hydrogel Tube Microenvironment Following Spinal Cord Injury.

Spinal cord injury (SCI) is a life-altering event, which often results in loss of sensory and motor function below the level of trauma. Biomaterial therapies have been widely investigated in SCI to promote directional regeneration but are often limited by their pre-constructed size and shape. Herein, the design parameters of microporous annealed particles (MAPs) are investigated with tubular geometries that conform to the injury and direct axons across the defect to support functional recovery. MAP tubes prepared from 20-, 40-, and 60-micron polyethylene glycol (PEG) beads are generated and implanted in a T9-10 murine hemisection model of SCI. Tubes attenuate glial and fibrotic scarring, increase innate immune cell density, and reduce inflammatory phenotypes in a bead size-dependent manner. Tubes composed of 60-micron beads increase the cell density of the chronic macrophage response, while neutrophil infiltration and phenotypes do not deviate from those seen in controls. At 8 weeks postinjury, implantation of tubes composed of 60-micron beads results in enhanced locomotor function, robust axonal ingrowth, and remyelination through both lumens and the inter-tube space. Collectively, these studies demonstrate the importance of bead size in MAP construction and highlight PEG tubes as a biomaterial therapy to promote regeneration and functional recovery in SCI.

Response Surface Methodology: A Versatile Tool for the Optimization of Particle Sizes of Cellulose Beads

Synthesis parameters are of utmost importance for controlling the particle sizes of cellulose beads. This study aims to investigate the effects of synthesis parameters e.g., stirring speed (250–1250 rpm), surfactant concentrations (0.5–6.0% w/v), cellulose concentrations (1–5% w/v), and reaction temperature (30-100°C) on the particle sizes for micron-sized cellulose beads (µCBs) as well as other parameters e.g. the volume (1.0 mL) and concentration (0.1–1.0% w/v) of cellulose for nanosized (nCBs) cellulose beads using the response surface methodology (RSM). A total of 27 runs were conducted applying RSM based on the central composite design approach with Minitab-19. Cellulose concentrations were shown to have the most significant effect on both µCBs and nCBs. Under optimized conditions, the minimum and maximum mean particle size of µCBs that could be achieved were 15.3 µm and 91 µm, respectively. The predicted mean particle size for nCBs was obtained at 0.01 nm as the smallest and 200 nm as the biggest particle size under the optimum conditions. This study envisages that RSM and experiments for targeted applications such as biomedicine and agriculture could optimize the particle sizes of cellulose beads.

Wet bead milling by dual centrifugation – An approach to obtain reproducible and differentiable suspensions

Aqueous nano- and microsuspensions containing poorly water-soluble, crystalline drug particles have in the recent years sparked an interest for the preparation of long-acting injectables (LAIs), which increase patient compliance for patients treated for long-term or chronic conditions. Nano- and microsuspensions are often prepared by top-down methods, such as wet bead milling, with the addition of stabilizers in the dispersion media, such as surfactants, which influence the particle sizes and physical stability of the suspension. To improve the efficacy of formulation screening for nano- and microsuspensions, dual centrifugation was utilized in this study whereby 40 samples could be manufactured simultaneously to support the formulation definition. Hence, the type and concentration of stabilizer as well as bead size and milling speed was investigated throughout the presented study, but also the ability of the method to produce consistent data was investigated. The obtained results demonstrated that the particle profile obtained after milling was very consistent from run to run and so was the observed stability data, i.e., running n = 1 experiment per combination could clearly be justified as a predictable approach for the formulation screening. The data also showed that the stabilizer, as well as its concentration highly influenced the physical stability of suspensions containing both the two investigated model compounds, i.e., both cinnarizine and indomethacin, where the biggest increase in particle sizes was observed within the first week. For short-term studies, polysorbate 20 was found to be a suitable stabilizer for suspensions of cinnarizine, whereas sodium dodecyl sulphate was more suitable for indomethacin suspensions immediately after the milling even with 1% (w/v) stabilizer solution, but not sufficient for short-term stability due to an insufficient stabilizer concentration. Smaller particles sizes could be achieved by milling the suspensions with the smallest bead sizes and at the highest speed of 1500 rpm without disrupting the crystal structure of the active pharmaceutical ingredient (API), which was confirmed by X-ray Powder Diffraction.

Fabrication, Characterization and in vitro Evaluation of Prednisolone Sustained Release Multiparticulate System for Colonic Targeting

Background: Prednisolone (PRD) is orally prescribed for inflammatory bowel syndrome (IBS) as the upper GIT is the main site of absorption; therefore, long-term PRD dosing decreases therapeutic effectiveness through systemic side effects. Objective: This work focused on formulating sustained-release alginate beads as a multiparticulate system for colon targeting using prednisolone (PRD) to be filled in an HPMC capsule. Methods: PRD beads were prepared by the ionotropic gelation technique using sodium alginate as the primary polymer and inulin, guar gum, and pectin as secondary polymers. In addition to the impact of polymer type and quantity, other factors were investigated: The CaCl2 concentration and tween 80 addition Thirteen formulations were successfully prepared, and their properties, such as bead size, morphology, percentage of encapsulation efficiency, yield, DL, in vitro release study in GIT buffer media, IBS media, SEM, and FTIR, were assessed. Results: The study showed that the beads were close in size, and the size was not an obstacle for loading the beads in HPMC capsules. Further, yield%, EE%, and DL% increased according to the bead’s content increase. Conclusions: The optimum formula was F3 that coated HPMC capsules with Eudragit S-100, which gave sustained release profiles in GIT and IBS simulating media, and F13 that could last the release in different pH media, pH 1.2, 6.8, and 7.4.

Oxidative stress and histopathological effects by microplastic beads, in the crayfish Procambarus clarkii, and fiddler crab Leptuca pugilator

The present study was aimed at evaluating the in vivo effects of microplastics (MP), in terms of oxidative stress and histopathological effects, in two crustacean species: Procambarus clarkii and Leptuca pugilator. In addition, MP accumulation in the hepatopancreas (HP) of both species was also determined. Adults of both crayfish and crabs were exposed for one month to fluorescent polystyrene beads (size: 1 μm) at nominal concentrations of 1000 or 5000 particles/mL. During the exposure, animals were maintained under controlled feeding, aeration, temperature, and photoperiod conditions. At the end of the exposure, HP and hemolymph (HL) samples were harvested for analysis of oxidative damage and total antioxidant levels. Additionally, the presence of MPs in both tissues was confirmed. Significant differences with the control groups were observed in lipid peroxidation levels in HP in animals exposed to the lowest concentration in P. clarkii and to the highest concentration in L. pugilator. A marked increase in antioxidant levels was also observed in the HL at both concentrations in P. clarkii, and at the highest MPs concentration in L. pugilator. Moreover, several histopathological changes were detected in both gills and HP, including hypertrophied lamellae, lifting or collapse of gill epithelia, loss of normal shape of hepatopancreatic tubules, and epithelial atrophy in the HP tissue. We conclude that exposure to MP beads at selected concentrations results in oxidative damage, induces histopathological changes in gills and HP, and triggers an antioxidant response in two crustacean species.

Alginate-based gel beads with bigel structures: Preparation, characterization and bioactive encapsulation

The current study developed novel gel beads with bigel structures based on alginate hydrogel and glycerol monostearate oleogel. Bigel beads with different structures were prepared by varying oleogel content, and the beads were also used to co-encapsulate lipophilic and hydrophilic biaoctives. All the beads had high sphericity (>0.94), and the bead size was increased with the increase in oleogel content. Beads with higher content of oleogel had lower shrinking rates and higher level of oil filling the gel pores. The oil droplets were generally acting as inactive fillers in the gel beads, as the mechanical strength (Young's modulus and hardness) was declining with the increase in oleogel content, and no interaction between the oleogel and hydrogel was detected by FTIR. Swelling studies revealed that beads in salt solution at higher temperature had higher swelling ratio, and the increase in oleogel content could inhibit the swelling. The bigel beads were able to encapsulate EGCG and curcumin simultaneously, and beads with higher oleogel content generally had lower encapsulation efficiency of EGCG but higher efficiency of curcumin. The gel structures provided good protection for curcumin, and about 70% of the original curcumin was retained after a 40-day storage test. The study provided novel information regarding the structure-function relationship of the bigel beads, which could be useful for the development of functional food materials.

Development and Characterization of Electrospun Composites Built on Polycaprolactone and Cerium-Containing Phases.

The current study reports on the fabrication of composite scaffolds based on polycaprolactone (PCL) and cerium (Ce)-containing powders, followed by their characterization from compositional, structural, morphological, optical and biological points of view. First, CeO2, Ce-doped calcium phosphates and Ce-substituted bioglass were synthesized by wet-chemistry methods (precipitation/coprecipitation and sol-gel) and subsequently loaded on PCL fibres processed by electrospinning. The powders were proven to be nanometric or micrometric, while the investigation of their phase composition showed that Ce was present as a dopant within the crystal lattice of the obtained calcium phosphates or as crystalline domains inside the glassy matrix. The best bioactivity was attained in the case of Ce-containing bioglass, while the most pronounced antibacterial effect was visible for Ce-doped calcium phosphates calcined at a lower temperature. The scaffolds were composed of either dimensionally homogeneous fibres or mixtures of fibres with a wide size distribution and beads of different shapes. In most cases, the increase in polymer concentration in the precursor solution ensured the achievement of more ordered fibre mats. The immersion in SBF for 28 days triggered an incipient degradation of PCL, evidenced mostly through cracks and gaps. In terms of biological properties, the composite scaffolds displayed a very good biocompatibility when tested with human osteoblast cells, with a superior response for the samples consisting of the polymer and Ce-doped calcium phosphates.

Topology optimization for material extrusion-based additive manufacturing processes with weak bead bonding

Topology optimization (TO) is a powerful design tool that has been used to design lightweight high-performing structures. Additive manufacturing (AM) is a favoured fabrication method for TO designs because of its high precision and flexibility to realize complex optimized structures. This paper describes a new TO approach that can account for fabrication characteristics and constraints of extrusion-based AM. The fabrication process is mimicked as the design is generated by enforcing a fixed radius feature size in design outputs, and introducing a secondary material between adjacent beads. Lowering the stiffness of this additional material allows for consideration of the weak bead bonds in extrusion-printed materials and promotes continuity of design features. The user can control the radius of the discrete feature size and the relative stiffness of the weak bond. The algorithm is demonstrated on benchmark TO problems in 2D. The design results contain both a description of the physical layout of the structure and a design variable distribution that can be used as a trace for the raster path. The design results are found to respond to user specifications on bead size and relative bond weakening. Continuity of the raster path increases as the stiffness of the bead bonding decreases.

Effects of WC ratios on bead size and crack initiation in forming WC-Co cemented carbides by the laser metal deposition

Enhancing the durability of molds, jigs, and tools is crucial for the industry, and one approach to achieve this is by forming a metallic layer with high hardness on their surfaces. Metallic layers with high hardness can be formed through laser metal deposition (LMD), which is one of the additive manufacturing processes, using cemented carbide powder. However, crack initiation typically occurs inside cemented carbide layers formed by the LMD. Therefore, achieving a cladding process for cemented carbide layers without cracks is desired for practical applications. In this study, the effects of tungsten carbide (WC) ratios in WC-Co cemented carbide granulated powder on formed bead size and crack initiation during the LMD processing were investigated. The number of cracks generated during the LMD processing was evaluated using an acoustic emission (AE) technique. The number of burst-type AE signals generated was counted as the number of cracks. Seven types of WC-Co cemented carbide granulated powders with WC ratios ranging from 30.5 to 92 mass% were prepared. Beads were formed using each powder through the LMD, with AE signals being measured. In the case of a WC ratio of 42.9 mass% or less, no crack was observed. On the other hand, cracks were observed when the WC ratio was 53.9 mass% or greater, and the number of cracks increased with an increase in the WC ratio.

Quantitative analysis of respiratory viruses based on lab-on-a-chip platform.

The quantitative analysis of respiratory viruses is of great importance for rapid diagnosis, precision medicine, and prognosis. Several current quantitative analysis systems have been proposed and commercialized. Although they have been proven in trials, quantitative analyzes based on real samples are still complex, time-consuming, and expensive. Therefore, they are not able to directly quantify real samples. In this work, we presented a lab-on-a-chip platform combined with an automated control system to achieve quantitative analysis from samples to results. We developed a multilayer integrated chip to rapidly extract and quantify RNA of coronavirus disease 2019 (COVID-19) pseudovirus from large-volume nasal swab samples. The dependence of the magnetic bead size and the interfacial effect was studied for the first time, and the conditions of immiscible filtration assisted by surface tension (IFAST) method for nucleic acid extraction were optimized to increase the nucleic acid recovery rate up to 85%. Inside the chip, a pneumatic valve was developed for automatic opening and closing of the liquid channel. The integrated chip platform and automatic control system presented here are advantageous for use in resource-limited settings (RLS). In addition, our method can be extended to other respiratory viruses and other sample types.

High-throughput extraction on a dynamic solid phase for low-abundance biomarker isolation from biological samples

Liquid biopsy, in particular circulating tumor DNA (ctDNA) analysis, has paved the way for a new noninvasive approach to cancer diagnosis, treatment selection and follow-up. As a crucial step in the analysis, the extraction of the genetic material from a complex matrix needs to meet specific requirements such as high specificity and low loss of target. Here, we developed a new generation of microfluidic fluidized beds (FBs) that enable the efficient extraction and preconcentration of specific ctDNA sequences from human serum with flow rates up to 15 µL/min. We first demonstrated that implementation of a vibration system inducing flow rate fluctuations combined with a mixture of different bead sizes significantly enhanced bead homogeneity, thereby increasing capture efficiency. Taking advantage of this new generation of high-throughput magnetic FBs, we then developed a new method to selectively capture a double-stranded (dsDNA) BRAF mutated DNA sequence in complex matrices such as patient serum. Finally, as proof of concept, ligation chain reaction (LCR) assays were performed to specifically amplify a mutated BRAF sequence, allowing the detection of concentrations as low as 6 × 104 copies/µL of the mutated DNA sequence in serum.

Effects of microfiber and bead microplastic exposure in the goldfish Carassius auratus: Bioaccumulation, antioxidant responses, and cell damage

We confirmed antioxidant-related gene expression, bioaccumulation, and cell damage following exposure to various microplastics in vivo and in vitro in the goldfish Carassius auratus. Exposure of C. auratus to a 500 µm fiber-type microplastic environment (MF; 10 and 100 fibers/L) and two sizes (0.2 and 1.0 µm) of beads (MB; 10 and 100 beads/L) for 120 h increased superoxide dismutase (SOD) mRNA expression in the liver until 24 h followed by a decrease. Whereas, catalase (CAT) mRNA expression increased from 12 h to the end of the in vivo experiment. In vitro experiments were conducted with diluted microfibers (1 and 5 fibers/L) and microbeads (1 and 5 beads/L) using cultured liver cells. The results of SOD and CAT mRNA expression analysis conducted in vitro showed a tendency similar to those of experiments conducted in vivo. The H2O2 level increased in the high-concentration experimental groups compared with that in the low-concentration groups of 0.2-µm beads. In addition, the H2O2 level increased in both MF and MB groups from 12 h of exposure. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) levels in plasma were used as indicators of liver damage in fish. The ALT and AST levels increased up to 120 h after exposure. Caspase-3 (casp-3) mRNA expression was higher in the MB group than in the MF group. We visually confirmed liver casp-3 mRNA signals using in situ hybridization. The degree of DNA damage in the MF and MB high-concentration groups increased with the exposure time. The tail length and percent of DNA in the tail of the MB group were significantly higher than those of the MF group, confirming that DNA damage was greater in the MB group. Both fiber- and bead-type microplastics induced oxidative stress in C. auratus, but the bead-type induced greater stress than the fiber-type.

Quantification and modeling of macroparticle-induced mechanical stress for varying shake flask cultivation conditions.

In biotechnological processes, filamentous microorganisms are known for their broad product spectrum and complex cellular morphology. Product formation and cellular morphology are often closely linked, requiring a well-defined level of mechanical stress to achieve high product concentrations. Macroparticles were added to shake flask cultures of the filamentous actinomycete Lentzea aerocolonigenes to find these optimal cultivation conditions. However, there is currently no model concept for the dependence of the strength and frequency of the bead-induced stress on the process parameters. Therefore, shake flask simulations were performed for combinations of bead size, bead concentration, bead density and shaking frequency. Contact analysis showed that the highest shear stresses were caused by bead-bottom contacts. Based on this, a newly generated characteristic parameter, the stress area ratio (SAR), was defined, which relates the bead wall shear and normal stresses to the total shear area. Comparison of the SAR with previous cultivation results revealed an optimum pattern for product concentration and mean product-to-biomass related yield coefficient. Thus, this model is a suitable tool for future optimization, comparison and scaling up of shear-sensitive microorganism cultivation. Finally, the simulation results were validated using high-speed recordings of the bead motion on the bottom of the shake flask.

Using the numerical simulation and artificial neural network (ANN) to evaluate temperature distribution in pulsed laser welding of different alloys

The temperature field during laser welding process plays an important role on determining the quality and quantity of the weld bead size, microstructure characterizations and mechanical properties of the welding interface in the thermal engineering applications. In this study, using the numerical simulation, the influence of pulse duration and frequency on the temperature distribution and velocity field in distinctive laser welding of stainless steel 420 (S.S 420)/stainless steel 304 (S.S 304), and Bohler 303 (B 303)/stainless steel 304 (S.S 304) was examined. The results of numerical modeling illustrated that shear stress of Marangoni and buoyancy force are the most curtail aspects in the formation of the flow of liquid metal. A novel artificial intelligence method is proposed to optimally predict the melting ratio, and maximum temperature of the materials. To this end, a combination of ANN and Particle Swarm Optimization (PSO) algorithms are employed. The PSO algorithm is used to optimize the architecture and training algorithm of the ANN, while the ANN is employed for the regression problem. Based on the results, a three-layer feed-forward architecture with sigmoid transfer functions having 17 and 8 neurons in the hidden layers combined with the scaled conjugate gradient backpropagation training scheme is recognized by the PSO as the optimal configuration. Application of optimal ANN to the regression problem results in an acceptable level of error for the training, validation, and test datasets. Finally, the optimized ANN can be utilized to anticipate the melting ratio and thereby the resultant temperature.

Do Mixtures of Beads with Different Sizes Improve Wet Stirred Media Milling of Drug Suspensions?

The impacts of bead sizes and bead mixtures on breakage kinetics, the number of milling cycles applied to prevent overheating, and power consumption during the nanomilling of drug (griseofulvin) suspensions were investigated from both an experimental and theoretical perspective. Narrowly sized zirconia beads with nominal sizes of 100, 200, and 400 µm and their half-and-half binary mixtures were used at 3000 and 4000 rpm with two bead loadings of 0.35 and 0.50. Particle size evolution was measured during the 3 h milling experiments using laser diffraction. An nth-order breakage model was fitted to the experimental median particle size evolution, and various microhydrodynamic parameters were calculated. In general, the beads and their mixtures with smaller median sizes achieved faster breakage. While the microhydrodynamic model explained the impacts of process parameters, it was limited in describing bead mixtures. For additional test runs performed, the kinetics model augmented with a decision tree model using process parameters outperformed that augmented with an elastic-net regression model using the microhydrodynamic parameters. The evaluation of the process merit scores suggests that the use of bead mixtures did not lead to notable process improvement; 100 µm beads generally outperformed bead mixtures and coarser beads in terms of fast breakage, low power consumption and heat generation, and low intermittent milling cycles.

Multilayered Gel-Spotting Device for In Vitro Reconstruction of Hair Follicle-like Microstructure.

Hair follicles play an important role in hair development. This study aimed to develop a microgel-spotting device to fabricate a multilayered gel bead culture model and to mimic the early development of skin appendages to regenerate hair follicles in vitro. The model consists of an alginate gel layer containing cytokines as the core layer, a collagen gel layer containing mouse embryonic stem cells as the middle layer, and a collagen gel layer containing fetus-derived epidermal cells as the outer layer. A concentration gradient of cytokines is formed, which promotes interactions between epidermal and stem cells. Histological and immunnohistological analyses confirmed the reconstruction of hair follicle structures. As a result, the cell number and gel bead size could be precisely controlled by the developed microgel-spotting device. In the multilayered gel bead, the embryonic and epidermal cells cultured with the cytokine gradient formed cell aggregates with keratinized tissue in the center similar to "native" hair follicle structure. Sweat gland-like luminal tissue and erector pilorum-like structures were also observed around aggregates with concentric structures. In conclusion, the multilayered gel bead culture model demonstrated potential for in vitro hair follicle regeneration. The findings of this study provide insight into the early development of skin appendages.

Optimization of fecal sample homogenization for untargeted metabolomics.

Fecal samples are highly complex and heterogeneous, containing materials at various stages of digestion. The heterogeneity and complexity of feces make stool metabolomics inherently challenging. The level of homogenization influences the outcome of the study, affecting the metabolite profiles and reproducibility; however, there is no consensus on how fecal samples should be prepared to overcome the topographical discrepancy and obtain data representative of the stool as a whole. Various combinations of homogenization conditions were compared to investigate the effects of bead size, addition of solvents and the differences between wet-frozen and lyophilized feces. The homogenization parameters were systematically altered to evaluate the solvent usage, bead size, and whether lyophilization is required in homogenization. The metabolic coverage and reproducibility were compared among the different conditions. The current work revealed that a combination of mechanical and chemical lysis obtained by bead-beating with a mixture of big and small sizes of beads in an organic solvent is an effective way to homogenize fecal samples with adequate reproducibility and metabolic coverage. Lyophilization is required when bead-beating is not available. A comprehensive and systematical evaluation of various fecal matter homogenization conditions provides a profound understanding for the effects of different homogenization methods. Our findings would be beneficial to assist with standardization of fecal sample homogenization protocol.

Nonlinear effects in optical trapping of titanium dioxide and diamond nanoparticles

Optical trapping in biophysics typically uses micron-scale beads made of materials like polystyrene or glass to probe the target of interest. Using smaller beads made of higher-index materials could increase the time resolution of these measurements. We characterized the trapping of nanoscale beads made of diamond and titanium dioxide (TiO2) in a single-beam gradient trap. Calculating theoretical expectations for the trapping stiffness of these beads, we found good agreement with measured values. Trap stiffness was significantly higher for TiO2 beads, owing to notable enhancement from nonlinear optical effects, not previously observed for continuous-wave trapping. Trap stiffness was over 6-fold higher for TiO2 beads than polystyrene beads of similar size at 70 mW laser power. These results suggest that diamond and TiO2 nanobeads can be used to improve time resolution in optical tweezers measurements.

Laminar Free Convection In Horizontal Annulus Filled With Glass Beads And With Annular Fins On The Inner Cylinder

An experimental and numerical study has been carried out to investigate the heat transfer by natural convection and radiation in a two dimensional annulus enclosure filled with porous media (glass beads) between two horizontal concentric cylinders. The outer cylinders are of (100, 82 and70mm) outside diameters and the inner cylinder of 27 mm outside diameter with (or without) annular fins attached to it. Under steady state condition; the inner cylinder surface is maintained at a high temperature by applying a uniform heat flux and the outer cylinder surface at a low temperature inside a freezer. The experiments were carried out for an annulus filled with glass beads at a range of modified Rayleigh number (4.9 ≤ Ra≤ 69), radiation parameter (0<Rd<10), with fin length of (Hf=3, 7 and 11mm), with radius ratios of (Rr=(r1/r2) =0.1405,0.2045, 0.293 and 0.3649 ), number of fins (n=0, 12, 23 and 45). Finite difference method with Boussinesq's approximation is used to solve the continuity, energy and momentum equations. The numerical solution is capable of calculating the streamline, the temperature field, the velocity field, the local and average Nusselt number. A computer program in Mat lab has been built to carry out the numerical solution. The numerical study was done for a range of modified Rayleigh number (4.9 ≤ Ra ≤ 300). Results show that the average Nusselt number is nearly constant for Ra less than 100 and increased with an increase in modified Rayleigh number.Nusselt number hardly affected by glass beads size and insignificant affected by Rd for Ra less than 100. Decreasing Rr cause clearly increase in average Nusselt number and increasing fin length or fin number decrease heat transfer.