In this paper, the nonlinear differential equation for the convection of the temperature distribution of a STRAIGHT n with the thermal conductivity depends on the temperature is solved using Adomian Decomposition Method and Pad approximation (PADM) for boundary problems. Actual results are then compared with results obtained previously using digital solution by RungeKutta method and a differential transformation method (DTM) in order to verify the accuracy of the proposed method.

In this paper, the Chebychev spectral collocation method is applied for the thermal analysis ofCONVECTIVE-radiative STRAIGHT FINs with the temperature-dependent thermal conductivity. The developed heat transfermodel was used to analyse the thermal performance, establish the optimum thermal design parameters, and also, investigate the effects of thermo-geometric parameters and thermal conductivity (nonlinear) parameters on thethermal performance of the FIN. The results of this study reveal that the rate of heat transfer from the FIN increases asthe CONVECTIVE, radioactive, and magnetic parameters increase. This study establishes good agreement between theobtained results using Chebychev spectral collocation method and the results obtained using Runge-Kutta methodalong with shooting, homotopy perturbation, and adomian decomposition methods.

In this study, thermal performance across STRAIGHT CONVECTIVE-radiative FIN with temperature dependent thermal conductivity is considered. The variation of parameters method (VPM) is adopted to analyze the nonlinear higher order differential equations arising due to thermal conductivity and heat transfer coefficient on temperature distribution. Where pertinent parameters such as thermo geometric and radiation parameters effect on temperature profile are investigated. Result obtained depicts quantitative increase of thermo geometric parameter causes significant increase in temperature distribution due to increasing ratio of CONVECTIVE/conduction heat transfer which influence is significant toward FIN base. While increasing radiation parameter leads to decrease in temperature distribution due to increasing heat transfer from FINs surface to ambient environment. Comparative analysis of result obtained in study against literature proves to be in satisfactory agreement. Therefore study provides useful insight to FINs operational performance in devices such as radiators, boilers, refrigerator, oil pipelines amongst other heat transfer applications.

The development and production of high performance equipment necessitate the use of passive cooling technology. In this paper, heat transfer study of CONVECTIVE-radiative STRAIGHT FIN with temperature-dependent thermal conductivity under the influence of magnetic field is carried out using Legendre wavelet collocation method. The numerical solution is used to investigate the effects of magnetic, CONVECTIVE and radiative parameters on the thermal performance of the FIN. From the results, it is established that increase in magnetic, CONVECTIVE and radiative parameters increase the rate of heat transfer from the FIN and consequently improve the thermal performance of the FIN. The results obtained are compared with the results established results in literature and good agreements are found. The analysis can help in enhancing the understanding and analysis of the problem. Also, they can provide platform for improvement in the design of extended surfaces in heat transfer equipment under the influence of magnetic field.

Due to increasing applications of extended surfaces as passive methods of cooling, study of thermal behaviors and development of mathematical solutions to nonlinear thermal models of extended surfaces have been the subjects of research in cooling technology over the years. In the thermal analysis of FIN, various methods have been applied to solve the nonlinear thermal models. This paper focuses on the application of Legendre wavelet collocation method to the prediction of temperature distribution in longitudinal rectangular FIN with temperature-dependent thermal conductivity and internal heat generation. The numerical approximations by the method are used to carry out parametric studies of the effects of the model parameters on the temperature distribution in the FIN. The results show that the thermal performance of the FIN is favoured at low values of thermogeometric parameter and internal heat generation decreases the performance of the FIN. The results can serve as verification of the solutions of other methods of analysis of the component.

In this study, by using the FINite volume method, the heat transfer in a CONVECTIVE STRAIGHT FIN withtemperature-dependent thermal properties and an internal heat generation under multi-boiling heat transfer modesare analyzed. In this regard, the local heat transfer coefficient is considered to vary within a power-law function oftemperature. In the present study, the coexistence of all the boiling modes is taken into consideration. Thedeveloped heat transfer models and the corresponding numerical solutions are used to investigate the effects ofvarious thermo-geometric parameters on the thermal performance of the longitudinal rectangular FIN. The resultsshows that the FIN temperature distribution, the total heat transfer, and the FIN efficiency are significantly affected bythe thermo-geometric parameters of the FIN and the internal heat generation within the FIN. The obtained results canprovide a platform for improvements in the design of the FIN in the heat transfer equipment.

The influence of slight inclination, ‘α’ (i. e., 10°, 15°, and 20°) of the channel comprised of shrouded vertical rectangular non-isothermal FIN array has been computationally investigated. Simulations are performed to obtain the CONVECTIVE coefficient of heat transfer for the different dimensionless FIN spacing (S*= 0. 2, 0. 3, 0. 5), non-dimensional FIN tip to shroud clearances (C*= 0. 1, 0. 2 and 0. 3), Grashof numbers (Gr= 1. 08×105, 4. 42×105 and 11. 5×105), FIN lengths (L= 0. 25m and 0. 5m) and FIN heights (H= 0. 025m, 0. 04m, and 0. 055m). Hydrodynamic behavior of the fluid indicates that a significant amount of flow reversal occurs near the entrance of the channel at very low inclination which vanishes with the increase in inclination. Further, at higher length, reverse flow is found to occur only in the clearance zone. An increase in the value of ‘α’ from 10° to 20°, results in enhancement of CONVECTIVE coefficient up to a maximum of 161%. An increase in the value of FIN spacing from 0. 2 to 0. 5 results in the enhancement of the CONVECTIVE heat transfer coefficient. At α= 15° and 20°, the heat transfer is enhanced by 84. 1% and 101. 6%, respectively, while at α=10°, the same is reduced by 33. 3%. At lower FIN spacing (S*<0. 3) increase in C* tends to reduce the efficiency. Further, the efficiency of the FINite conductive FIN is found to reduce by almost 8% with an increase in Grashof number.

The aim of this study is to develop a unique perforated trapezoid-shaped plate-FIN channel. So, a numerical simulation is performed on the mentioned plates with different geometries. The laminar airflow (10≤Re≤1000) passes through the inter-FIN passages with perforated FINs, whose perforations are distributed equally throughout the duct. The effects of corrugation angle (ϕ), cross-section aspect ratio (α=H/Savg), and cross-section inclination angle (Ψ) are studied. This study has identified the improved performance of the Nusselt number and the Fanning friction factor (f) in a variety of Reynolds. A quantitative assessment of the improvement is done by measuring the area goodness factor (j/f) compared with a plain flat channel. Based on the results, with increasing ϕ from 30˚ to 45˚, the mentioned channel's performance improves. However, as the angle increases more, performance begins to decrease. The channel's performance improves with increasing α. Also, the performance improves by changing Ψ from 90˚ to 76.60˚. Based on the results, for a perforated case with ϕ=45˚, α=10, and Ψ=90˚ at Re=200, versus the non-perforated FIN, f decreases ~9%, and j/f increases ~61%. Also, for the above-mentioned perforated case, when Ψ is changed from 90˚ to 76.60˚, at Re=200, f decreases ~1.3%, and j/f increases ~8.2%.

Introduction: Broccoli is a rich source of minerals such as potassium, phosphorus, calcium and sodium. Additionally, broccoli provides vitamins, especially vitamin C, vitamin A and folic acid. In addition, it has been reported as a one of the main sources of natural antioxidants such as phenolic compounds, glucosinolates and isothiocyanates. Because of the high corruptibility of broccoli, it is very important to keep its effective components as much as possible. Drying is the most common method for enhance the shelf life of food products. The foam mat drying method was developed in the 1960s. This method involves mixing pulp or fruit and vegetable juices with a foaming agent and a foam stabilizer to prepare a stable foam that is spread and dried on a tray, then the dried product is ground to a powdered product. In this technique, due to increasing of the material area, the drying rate is high. CONVECTIVE hot air is generally chosen as the drying medium of the foam mat method. The disadvantage of this drying method is the poor heat transfer of the air around the foam. Microwave heating, with its ability to produce volumetric heat inside the material, can overcome this limitation. Microwave energy can penetrate directly into the foamed pulp to evaporate moisture inside the foam,continuously generated vapors stimulate foam bubbles, which expand the evaporation level and speed up the drying process even more. There are many strategies to improve the quality of microwave-dried products, such as combining microwave and CONVECTIVE hot air, intermittent drying, and microwave-vacuum drying. The combination of microwave and CONVECTIVE hot air has been used successfully for a number of agricultural products such as garlic, grapes, carrots, kiwis and blueberries. The combination of these two methods has a shorter drying time than single CONVECTIVE hot air, and the FINal sample will have higher quality. Material and methods: Broccoli was purchased from the local market of Tabriz and its enzymes were inactivated by blanching in 90°, C hot water for 4 minutes and then immediately cooled in ice water for 5 minutes. It was then pulped and stored in a freezer at minus 18°, C until drying experiments were performed. Broccoli pulp was first thawed before drying experiments. 3% (w/w) egg white as foaming agent and 0. 5% (w/w) methyl cellulose solution as stabilizer agent were used to prepare the broccoli foam. The foam was spread to a thickness of 5 mm on a glass plate and then it was dried with different drying methods including CONVECTIVE hot air (at 40°, C and air velocity of 1m/s), microwave (90w) and combination of microwave and convection as pre and post treatment (MWCHA and CHA-MW). The moisture content of samples was measured at 10 minute intervals (in CHA method) and at 2 minute intervals (in MW method), and the drying process was terminated when moisture content of the samples reached 0. 04 g water/g dry solids. The produced powders were then scratched off by a special spatula and were immediately ground in a crucible in order to prevent further moisture absorption and kept in the refrigerator until further testing. Results and discussion: The combination of microwave and CONVECTIVE hot air (in both pre and post treatment) compared to microwave method, had lower effective moisture diffusivity coefficient and drying rate but higher energy consumption. The average of moisture content and moisture ratio was also affected by drying method and the combination of microwave and CONVECTIVE hot air (MW-CHA and CHA-MW). In MW-CHA, the average of moisture content and moisture ratio was higher than MW and CHA drying method, but in CHA-MW, the average of moisture content and the moisture ratio was the lowest obtained. Among the four drying methods, the hot air drying method had the lowest drying rate due to the hardening of the surface due to the loss of surface moisture. This phenomenon slows down the exit of moisture from the product and reduces the drying speed. In the microwave method, in the early stages of drying, the samples have high humidity. High humidity is the main reason for volumetric heating in the microwave method, in that bipolar molecules absorb a significant part of the microwave energy and lead to an increase in product temperature and rapid transfer of moisture to the surface. The flow of water vapor from the inner parts to the surface of the product creates a porous structure, resulting in faster evaporation of moisture, and ultimately increases the drying speed. Therefore, the highest drying rate was observed in the microwave drying method. The passage of time and the reduction of moisture in the product reduce the absorption of microwave power and, as the drying process progresses, leads to a slowdown in the drying speed. Compared to the combined drying methods, due to the prevention of surface drying in the microwave-hot air (MWCHA) method, this method had a higher drying rate than the hot air-microwave (CHA-MW) method and hot air alone. The mean drying time were from low to high: microwave (48 minutes), hot airmicrowave (70 minutes), microwave-hot air (102. 16 minutes) and hot air (120 minutes), respectively. The effective moisture diffusion coefficient of all four drying methods was significantly different from each other at the level of 5% probability and were from high to low related to microwave, hot air-microwave, microwave-hot air and hot air, respectively. The high effective diffusion coefficient of moisture in microwave drying is related to its volumetric heating mechanism. In a microwave field, the core temperature of the product rises, creating a pressure difference between the core and the surface of the product (Junkoria et al. 2017), creating a more porous structure and more vapor permeability, and ultimately increasing the effective moisture diffusion coefficient due to faster heating. (Dehghani Khiavi et al. 1399). Hot air method has the lowest effective moisture diffusion coefficient value, due to the low air temperature (40°, C), because there is a direct relationship between the effective diffusion coefficient of humidity and temperature, and on the other hand, the hot air energy for moisture exit is lower than other methods, so the effective moisture diffusion coefficient in this method is at its lowest value compared to other drying methods, and this is the reason for the slower drying speed in this method. In the combination of hot air and microwave, when hot air (as a pre-treatment) is applied at the beginning of the process, the drying and dehumidification process is controlled by the microwave and the effective moisture diffusion coefficient in this method are higher than hot air. When hot air is applied at the end of the process (as a post-treatment), the drying process is controlled by hot air and the effective moisture diffusion coefficient are lower than hot airmicrowave, but higher than hot air alone. Conclusion: According to the least energy consumption, drying time, moisture content, moisture ratio and the most effective moisture diffusivity coefficient and drying rate, MW and CHA-MW were the optimum methods for drying the broccoli foam (with 0. 88 and 0. 7 desirability, respectively). The use of microwave energy as a pretreatment for hot air (CHA-MW) was able to significantly reduce the average moisture content and moisture ratio compared to the microwave method alone, and produce a powder with lower moisture content and longer shelf life.