This study investigates heat, mass transport, and entropy production in Ellis nanofluid flow through an inclined permeable microchannel, considering Navier's slip effects with convective boundary conditions. It incorporates nanoparticle's thermophoresis and Brownian motion effects under a transverse magnetic field, with fluid suction and injection at microchannel walls. Under appropriate physical assumptions, the problem is presented as nonlinear ordinary differential equations, which are later nondimensionalized. The MATLAB bvp4c solver is used for numerical solutions of the transformed equations. Graphical depictions in the study illustrate how various factors influence velocity, temperature, concentration, Bejan number, and entropy generation. Engineering parameters, affected by changes in critical factors, are presented in tabular format, including the skin friction coefficient, Nusselt number, and Sherwood number. Notably, the enhancement in Ellis fluid parameter has a dual effect, enhancing velocity and Bejan number in the microchannel's lower half, while reversing in the upper half. For the increment in Ellis parameter, the impact on Bejan number for 0.5 is significant and the effect on entropy production contrasts with that of Bejan number. This research offers practical insights for designing efficient microfluidic heat exchangers and developing advanced nanofluids for improved thermal performance while minimizing entropy generation. Additionally, it underscores the potential for innovation within the domain of microfluidics and nanomaterial‐driven heat transfer systems. Furthermore, it should be noted that the flow behavior of Ellis nanofluids within microchannels can closely replicate natural flow patterns found in biological systems, offering insights that could have numerous applications in biology and related fields.
{"title":"Analysis of entropy generation and MHD thermo‐solutal convection flow of Ellis nanofluid through inclined microchannel","authors":"Debabrata Das, O. D. Makinde, R. R. Kairi","doi":"10.1002/zamm.202300831","DOIUrl":"https://doi.org/10.1002/zamm.202300831","url":null,"abstract":"This study investigates heat, mass transport, and entropy production in Ellis nanofluid flow through an inclined permeable microchannel, considering Navier's slip effects with convective boundary conditions. It incorporates nanoparticle's thermophoresis and Brownian motion effects under a transverse magnetic field, with fluid suction and injection at microchannel walls. Under appropriate physical assumptions, the problem is presented as nonlinear ordinary differential equations, which are later nondimensionalized. The MATLAB bvp4c solver is used for numerical solutions of the transformed equations. Graphical depictions in the study illustrate how various factors influence velocity, temperature, concentration, Bejan number, and entropy generation. Engineering parameters, affected by changes in critical factors, are presented in tabular format, including the skin friction coefficient, Nusselt number, and Sherwood number. Notably, the enhancement in Ellis fluid parameter has a dual effect, enhancing velocity and Bejan number in the microchannel's lower half, while reversing in the upper half. For the increment in Ellis parameter, the impact on Bejan number for 0.5 is significant and the effect on entropy production contrasts with that of Bejan number. This research offers practical insights for designing efficient microfluidic heat exchangers and developing advanced nanofluids for improved thermal performance while minimizing entropy generation. Additionally, it underscores the potential for innovation within the domain of microfluidics and nanomaterial‐driven heat transfer systems. Furthermore, it should be noted that the flow behavior of Ellis nanofluids within microchannels can closely replicate natural flow patterns found in biological systems, offering insights that could have numerous applications in biology and related fields.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141922550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Philopatir B. Raafat, Muhammad AbuGhanem, Fayez N. Ibrahim
In this paper, we delve into the behavior of binary micropolar nanofluids, specifically micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade, within the parabolic trough solar collector (PTSC) configurations. The primary objective is to enhance the collective efficiency of this device by means of a comprehensive comparison amongst the three aforementioned nanofluids. The governing equations, including continuity, linear momentum, angular momentum, and energy equations, were systematically formulated. Subsequently, the introduction of suitable similarity variables facilitated the transformation of the intricate partial differential equations into manageable ordinary differential equations. These resultant equations were then tackled utilizing the shooting method via the bvp4c numerical package in MATLAB. The study critically examines the influence of diverse parameters that dictate the flow dynamics of the nanofluids. This encompasses nanofluid velocity, angular velocity, temperature distribution, entropy generation, skin friction coefficient, and local Nusselt number. Remarkably, the research uncovers that the maximum temperature levels experienced enhancements of 12.1134%, 12.0616%, and 11.0645% for the micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade nanofluids, respectively. These results imply that the introduction of these binary micropolar nanofluids leads to notable thermal enhancements in the PTSCs settings.
{"title":"Comparative characterization of heat transfer and entropy generation of micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade binary nanofluids in PTSCs settings","authors":"Philopatir B. Raafat, Muhammad AbuGhanem, Fayez N. Ibrahim","doi":"10.1002/zamm.202400028","DOIUrl":"https://doi.org/10.1002/zamm.202400028","url":null,"abstract":"In this paper, we delve into the behavior of binary micropolar nanofluids, specifically micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade, within the parabolic trough solar collector (PTSC) configurations. The primary objective is to enhance the collective efficiency of this device by means of a comprehensive comparison amongst the three aforementioned nanofluids. The governing equations, including continuity, linear momentum, angular momentum, and energy equations, were systematically formulated. Subsequently, the introduction of suitable similarity variables facilitated the transformation of the intricate partial differential equations into manageable ordinary differential equations. These resultant equations were then tackled utilizing the shooting method via the bvp4c numerical package in MATLAB. The study critically examines the influence of diverse parameters that dictate the flow dynamics of the nanofluids. This encompasses nanofluid velocity, angular velocity, temperature distribution, entropy generation, skin friction coefficient, and local Nusselt number. Remarkably, the research uncovers that the maximum temperature levels experienced enhancements of 12.1134%, 12.0616%, and 11.0645% for the micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade nanofluids, respectively. These results imply that the introduction of these binary micropolar nanofluids leads to notable thermal enhancements in the PTSCs settings.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141924087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present paper is concerned with a fourth‐order Allen–Cahn model with logarithmic potential and mass source that describes the process of phase separation in two‐component systems accompanied by a flux of material. The existence of a global weak solution is obtained under appropriate hypotheses on the source term. Furthermore, we study its Cahn–Hilliard limit as a small parameter goes to zero. The main difficulty in the mathematical analysis of the model lies in the presence of the source term that leads to the nonconservation of mass, contrary to the original Cahn–Hilliard theory.
{"title":"A generalized Allen–Cahn model with mass source and its Cahn–Hilliard limit","authors":"Wei Shi, Xinbo Yang, Lubin Cui, Alain Miranville","doi":"10.1002/zamm.202301026","DOIUrl":"https://doi.org/10.1002/zamm.202301026","url":null,"abstract":"The present paper is concerned with a fourth‐order Allen–Cahn model with logarithmic potential and mass source that describes the process of phase separation in two‐component systems accompanied by a flux of material. The existence of a global weak solution is obtained under appropriate hypotheses on the source term. Furthermore, we study its Cahn–Hilliard limit as a small parameter goes to zero. The main difficulty in the mathematical analysis of the model lies in the presence of the source term that leads to the nonconservation of mass, contrary to the original Cahn–Hilliard theory.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141923379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad AbuGhanem, Philopatir B. Raafat, Fayez N. Ibrahim
Solar energy holds promise as a sustainable and environmentally friendly source of power. In this study, we focus on improving the thermal efficiency of parabolic trough solar collectors (PTSCs) by investigating the performance of three different binary micropolar nanofluids – micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson – when used as heat transfer fluids within these collectors, with engine oil as the base fluid. The problem studied revolves around enhancing the heat transfer characteristics within PTSCs, crucial for maximizing energy conversion efficiency in solar power generation. By exploring the behavior of these nanofluids under various flow conditions, we aim to optimize the design and operation of PTSC systems for improved performance and sustainability. The importance of this research lies in its potential to significantly enhance the efficiency of solar energy harvesting, thereby contributing to the transition toward cleaner energy sources and reducing dependence on fossil fuels. Additionally, the findings have implications for diverse applications, including solar aviation, solar‐powered maritime vessels, solar thermal power plants, industrial process heating, and solar‐driven water pumping mechanisms, where improved heat transfer efficiency is paramount for enhancing overall system performance and reducing operational costs. Furthermore, the investigation delves into the influence of various factors governing the flow of these binary micropolar nanofluids within PTSC setups, including aspects such as velocity, thermal characteristics, entropy generation, skin friction, drag force, and local Nusselt number. The results notably reveal substantial enhancements in thermal efficiency, with maximal relative enhancements quantified as 22.1768%, 19.3662%, and 17.7349% for micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson nanofluids, respectively.
{"title":"An in‐depth comparative analysis of entropy generation and heat transfer in micropolar‐Williamson, micropolar‐Maxwell, and micropolar‐Casson binary nanofluids within PTSCs","authors":"Muhammad AbuGhanem, Philopatir B. Raafat, Fayez N. Ibrahim","doi":"10.1002/zamm.202300912","DOIUrl":"https://doi.org/10.1002/zamm.202300912","url":null,"abstract":"Solar energy holds promise as a sustainable and environmentally friendly source of power. In this study, we focus on improving the thermal efficiency of parabolic trough solar collectors (PTSCs) by investigating the performance of three different binary micropolar nanofluids – micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson – when used as heat transfer fluids within these collectors, with engine oil as the base fluid. The problem studied revolves around enhancing the heat transfer characteristics within PTSCs, crucial for maximizing energy conversion efficiency in solar power generation. By exploring the behavior of these nanofluids under various flow conditions, we aim to optimize the design and operation of PTSC systems for improved performance and sustainability. The importance of this research lies in its potential to significantly enhance the efficiency of solar energy harvesting, thereby contributing to the transition toward cleaner energy sources and reducing dependence on fossil fuels. Additionally, the findings have implications for diverse applications, including solar aviation, solar‐powered maritime vessels, solar thermal power plants, industrial process heating, and solar‐driven water pumping mechanisms, where improved heat transfer efficiency is paramount for enhancing overall system performance and reducing operational costs. Furthermore, the investigation delves into the influence of various factors governing the flow of these binary micropolar nanofluids within PTSC setups, including aspects such as velocity, thermal characteristics, entropy generation, skin friction, drag force, and local Nusselt number. The results notably reveal substantial enhancements in thermal efficiency, with maximal relative enhancements quantified as 22.1768%, 19.3662%, and 17.7349% for micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson nanofluids, respectively.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141926657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Saima Afzal, I. Siddique, Sohaib Abdal, Sajjad Hussain, M. Salimi, Ali Ahmadian
The utilization of nanoentities in common fluids has opened new opportunities in the area of heat transportation. The rising requirements to enhance the efficiency of compact heat exchangers can be achieved by using various nanofluids. In this article, the thermal output of Maxwell and Williamson nanofluids transport over a prolonging sheet with bioconvection of self‐motivated organisms is scrutinized. A magnetic flux and the porous effects of a medium influence the flow of fluids. The fundamental principles for conservation of mass, concentration, momentum, and energy yield a nonlinear set of partial differential equations that can then be altered into ordinary differential form. A heat transfer flux is presented along with temperature boundary conditions, PST, and PHF (prescribed surface temperature and prescribed heat flux). The numerical results are acquired by executing the Runge–Kutta method with a shooting procedure in MATLAB coding. By fluctuating the inputs of influential variables of the dependent functions, a precise overview of the scheme is acquired. It can be seen that velocity decreases with the rising values of buoyancy ratio, magnetic force, Raleigh number, and porosity. Also, the temperature of the fluids begins to rise directly with the rising values of thermophoresis and Brownian motion parameters. The present study addresses bioconvection, non‐Fourier heat flow, and thermal radiations while combining the special properties of Williamson and Maxwell nanofluids. The field of biomedical engineering may benefit from this study, particularly with regard to therapies for hyperthermia and drug delivery systems. This study can be useful in cutting‐edge cooling systems, bioengineering, solar energy conversion and biotechnology.
{"title":"The effects of bioconvection, non‐Fourier heat flux, and thermal radiations on Williamson nanofluids and Maxwell nanofluids transportation with prescribed thermal conditions","authors":"Saima Afzal, I. Siddique, Sohaib Abdal, Sajjad Hussain, M. Salimi, Ali Ahmadian","doi":"10.1002/zamm.202300255","DOIUrl":"https://doi.org/10.1002/zamm.202300255","url":null,"abstract":"The utilization of nanoentities in common fluids has opened new opportunities in the area of heat transportation. The rising requirements to enhance the efficiency of compact heat exchangers can be achieved by using various nanofluids. In this article, the thermal output of Maxwell and Williamson nanofluids transport over a prolonging sheet with bioconvection of self‐motivated organisms is scrutinized. A magnetic flux and the porous effects of a medium influence the flow of fluids. The fundamental principles for conservation of mass, concentration, momentum, and energy yield a nonlinear set of partial differential equations that can then be altered into ordinary differential form. A heat transfer flux is presented along with temperature boundary conditions, PST, and PHF (prescribed surface temperature and prescribed heat flux). The numerical results are acquired by executing the Runge–Kutta method with a shooting procedure in MATLAB coding. By fluctuating the inputs of influential variables of the dependent functions, a precise overview of the scheme is acquired. It can be seen that velocity decreases with the rising values of buoyancy ratio, magnetic force, Raleigh number, and porosity. Also, the temperature of the fluids begins to rise directly with the rising values of thermophoresis and Brownian motion parameters. The present study addresses bioconvection, non‐Fourier heat flow, and thermal radiations while combining the special properties of Williamson and Maxwell nanofluids. The field of biomedical engineering may benefit from this study, particularly with regard to therapies for hyperthermia and drug delivery systems. This study can be useful in cutting‐edge cooling systems, bioengineering, solar energy conversion and biotechnology.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141927926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Faizan Ahmed, Humaira Yasmin, F. Ali, Z. Raizah, S. Lone, Anwar Saeed
In order to keep mechanical processes running smoothly, there is a growing need for effective heat transport. The present study aims to explore the variation of heat on time‐dependent maximum hydrodynamic drag (MHD) second‐grade nanofluids perceiving motile gyrotactic microbe with stretchable sheets. We process the analysis of the thermal energy distribution by using the convective boundary conditions. In addition to this, we take both the chemical reaction and the heat radiation into consideration. The governing nonlinear (PDEs) are converted into (ODEs) by a similarity transformation and then computed BVP4c technique. The multiple results are marked in the range of opposing flows only. Then, the effects of numerous physical variables on temperature, concentration, fluid velocity, and motile microorganisms are scrutinized using different graphical representations. The unsteady parameter and second‐grade fluid also strengthen for higher qualities, while inverse conduct is identified for a magnetic field framework. Finally, the temperature field cultivates a more significant assessment of the Biot number, and reverse behavior is observed for the Prandtl number. The obtained results are found appropriate to the existing literature.
{"title":"MHD flow of second‐grade fluid containing nanoparticles having gyrotactic microorganisms across heated convective sheet","authors":"Muhammad Faizan Ahmed, Humaira Yasmin, F. Ali, Z. Raizah, S. Lone, Anwar Saeed","doi":"10.1002/zamm.202300950","DOIUrl":"https://doi.org/10.1002/zamm.202300950","url":null,"abstract":"In order to keep mechanical processes running smoothly, there is a growing need for effective heat transport. The present study aims to explore the variation of heat on time‐dependent maximum hydrodynamic drag (MHD) second‐grade nanofluids perceiving motile gyrotactic microbe with stretchable sheets. We process the analysis of the thermal energy distribution by using the convective boundary conditions. In addition to this, we take both the chemical reaction and the heat radiation into consideration. The governing nonlinear (PDEs) are converted into (ODEs) by a similarity transformation and then computed BVP4c technique. The multiple results are marked in the range of opposing flows only. Then, the effects of numerous physical variables on temperature, concentration, fluid velocity, and motile microorganisms are scrutinized using different graphical representations. The unsteady parameter and second‐grade fluid also strengthen for higher qualities, while inverse conduct is identified for a magnetic field framework. Finally, the temperature field cultivates a more significant assessment of the Biot number, and reverse behavior is observed for the Prandtl number. The obtained results are found appropriate to the existing literature.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bathmanaban Paandurangan, Siva Errappa Parthasarathy, Dharmendra Tripathi, O. A. Bég
The primary objective of the present article is to investigate the heat and mass transfer in mixed convection peristaltic flow of Casson nanofluid through an asymmetric permeable channel filled with a porous medium in the presence of electroosmosis. Magnetohydrodynamics and radiative heat transfer are also considered. The study is motivated by industrial micro‐pumping systems utilizing multi‐functional nanomaterials. Researchers have investigated the distinct temperature and rheological properties of Casson nanofluids. Solutal molecular diffusion and nanoparticle diffusion are both examined. Mixing nanoparticles with Casson fluid alters its flow characteristics and heat transmission, amalgamating different properties that are useful in a wide range of industrial and scientific applications. Buongiorno's two‐component nanoscale model is deployed for simulating nanofluid transport, and the Rosseland diffusion flux is utilized for optically thick electromagnetic liquids. Heat generation or absorption and cross‐diffusion (Soret and Dufour) effects are also incorporated in the model. An efficient analytical approach known as the long wavelength‐low Reynolds number lubrication approximation (LWL‐LRN) is utilized to solve the non‐dimensional boundary value problem. Validation of the solutions with previous studies is included. Graphs are presented using MATLAB 2022b to visualize the influence of key parameters including permeability, magnetic field, thermal radiation, Grashof number, Brownian motion, thermophoresis, electrical field and Prandtl number on transport characteristics (velocity, temperature, concentration), and trapping phenomena associated with peristaltic propulsion. As thermophoresis and Brownian parameters are intensified, there is a strong response in nanoparticles which induces axial acceleration, as observed at locations y = 0.15, where u = 0.191, and y = 0.33, where u is elevated to 0.14. An increase in radiation parameter () results in a depletion in axial velocity magnitudes along the left half of the wall and also modifies velocity distribution in the right section of the microchannel. An increase in the thermal radiation parameter (Rn) and heat absorption (sink) is found to suppress temperatures. Increasing heat generation, thermal Grashof number (Gr), and solutal Grashof number (Gc) decelerate axial flow in the left half space but accelerate flow in the right half space of the micro‐channel. Increasing radiation parameters and thermal Biot number boost temperatures when heat sink is present but reduce them when heat source (generation) is present. Increasing radiation parameter boosts nanoparticle volume fraction (concentration) whereas an elevation in heat generation and thermal Biot number both induce the opposite effect. Increasing the magnetic field damps the flow and reduces the number of boluses present. However, bolus volume increases with greater thermal Grashof Number , Darcy (permeability) number , and Helmholtz‐Smoluc
本文的主要目的是研究在电渗存在的情况下，卡松纳米流体通过充满多孔介质的非对称渗透通道的混合对流蠕动流中的传热和传质问题。同时还考虑了磁流体力学和辐射传热。这项研究的动机是利用多功能纳米材料的工业微泵系统。研究人员已经研究了卡松纳米流体的独特温度和流变特性。对溶液分子扩散和纳米粒子扩散进行了研究。纳米粒子与卡松流体的混合改变了其流动特性和热传导，融合了不同的特性，这些特性在广泛的工业和科学应用中非常有用。Buongiorno 的双组分纳米尺度模型用于模拟纳米流体的传输，而 Rosseland 扩散通量则用于光厚电磁液体。该模型还纳入了热量产生或吸收以及交叉扩散（索雷特和杜福尔）效应。利用被称为长波长-低雷诺数润滑近似（LWL-LRN）的高效分析方法来解决非维度边界值问题。此外，还将根据之前的研究对解决方案进行验证。使用 MATLAB 2022b 绘制了图表，以直观显示关键参数的影响，包括渗透率、磁场、热辐射、格拉肖夫数、布朗运动、热泳、电场和普朗特尔数对传输特性（速度、温度、浓度）的影响，以及与蠕动推进相关的捕获现象。随着热泳和布朗运动参数的增加，纳米粒子会产生强烈的反应，从而引起轴向加速，如在 y = 0.15（u = 0.191）和 y = 0.33（u 升至 0.14）处观察到的情况。辐射参数（）的增加会导致沿左半壁的轴向速度减弱，同时也会改变微通道右段的速度分布。热辐射参数（Rn）和吸热（sink）的增加会抑制温度。增加发热量、热格拉肖夫数（Gr）和溶质格拉肖夫数（Gc）会减缓微通道左半部空间的轴向流动，但会加速微通道右半部空间的流动。增加辐射参数和热毕奥特数会在有散热器时提高温度，但在有热源（发电）时则会降低温度。增加辐射参数会提高纳米粒子的体积分数（浓度），而增加发热量和热毕奥特数则会产生相反的效果。增加磁场会抑制气流并减少栓子的数量。然而，随着热格拉肖夫数、达西（渗透）数和亥姆霍兹-斯莫卢霍夫斯基速度（即更强的轴向电场）的增加，颗粒体积也会增加。
{"title":"The impact of double‐diffusive convection on electroosmotic peristaltic transport of magnetized Casson nanofluid in a porous asymmetric channel","authors":"Bathmanaban Paandurangan, Siva Errappa Parthasarathy, Dharmendra Tripathi, O. A. Bég","doi":"10.1002/zamm.202300771","DOIUrl":"https://doi.org/10.1002/zamm.202300771","url":null,"abstract":"The primary objective of the present article is to investigate the heat and mass transfer in mixed convection peristaltic flow of Casson nanofluid through an asymmetric permeable channel filled with a porous medium in the presence of electroosmosis. Magnetohydrodynamics and radiative heat transfer are also considered. The study is motivated by industrial micro‐pumping systems utilizing multi‐functional nanomaterials. Researchers have investigated the distinct temperature and rheological properties of Casson nanofluids. Solutal molecular diffusion and nanoparticle diffusion are both examined. Mixing nanoparticles with Casson fluid alters its flow characteristics and heat transmission, amalgamating different properties that are useful in a wide range of industrial and scientific applications. Buongiorno's two‐component nanoscale model is deployed for simulating nanofluid transport, and the Rosseland diffusion flux is utilized for optically thick electromagnetic liquids. Heat generation or absorption and cross‐diffusion (Soret and Dufour) effects are also incorporated in the model. An efficient analytical approach known as the long wavelength‐low Reynolds number lubrication approximation (LWL‐LRN) is utilized to solve the non‐dimensional boundary value problem. Validation of the solutions with previous studies is included. Graphs are presented using MATLAB 2022b to visualize the influence of key parameters including permeability, magnetic field, thermal radiation, Grashof number, Brownian motion, thermophoresis, electrical field and Prandtl number on transport characteristics (velocity, temperature, concentration), and trapping phenomena associated with peristaltic propulsion. As thermophoresis and Brownian parameters are intensified, there is a strong response in nanoparticles which induces axial acceleration, as observed at locations y = 0.15, where u = 0.191, and y = 0.33, where u is elevated to 0.14. An increase in radiation parameter () results in a depletion in axial velocity magnitudes along the left half of the wall and also modifies velocity distribution in the right section of the microchannel. An increase in the thermal radiation parameter (Rn) and heat absorption (sink) is found to suppress temperatures. Increasing heat generation, thermal Grashof number (Gr), and solutal Grashof number (Gc) decelerate axial flow in the left half space but accelerate flow in the right half space of the micro‐channel. Increasing radiation parameters and thermal Biot number boost temperatures when heat sink is present but reduce them when heat source (generation) is present. Increasing radiation parameter boosts nanoparticle volume fraction (concentration) whereas an elevation in heat generation and thermal Biot number both induce the opposite effect. Increasing the magnetic field damps the flow and reduces the number of boluses present. However, bolus volume increases with greater thermal Grashof Number , Darcy (permeability) number , and Helmholtz‐Smoluc","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work investigates the bioconvection flow of oxytactic microorganisms and nanoparticle‐enhanced phase change material (NEPCM) within a hexagonal‐shaped cavity containing a rotated cross fin, utilizing the incompressible smoothed particle hydrodynamics (ISPH) method based on a time‐fractional derivative. The study considers the circular rotation of an inner cross fin and the presence of two rectangular heat sources on the plane walls inside the hexagonal cavity. The novelty of this work is its integration of a hexagonal‐shaped cavity with a rotated cross fin and the use of a time‐fractional derivative in the ISPH method to analyze bioconvection flow, offering new insights into the interaction between microorganism motion and heat transfer dynamics in complex geometries. The effects of Darcy, Hartmann, Lewis, Peclet, Rayleigh, and bioconvection Rayleigh numbers on isotherms, heat capacity ratio, microorganism density, velocity fields, and average Nusselt number are analyzed. The key findings demonstrate the significant impact of Rayleigh and bioconvection Rayleigh numbers in enhancing heat distribution and velocity fields, thereby significantly influencing microorganism motion. Due to Lorentz forces, the velocity field decreases by with an increase in the Hartmann number from 0 to 50. The resistance of the nanofluid's velocity becomes apparent as the Darcy number decreases. Increasing Lewis and Péclet numbers cause the microorganisms to shift towards the cavity's boundaries.
{"title":"The time‐fractional ISPH method for fin circular rotation on MHD bioconvection flow of oxytactic microorganisms and NEPCM within a hexagonal‐shaped cavity","authors":"Fawzia Awad, Z. Raizah, Abdelraheem M. Aly","doi":"10.1002/zamm.202400132","DOIUrl":"https://doi.org/10.1002/zamm.202400132","url":null,"abstract":"This work investigates the bioconvection flow of oxytactic microorganisms and nanoparticle‐enhanced phase change material (NEPCM) within a hexagonal‐shaped cavity containing a rotated cross fin, utilizing the incompressible smoothed particle hydrodynamics (ISPH) method based on a time‐fractional derivative. The study considers the circular rotation of an inner cross fin and the presence of two rectangular heat sources on the plane walls inside the hexagonal cavity. The novelty of this work is its integration of a hexagonal‐shaped cavity with a rotated cross fin and the use of a time‐fractional derivative in the ISPH method to analyze bioconvection flow, offering new insights into the interaction between microorganism motion and heat transfer dynamics in complex geometries. The effects of Darcy, Hartmann, Lewis, Peclet, Rayleigh, and bioconvection Rayleigh numbers on isotherms, heat capacity ratio, microorganism density, velocity fields, and average Nusselt number are analyzed. The key findings demonstrate the significant impact of Rayleigh and bioconvection Rayleigh numbers in enhancing heat distribution and velocity fields, thereby significantly influencing microorganism motion. Due to Lorentz forces, the velocity field decreases by with an increase in the Hartmann number from 0 to 50. The resistance of the nanofluid's velocity becomes apparent as the Darcy number decreases. Increasing Lewis and Péclet numbers cause the microorganisms to shift towards the cavity's boundaries.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141927761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this study is to minimize entropy in the MHD Eyring‐Powell fluid through a semi‐porous curved channel. The flow phenomena are examined under the consideration of joule heating, viscous heating, thermophoresis, and Brownian motion. The motivation of this research is to minimize entropy production in curved porous channel because thermal systems become more efficient as a result of decreased energy consumption, operational expenses, and experimental costs. This approach is useful in designing industrial equipment that requires efficient thermal management, such as fuel cells, chemical processing, and advanced refrigeration systems. The coupled boundary layer equations of the problem are highly nonlinear PDEs, which are transformed into systems of coupled ODEs by using similarity variables. The solution of a coupled system of ODEs is obtained numerically via Bvp4c. The effect of several physical parameters for entropy analysis, Bejan number, concentration, and velocity/temperature are illustrated and analyzed using graphs. Furthermore, the computational outcomes of physical quantities, for example, heat and mass transfer rate are also presented. Results indicated that the increasing value of the Reynolds number increases the entropy generation rate, while the reverse tendency is noticed for the Eyring‐Powell parameter. The rising values of the Brownian parameter increase the Bejan number after its decrease, while reverse behavior is observed for the thermophoresis parameter.
{"title":"Irreversibility analysis of Eyring Powell nanofluid flow in curved porous channel","authors":"Muhammad Sami‐Ul‐Haq, Muhammad Bilal Ashraf","doi":"10.1002/zamm.202300848","DOIUrl":"https://doi.org/10.1002/zamm.202300848","url":null,"abstract":"The aim of this study is to minimize entropy in the MHD Eyring‐Powell fluid through a semi‐porous curved channel. The flow phenomena are examined under the consideration of joule heating, viscous heating, thermophoresis, and Brownian motion. The motivation of this research is to minimize entropy production in curved porous channel because thermal systems become more efficient as a result of decreased energy consumption, operational expenses, and experimental costs. This approach is useful in designing industrial equipment that requires efficient thermal management, such as fuel cells, chemical processing, and advanced refrigeration systems. The coupled boundary layer equations of the problem are highly nonlinear PDEs, which are transformed into systems of coupled ODEs by using similarity variables. The solution of a coupled system of ODEs is obtained numerically via Bvp4c. The effect of several physical parameters for entropy analysis, Bejan number, concentration, and velocity/temperature are illustrated and analyzed using graphs. Furthermore, the computational outcomes of physical quantities, for example, heat and mass transfer rate are also presented. Results indicated that the increasing value of the Reynolds number increases the entropy generation rate, while the reverse tendency is noticed for the Eyring‐Powell parameter. The rising values of the Brownian parameter increase the Bejan number after its decrease, while reverse behavior is observed for the thermophoresis parameter.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141927055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hassan Waqas, Md. Jahid Hasan, Shahrin Jahan Jaima, Syed Muhammad Raza Shah Naqvi, U. Manzoor, Dong Liu, Taseer Muhammad
The investigation of mixed convective flow involving microorganisms in nanofluid has garnered considerable interest in recent times owing to its extensive applicability in the biomedical domain. However, there has been a lack of study investigating a comprehensive parameter analysis for the flow of a third‐grade nanofluid around a cylinder in the presence of microorganisms. This study focuses on numerically investigating the flow of nanofluid around a stretched cylinder in the presence of motile microorganisms. The study also considers convective boundary conditions. Moreover, this study explores the nanofluid qualities related to Brownian motion and thermophoresis diffusion characteristics. The variable parameters include the Prandtl number (Pr), Peclet number (Pe), buoyancy ratio parameter (Nr), mixed convection parameter (), bioconvection Lewis number (Lb), Biot number (Bi), and Marangoni number (Ma). The bvp4c issue solver tool in MATLAB is used to numerically solve the nonlinear governing differential equations. The numerical model has been validated using prior papers. Graphical representations are created to depict several important measurements, such as velocity streamlines, velocity profiles, temperature distributions, nanoparticle concentrations, densities of gyrotactic motile microorganisms, local Nusselt numbers, skin friction, and Sherwood numbers. The link between the Nusselt number and the parameters Nt and Rd suggests that as Nt falls and Rd increases, the Nusselt number increases. The skin friction value is directly proportional to the values of Nr and Nc. There is a positive correlation between the rise in the local mass transfer rate and the values of Rd and Nt. The population of mobile microorganisms grows as the values of Lb and Pe decrease.
由于纳米流体在生物医学领域的广泛应用，涉及微生物的纳米流体混合对流研究近来引起了人们的极大兴趣。然而，目前还缺乏对存在微生物的第三级纳米流体在圆柱体周围流动的综合参数分析研究。本研究的重点是对运动微生物存在时纳米流体在拉伸圆柱体周围的流动进行数值研究。研究还考虑了对流边界条件。此外，本研究还探讨了与布朗运动和热泳扩散特性相关的纳米流体质量。可变参数包括普朗特数（Pr）、佩克莱特数（Pe）、浮力比参数（Nr）、混合对流参数（）、生物对流刘易斯数（Lb）、毕奥特数（Bi）和马兰戈尼数（Ma）。MATLAB 中的 bvp4c 问题求解工具用于对非线性控制微分方程进行数值求解。数值模型已通过先前的论文进行了验证。创建了图形表示法来描述一些重要的测量数据，如速度流线、速度剖面、温度分布、纳米粒子浓度、回旋运动微生物的密度、局部努塞尔特数、皮肤摩擦力和舍伍德数。努塞尔特数与参数 Nt 和 Rd 之间的联系表明，随着 Nt 的下降和 Rd 的增加，努塞尔特数也会增加。皮肤摩擦值与 Nr 和 Nc 值成正比。局部传质速率的上升与 Rd 和 Nt 的值呈正相关。移动微生物的数量随着 Lb 和 Pe 值的降低而增加。
{"title":"Numerical study of third‐grade nanofluid flow with motile microorganisms under the mixed convection regime over a stretching cylinder","authors":"Hassan Waqas, Md. Jahid Hasan, Shahrin Jahan Jaima, Syed Muhammad Raza Shah Naqvi, U. Manzoor, Dong Liu, Taseer Muhammad","doi":"10.1002/zamm.202400024","DOIUrl":"https://doi.org/10.1002/zamm.202400024","url":null,"abstract":"The investigation of mixed convective flow involving microorganisms in nanofluid has garnered considerable interest in recent times owing to its extensive applicability in the biomedical domain. However, there has been a lack of study investigating a comprehensive parameter analysis for the flow of a third‐grade nanofluid around a cylinder in the presence of microorganisms. This study focuses on numerically investigating the flow of nanofluid around a stretched cylinder in the presence of motile microorganisms. The study also considers convective boundary conditions. Moreover, this study explores the nanofluid qualities related to Brownian motion and thermophoresis diffusion characteristics. The variable parameters include the Prandtl number (Pr), Peclet number (Pe), buoyancy ratio parameter (Nr), mixed convection parameter (), bioconvection Lewis number (Lb), Biot number (Bi), and Marangoni number (Ma). The bvp4c issue solver tool in MATLAB is used to numerically solve the nonlinear governing differential equations. The numerical model has been validated using prior papers. Graphical representations are created to depict several important measurements, such as velocity streamlines, velocity profiles, temperature distributions, nanoparticle concentrations, densities of gyrotactic motile microorganisms, local Nusselt numbers, skin friction, and Sherwood numbers. The link between the Nusselt number and the parameters Nt and Rd suggests that as Nt falls and Rd increases, the Nusselt number increases. The skin friction value is directly proportional to the values of Nr and Nc. There is a positive correlation between the rise in the local mass transfer rate and the values of Rd and Nt. The population of mobile microorganisms grows as the values of Lb and Pe decrease.","PeriodicalId":509544,"journal":{"name":"ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141926603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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