Heat transfer in flows due to stretching surface is prominent for polymer extrusion, continuous casting, hot rolling, paper production and metallurgy. The current analysis explores magnetohydrodynamic fluid flow by curved stretching sheet. Correct concept of Darcy-Forchheimer relation in view of Cattaneo-Christov theory is under consideration. Energy equation consists of viscous dissipation, Darcy-Forchheimer relation, thermal radiation, heat generation and Ohmic heating. First order chemically reactive flow is considered. Entropy generation with Cattaneo-Christov theory through entire new concept of Darcy-Forchheimer relation, radiation, magnetohydrodynamics, dissipation and heat generation is formulated. Appropriate transformations are used to develop dimensionless ordinary expressions. Convergent series solutions are constructed by employing Optimal homotopy analysis method (OHAM). Graphical analysis of entropy generation, temperature, flow and concentration for influential variables are explored. Higher magnetic field witness temperature and entropy generation enhancement while opposite response noticed for velocity. Higher Forchheimer number correspond to enhancement of entropy generation. Higher thermal relaxation time give rise to entropy generation. An increase in entropy generation through heat generation is noticed.

Nanoparticles dispersed in conventional material result in nanoliquid which serve as working substances in various energy storage systems particularly in thermal energy storage devices including solar power plants, heat exchangers, automobile radiators, photovoltaic cells, nuclear reactors, boilers and heat pipes etc. Recent researchers have keen interest in efficient cheap heat storage technology. Such technology has special relevance for electrical, solar and power energy and waste heat recovery. Besides these some prominent applications of entropy generation are light emitting diode (LED), thin film technology, internal combustion engines, lubrication, extrusion process, heat pump, air conditioning, solar energy, steam turbine, energy dissipation and many others. Through such facts in mind the objective here is to consider Cattaneo-Christov fluxes in for entropy optimized hydromagnetic flow of rheological (Walter-B) nanomaterial. Energy expression for reactive flow with Brownian motion, Joule heating and thermophoresis is correctly modeled. Brownian movement, radiation, thermophoresis and Ohmic heating is under consideration. Analysis is carried out in presence of first order reaction and Soret effects. Entropy generation for flow with radiation and Joule heating is first time correctly modeled in presence of Cattaneo-Christov theory. In fact, additional terms due to Cattaneo-Christov flux for radiation and Joule heating in entropy rate were missed. Related nonlinear expressions are converted into non-dimensional ordinary systems through suitable variables. Convergence solutions have been developed through Optimal homotopy analysis method (OHAM). Solutions convergence by individual and total residual errors is examined. Graphical results illustrating the impact of emerging parameters for entropy rate, flow, temperature and concentration are arranged. Performance for sundry variables on quantities under interest are examined. It is witnessed that Nusselt number and temperature have similar effects through Hartmann number. Reverse impact for entropy rate and liquid flow against Hartmann number is noticed. An increment in thermal relaxation time leads to amplify thermal field. An intensification in surface drag force coefficient through viscoelastic variable is noticed whereas an opposite impact holds for velocity.

Time-dependent bioconvection flow of Sutterby nanoliquid is examined. Variable thermal conductivity is taken into account. Thermal equation includes heat generation and radiation. The properties of thermophoresis and Brownian motion are examined. Additionally, activation energy and chemical reaction factors are analyzed. Nonlinear partial differential systems are transformed into ordinary systems through appropriate transformations. The dimensionless nonlinear differential equations are computed using the bvp4c technique. The study examines performance in liquid flow, concentration and microorganism dynamic and thermal fields. Computations for the Sherwood number, heat transfer rate and microbe density number are organized. Concentration, velocity, and thermal distribution for various parameters of interest are examined. Velocity is enhanced for Sutterby parameter and power law index. An increase in temperature through thermal Biot number is observed. There is a noticeable increase in density number in relation to Peclet and bioconvection Lewis numbers.

Research about heat and mass transfer is important through its significance for technological and industrial sectors. Here attention is given to magnetohydrodynamic (MHD) flow due to coaxial cylinders. An inner cylinder stretches whereas the outer rotates. Simultaneously effects of heat and mass transfer are taken. Analysis with pollutant concentration for thermal and concentration slip conditions is made. Correct version of velocity slip condition for outer cylinder is utilized. Resulting problems are computed by BVP4c LM-BNNs. This creates a reference dataset for scenario-based, specific cases. For LM-BNNs, the approximate solutions are interpreted in different cases following validation and checking across training testing and validation phase. Importance of LM-BNNs has been assessed from performance measures like Mean Square Error (MSE), correlation index, regression analysis and error histogram. Velocity, temperature and concentration are analyzed.

Attention here is focused to address the artificial neural networks study for magnetohydrodynamic flow of second grade material by stretched surface. Furthermore, employing advanced artificial neural networks based computational techniques such as multi-layer neural networks provide exceptional capabilities in precisely capturing the complex nature of thermal and solutal transport in liquid flow problems. Energy expression comprises heat generation and thermal radiation. Entropy generation rate with heat generation and radiation impacts is under consideration. Isothermal chemical reaction of first order is taken. Dimensionless ordinary systems are developed. The obtained nonlinear expressions are numerically computed by Bvp4c via MATLAB and then advanced artificial neural networks computational algorithm is employed to train the obtained datasets to improve predictive capabilities for advanced solutions. Velocity, entropy rate, concentration and thermal distribution against sundry variables are examined. Artificial neural networks is used to optimize interesting quantities data through training, validation, and testing in order to verify validation of given data. Additionally, the comparison of Bvp4c method and artificial neural networks algorithm is given. Here we concluded that an increase in liquid flow via larger material variable is witnessed whereas decreasing impact holds for magnetic field parameter. An increase in entropy generation through heat generation variable is detected. Larger Schmidt number corresponds to concentration reduction. Through comparative study it is noticed that numerical computation through ANNs model aligns well with Bvp4c results.

Fluids undergo endothermic and exothermic reactions due to the significant use of heat generation in numerous physical problems. Heat generation is usually categorized as the sum of irreversible and reversible heat sources. This phenomenon has variety of applications including automobile manufacturing, turbines, heat exchangers, petrochemical industry, exhaust gases, boilers, aerodynamic extrusion, refining processes, HVAC systems, sterilizing, nuclear power plants, insulations, electronics etc. Present analysis deals with non-similar solution development for rotating flow involving Soret and Dufour effects. Such investigation is considered through thermal and solutal convective conditions. Constitutive relation for second grade liquid is considered. Energy expression involves radiation, magnetohydrodynamics, heat source and viscous dissipation. Buiongiorno’s model captures random movement and thermophoresis. First order reaction is considered. Rate of entropy in presence of heat source, magnetohydrodynamic, radiation and dissipation is discussed. Related partial differential systems (PDEs) are converted into dimensionless ordinary systems by using adequate transformations. Convergent solution is constructed through optimal homotopy analysis method (OHAM). Residual errors guarantee the convergence analysis. Important results for rate of entropy, liquid flow, concentration and thermal field against pertinent parameters are graphically explored. Attention is focused to the outcomes of drag force coefficient, Sherwood number and heat transport rate for influential variables. Similar response for drag force coefficient and liquid flow through material parameter is noticed. Higher magnetic field lead to intensify thermal transport rate and entropy rate whereas reverse trend for velocity witnessed. Similar impact for Nusselt number and entropy rate through radiation is observed. Higher solutal Biot number lead to augments concentration. Reverse response for mass transport rate and concentration through Soret number is detected. Dufour number correspond to thermal field enhancement.

Present analysis addresses magnetohydrodynamic flow of Walter-B nanomaterial in a rotating frame. Convective constraints for thermal and solutal transfer are considered. Buongiorno’s model is employed to explore nanoliquid features through random movement and thermophoresis. Heat source, Ohmic heating, viscous dissipation and heat and mass transport rates in entropy generation expression are explored. Heat transmission for heat generation, magnetohydrodynamics and dissipation is considered. Isothermal first order reaction along with Soret effect is considered. In recent times main purpose for scientists is to establish a new mechanism that can manage the utilization of suitable amounts of heat energy. Entropy optimization is directly connected to reducing heat energy in thermodynamic systems. Related expressions (PDEs) are converted into dimensionless ordinary systems by suitable transformations. Development of convergent solution through Optimal homotopy analysis method (OHAM) is made. Results illustrating effects of influential variables for entropy rate, flow, temperature and concentration are organized. Skin friction coefficient and heat and mass transport rates are given due attention. Here an increase in Nusselt number and rate of entropy is witnessed while reverse response holds for velocity. Similar response hold for entropy rate and Nusselt number through heat generation. Larger estimation of thermal Biot number lead to rise temperature whereas reverse response for heat transport rate witnessed. Opposite response holds drag force coefficient and flow through viscoelastic variable. Concentration shows improvement against higher solutal Biot number. Reverse behavior of concentration and Sherwood number against higher Schmidt number is witnessed. Bejan number and entropy rate through Brinkman number are different.

Non-Newtonian materials have tremendous applications in industries, pharmaceuticals, manufacturing, substance designing and natural procedures. These materials are utilized in surface coating, penetrating activities, printing, cooling of metallic plates, damping and braking devices and many others. In view of such innovative applications here we communicate Soret and Dufour impacts in Jeffrey liquid flow caused by curved stretching surface. Thermal conductivity and mass diffusivity are temperature and concentration dependent respectively. Convective conditions are utilized. Radiation, first order chemical reaction, heat generation and Ohmic heating in present attempt are taken into account. Adequate transformations lead to resulting nonlinear differential system. Such system is computed successfully through Optimal homotopy analysis method (OHAM). Skin friction coefficient and Nusselt and Sherwood numbers in addition to velocity, temperature and concentration are examined. Here skin friction and temperature against magnetic field are opposite when compared with velocity. Temperature through Dufour number and radiation has increasing impact. Concentration for variable mas diffusivity and solutal Biot number has opposite response. An increase in thermal transport rate through Eckert number is detected. Sherwood number for curvature and variable mass diffusivity has opposite response. Larger approximation of reaction variable leads to decay concentration.

Attention here is focused to the development of dual solutions. For such objective the flow of magnetohydrodynamic (MHD) Jeffrey nanoliquid by shrinking permeable inclined cylinder is attended. Influences of radiation, Ohmic heating and heat generation are not ignored. Soret and Dufour impacts in chemically reactive flow are studied. In addition, the total entropy generation rate is investigated. Nanoliquid features through Brownian movement and thermophoresis are declared. Particular ranges of physical parameters regarding existence of dual solutions are pointed out. Quantities of interest with reference to existing of dual solutions are analyzed in detail. Novel results are summarized in key findings.

Presently, the concept of artificial neural networks represents an innovative and transformative approach with wide-ranging applications across industrial, mechanical, pharmaceutical, and automotive domains. This article employs numerical computing approach for chemically reactive flow of an incompressible Jeffrey nanofluid between coaxial cylinders. Backpropagated neural networks (BNNs) are utilized. Outer cylinder remains stationary while the inner cylinder is stretched. Presence of gyrotactic microorganism is ensured. Besides this the salient features of thermophoresis, radiation and Brownian movement. Convection conditions of heat and mass transfer in presence of Soret and Dufour features are explored. The relevant problems are computed through BVP4c for reference data used in view of training Levenberg-Marquardt algorithm based upon (LMA-BNNs). The neural networks are trained, validated and tested to obtain optimal level of generalization and learning. The Levenberg-Marquardt backpropagation algorithm is utilized to minimize mean square error (MSE) in order to predict accurate solution under different parametric conditions. Comparative analyses (using statistical measures such as correlation coefficient, MSE, regression plot and error histogram) confirm the strength and validity of BNN treatment. Finally, the physical quantities of interest for influential variables are examined. Main results are concluded. Both temperature and Nusselt number against thermal Biot number have same response qualitatively.

Background and objective: This study explores the magnetohydrodynamic dissipative flow of rheological material by stretched cylinder. Furthermore, the advanced computational method of neural networks constructed Levenberg Marquardt technique provide outstanding skills in precisely obtaining the sophisticated solutions of solutal and thermal transfer rates in highly nonlinear fluid flow problems. In the field of artificial neural networks approach the Levenberg-Marquardt technique is identified through its innovative stability and provides computational outcomes of the Reiner-Rivlin material flow employing mean square errors, validation check, error histogram, regression plots, fitness curve and comparison solution. Entropy rate in presence of heat generation, dissipation and Joule heating is deliberated. Chemical reaction of first order is taken. Ohmic heating, heat generation/absorption and dissipation are considered in heat equation. Methodology: Nonlinear ordinary expressions are obtained through employing suitable transformations. The dimensionless ordinary differential expressions are solved employing bvp4c via MATLAB and then advanced computational technique of artificial neural networks is implemented to train the given datasets to increase predictive capabilities for advanced solutions. Results: Physical description for rate of entropy, temperature, liquid flow and concentration are examined. The designed approach covers a series of actions depending on training, authentication and testing by employing a given datasets for different flow problems components. Furthermore, the comparison of artificial neural networks algorithm and bvp4c method is discussed. Clearly one can find that higher magnetic field leads to velocity reduction. Higher estimation of heat generation parameter correspond to intensify the thermal field. Decreasing trend for concentration for larger Schmidt number is detected. An intensification in entropy rate through larger Brinkman number is witnessed.

Thermal management through rheological nanomaterial is influential in the heat exchangers, chemical reactions, automation and energy and cooling systems. Heat transfer investigation in flow by stretching boundary with slip condition has key role for material processing and thermal management situations. To our knowledge the correct velocity slip condition for an Oldroyd-B fluid is first time developed. Such consideration is vital for microfluidics. Specifically, the slip condition at boundary is useful for polymer process and development of microscale heat exchangers. Significance of thermal transport through Buongiorno's model is described. Energy equation with heat generation is discussed. Concentration expression is with chemical reaction of first order. Fluid is considered magnetohydrodynamic (MHD). Dimensionless ordinary differential systems are obtained. Numerical solutions by employing Newton built in-shooting scheme are arranged. Physical quantities for fluid flow, concentration and temperature are graphically examined. Physical interpretation of thermal and mass transport rates is organized. Higher magnetic field and retardation time Deborah number have reverse response for velocity. However, velocity field for slip variable and Deborah number for relaxation time has similar response. Thermal distribution for Prandtl number is different when compared with random motion variable. Thermal distribution augmentation is witnessed for thermophoresis and heat generation variables. Larger Schmidt number lead to decrease in concentration. Concentration has reverse impact for reaction and thermophoresis variables. Thermal and mass transport rates for Deborah number through relaxation and retardation times have opposite response.

Background and objective Thermal transport process has attracted researchers and engineers in recent time. It is due to innovative applications of heat transfer in various industrials, pharmaceutical and manufacturing fields. These applications include extraction of geothermal energy, solar thermal collectors, polymer extrusion, cooling of glass sheets, fertilizer production, oil recovery, nuclear reactors etc. In view of such consideration the magnetohydrodynamic Reiner-Rivlin nanoliquid flow invoking Cattaneo-Christov flux theory is considered. Flow induced is by curved stretched surface. Solutal and thermal transportation processes are discussed through Cattaneo-Christov fluxes model. Brownian movement and thermophoresis features are addressed. Heat equation comprises magnetohydrodynamics and thermal radiation. Isothermal reaction of first order is considered. Methodology Convergent series solutions of differential systems employing Optimal homotopy analysis method (OHAM) are constructed. Convergence regions for solutions are discussed through total and individual residual errors. Results Graphical description of temperature, liquid motion and concentration for emerging variables are examined. Nusselt number, drag force coefficient and rate of mass transport are explored. Opposite response for drag force coefficient and velocity occurs through material variable. Larger magnetic variable lead to decay liquid motion whereas reverse impact for temperature and drag force coefficient witnessed. Similar response for Nusselt number and temperature through thermal relaxation time variable is witnessed. Higher radiation corresponds to rise the thermal transport rate. Reverse behavior for concentration and mass transport rate through solutal relaxation time variable is found. It should be pointed out here that present formulation corrects the existing modeling for MHD flows by curved stretching surfaces beyond classical concepts of heat and mass fluxes through Fourier's and Fick's expressions respectively.

Traditional fossil fuels significantly contribute to energy supply, economic development, and advancements in science and technology. However, prolonged and extensive use of fossil fuels has resulted in increasingly severe environmental pollution. Consequently, it is imperative to develop new, clean, and pollution-free energy sources with high energy density and versatility as substitutes for conventional fossil fuels, although this remains a considerable challenge. Simultaneously, addressing water pollution is a critical concern. The development, design, and optimization of functional nanomaterials are pivotal to advancing new energy solutions and pollutant remediation. Emerging porous framework materials such as metal-organic frameworks (MOFs) and covalent organic frameworks (COFs), recognized as exemplary crystalline porous materials, exhibit potential in energy and environmental applications due to their high specific surface area, adjustable pore sizes and structures, permanent porosity, and customizable functionalities. This work provides a comprehensive and systematic review of the applications of MOFs, COFs, and their derivatives in emerging energy technologies, including the oxygen reduction reaction, oxygen evolution reaction, hydrogen evolution reaction, lithium-ion batteries, and environmental pollution remediation such as the carbon dioxide reduction reaction and environmental pollution management. In addition, strategies for performance adjustment and the structure-effect relationships of MOFs, COFs, and their derivatives for these applications are explored. Interaction mechanisms are summarized based on experimental discussions, theoretical calculations, and advanced spectroscopy analyses. The challenges, future prospects, and opportunities for tailoring these materials for energy and environmental applications are presented.

Here nonlinear mixed convective flow of magnetized Eyring-Powell fluid is addressed. Energy expression comprised of heat generation/absorption, Ohmic heating and dissipation. Formulation for nonlinear radiative flow is made. Convective conditions are deliberated for mass and heat transfer. Entropy optimized flow is organized. Aspect of Arrhenius activation energy is explored. Relevant problem is formulated into dimensionless ordinary differential system (ODEs). ND-Solve scheme is employed to develop numerical solution. Graphs are organized for liquid flow, entropy rate and temperature and concentration distributions. Numerical outcomes for surface drag force and Nusselt and Sherwood numbers regarding interesting quantities are studied. Higher Biot numbers augment concentration and temperature fields. Larger magnetic field decay liquid flow while opposite occurs for liquid parameter. An intensification in entropy holds for Brinkman number and magnetic effect. Concentration declines against reaction variable. Concentration augments through higher activation energy and solutal Biot parameter. Higher approximation of buoyancy ratio give rise to liquid flow whereas reverse situation occurs for surface drag force. Nusselt number for Eckert number and radiation has opposite impacts whereas Schmidt number and activation energy enhance for Sherwood number.

MHD consideration has significance in thermoelectric power energy, polymer extrusion, MHD generators, polymeric solutions, cable coating, refrigeration equipment, filament spinning, thermal storage and metallurgy. Such consideration has utilization in dialysis machines and other medical devices as well as treatment for hyperthermia. In view of such consideration the magnetohydrodynamic (MHD) radiative Reiner-Rivlin material flow is addressed. Flow generated is by curved stretching sheet. Energy relation comprises heat generation and thermal radiation. Chemically reactive flow of first order is accounted. Nonlinear ordinary differential expressions are developed involving adequate transformations. Governing problems are computed numerically. Features of liquid flow, concentration and temperature are examined. Clearly an increment in velocity through curvature variable is noticed while reverse effect seen for concentration and thermal fields. Reduction in liquid flow through magnetic field is witnessed. Higher radiation parameter correspond to temperature and Nusselt number enhancement. An improvement in temperature for heat generation variable is witnessed. Concentration decays through higher reaction parameter.

[This corrects the article DOI: 10.1016/j.heliyon.2023.e18603.].

Nanofluid flow has attracted the attention of researchers across the globe. It is because of its innovative utilization in various industrial, manufacturing, pharmaceutical, engineering and nano cryosurgery fields. Here intension is to examine flow of Prandtl nanoliquid bounded by an infinite porous plate. Presence of gyrotactic microorganisms and heat generation is addressed. Physical features of irreversibility analysis in hydromagnetic flow are addressed. Thermal expression is discussed subject to magnetohydrodynamics, heat generation, dissipation and radiation. Innovative characteristics regarding Brownian diffusion and thermophoresis are also considered. Further chemical reaction of first order is discussed. The governing flow expression are converted into non-dimensional partial differential system through adequate variables. Numerical computations of resultant nonlinear partial differential system are developed by implementation of finite difference method (FDM). Consequences of various sundry parameters for flow, microorganism field, entropy generation, concentration and temperature are graphically explored. An intensification of thermal field and entropy rate for magnetic field noticed while reverse trend seen for velocity. Higher radiation variable on entropy rate and temperature has same effect. An opposite effect for concentration against random motion and chemical reaction is noticed. Reverse results for concentration and thermal distribution are detected for thermophoresis variable. A reduction in concentration occurs for Schmidt number. Higher Peclet number yields to microorganisms’ reduction. Entropy rate against Brinkman number is enhanced.