Variable Heat Source Research Articles

Nanoparticle aggregation effect on nonlinear convective nanofluid flow over a stretched surface with linear and exponential heat source/sink

A nanofluid flow (TiO2/Ethylene Glycol) over a stretched surface caused by the considerable nonlinear convection is investigated with the nanoparticle aggregation effect in the presence of quadratic thermal radiation. The modified Maxwell model and Bruggeman model are utilized, which depict the nanoparticle aggregation effect. In addition, the system employs two separate variable heat sources i.e., linear heat source and exponential heat source. The similarity transformations are utilized to convert the basic governing PDEs to ODEs. The “bvp4c function” in MATLAB is used to numerically handle the resultant nonlinear system. The impact of the involved parameters is explored on the non-dimensional fields of velocity boundary layer patterns, velocity, streamlines, temperature, and heat transfer rate. Graphs compare and display the control of pertinent parameters on the distinct flow properties. A comparison of the behavior of the solution profiles with and without the influence of nanoparticle aggregation is illustrated. The nanoparticle aggregates significantly enhance the velocity and heat transmission mechanism. Furthermore, the influence of varied heat sources (linear and exponential) aids in growing the thermal boundary layer. Nanofluid flow with nanoparticle aggregation has a 5.36% higher Nusselt number value in comparison to flow without aggregation effect when the volume fraction of nanoparticles is varied from 0 to 0.1. The results of the study will be helpful in the fields where applications of a continuously stretching/shrinking surface are used like in many engineering processes and industries, glass-fiber production, aerodynamic extrusion of plastic sheets, and manufacturing of paper and rubber sheets.

Numerical solution of heat and mass transfer using buongionro nanofluid model through a porous stretching sheet impact of variable magnetic, heat source, and temperature conductivity.

Fluid flow chronologically is widely recognized due to its various uses in turbines, the framework of spinning magnet stars, gyromagnetic generators, and chemical engineers observing the progression of petroleum through the aquifer, and blood vessels in the respiratory alveolar plate. Tropical cyclones, pools of water, and storms all exhibit rotational movement. The current investigation aims to analyse the micro polar fluid flow between two infinite vertical discs enclosing Hall impact, varying thermal conductivity, heat flux as well as anomalous heat generation. The implication of a chemical change combined with chemical potential improves mass propagation. Suitable similarity conversions are used to convert the defined problems into conventional differential equations (ODEs). Furthermore, by introducing new variables the ODEs are transformed into nonlinear coupled ODEs and then solved numerically by the RK 4th order along with the shooting technique. The velocity profiles decrease as suction parameter increases. The temperature field exhibits a rising behaviour for the increasing values of thermophoresis, Brownian and radiations parameters while the concentration field shows a decreasing behaviour. Shear stress at the upper wall increases when the rotation variable and suction variable are augmented. Heat transmission escalations at the bottom wall when Prandtl number and radiation factor are enhanced. The novelty of the present work is to examine the Buongionro model in the presence of a heat source and chemical reaction inside the Darcian porous rotating channel, which has not been investigated yet. In some limiting cases, a comparison of the on-going study with existing literature is also included to justify the contemplated problem.

Effect of Variable Heat Source and Gravity Variance on the Convection in Porous Layer with Temperature-Dependent Viscosity

Effect of Variable Heat Source and Gravity Variance on the Convection in Porous Layer with Temperature-Dependent Viscosity

Influence of Variable Viscosity on Entropy Generation Analysis Due to Graphene Oxide Nanofluid Flow

Conventional investigations on fluid flows are undertaken with an assumption of constant fluid properties. But in reality, the properties such as viscosity and thermal conductivity vary with temperature. In such cases, considering these variabilities aids in modelling the flows with accuracy. Particularly, studying the flow of graphene based nanofluids with variable properties makes the best of both the advantageous thermophysical properties of graphene nanoparticles in heat transfer and the variable fluid properties in accuartely modelling the flow. In this article, the flow of graphene oxide nanofluid along a linearly stretching cylinder under no-slip and convective boundary conditions is investigated, by taking the base fluid viscosity to be a temperature dependant function. Buongiorno model is adapted to develop the flow of graphene nanofluids including the influence of variable heat source, cross-diffusion effects and the effects of nanoparticle characteristics such as thermophoresis and Brownian motion. The modelled equations are transformed and are numerically solved using linearization method. The impacts of embedded parameters including the Dufour and Soret numbers on temperature, concentration and velocity profiles of the chosen nanofluid and their consequent impacts on the predominant cause for the generated entropy are studied. The obtained results are depicted and interpreted in detail. From the tabulated values of skin friction and the values of Sherwood and Nusselt numbers, it is inferred that the conductive heat and mass transfer can be enhanced by variable viscosity parameter and skin friction can be reduced by Soret number. Furthermore, entropy generation is analysed and Bejan number is calculated to be lesser than 0.5, thus demonstrating the dominance of irreversibilty to fluid friction and mass transfer.

Water thermal enhancement in a porous medium via a suspension of hybrid nanoparticles: MHD mixed convective Falkner's-Skan flow case study

Keeping in mind the whispered applications of Falkner's-Skan Flows, the present hydrothermal scrutinization intended to explore the two-dimensional flow pattern and thermal characteristics featuring the steady mixed convective motion of a radiating homogeneous hybrid nanofluidic mixture (Ag+TiO2)−H2O (i.e., a homogeneous aquatic mixture containing spherical silver and titanium dioxide nanoparticles) over a non-movable wedge surface. By combining Darcy's-Brinkman and single-phase models, the conservation equations are stated properly in the case where the hydrothermal impacts of specific variable heat and magnetic sources are taken into account effectively in the present flow problem. After many simplifications and rearrangements, the derived boundary layer equations are handled numerically with the help of a robust iterative GDQM-NRT algorithm, whose accurate results are presented graphically and tabularly. As the main findings, it is evidenced that the thermal buoyancy forces, as well as Lorentz's and Darcy's forces, act as assisting factors, which exert a cooling impact throughout the hybrid nanofluidic mixture (Ag+TiO2)−H2O due to the imposed axial pressure gradient. Energetically, it is demonstrated that the silver nanoparticles play a noteworthy role in the enhancement of the heat transfer rate at the wedge surface with a strengthening in the resulting surface viscous drag forces.

Dynamics of Heat Transfer in Magneto-Micropolar Fluids Flow Past a Vertically Expanding Sheet Featuring Prescribed Wall Temperature (PWT)

This study assesses the motion and the dynamics of heat propagation in magneto-micropolar fluid along a sheet which vertically stretches on a two-dimensional plane in a porous material. The heat distribution is developed and evaluated under the condition of the prescribed wall temperature, constant magnetic field, thermal radiation, variable heat source and viscous dissipation. The main equations are re-formulated from partial to ordinary derivatives using similarity tools and consequently solved numerically by shooting and the Runge-Kutta Fehlberg approach. The parameters of interest are presented graphically to demonstrate their reactions on the velocity profiles, thermal field and heat transfer mechanism of the problem. The outcomes of the current investigation reveal that the heat transfer appreciates in the presence of higher Prandtl number, temperature exponent term and material parameter but decreases as the magnetic field term soars.Besides, the heat boundary structure expands and heat spread occurs as the thermal radiation, magnetic field and Eckert number terms escalates but a reverse trend is encountered as the Prandtl number, material micropolar term, Grashof number and heat exponent terms grows in magnitude. Under some limiting scenarios, the obtained data strongly correspond to the published studies in the open literature.

Extremum seeking control for real-time optimization of high temperature heat pump systems incorporating vapor injection

In order to minimize the power consumption of a vapor-injected high temperature heat pump system with R245fa as refrigerant, a control strategy, namely Extremum seeking control, is proposed. It can implement real-time model-free optimization control of plants with concave and convex properties. Modelica-based dynamic simulation model of the proposed system is developed. The Newton-based Extremum seeking control is used to optimize the intermediate pressure of the proposed system to obtain the minimum power consumption of the compressor at a fixed heating capacity (200 kW). The adopted ESC strategy requires four measured quantities, namely, injection pressure, condenser outlet water temperature, evaporator outlet superheat and compressor power consumption, to achieve optimal control of the system in real time. Two operation scenarios are simulated: stable and freely variable heat source temperature. For both scenarios, the condenser outlet water temperature was set to 140 °C. The simulation results show that at stable heat source temperature, the power consumption is reduced by 5.2% and the COP is increased by 7.7% compared to a fixed initial intermediate pressure. Under the free-variable heat source condition, the power consumption can be reduced by up to 5 kW compared to a constant input. A total of 283 kWh of power was saved during the 48 h simulation. Thus, the Newton-based extremum seeking control strategy can optimize the intermediate pressure to achieve the minimum power consumption while maintaining excellent transient performance, and demonstrate the superiority of the ESC strategy for real-time optimization..

Multi-variable extremum seeking control for high temperature heat pump system incorporating double refrigerant injection

The use of refrigerant injection technology to enhance the heating efficiency of heat pumps with larger temperature lifts is becoming more common. Heat pumps with double refrigerant injection loops have better energy efficiency than traditional ones with single refrigerant injection loops. A multi-variable extremum seeking control (ESC) strategy for a high-temperature heat pump system with double refrigerant injection technology is proposed in this study. A Modelica-based dynamic simulation model of the considering system is established in Dymola, and a co-simulation with the proposed ESC strategy is built to validate the effectiveness of this control strategy to minimize power consumption. The strategy uses compressor power consumption as the feedback. The effective throttling area of the upper and lower EEVs is adjusted by a PI controller to manipulate the low and high-pressure vapor injection pressures. Three scenarios were simulated for control: stable, step curve, and freely variable heat source temperature conditions. The simulation results demonstrate that the multi-variable ESC has excellent convergence performance and confirm its effectiveness in searching for the optimal operating point.

Thermal instability analysis in magneto-hybrid nanofluid layer between rough surfaces with variable gravity and space-dependent heat source

The onset of thermal instability with hybrid nanoparticles Al2O3–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters ([Formula: see text]), Darcy number (Da), gravity variation function ([Formula: see text]), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number [Formula: see text] which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ([Formula: see text]) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and [Formula: see text] (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

A synergistic multi-objective optimization mixed nonlinear dynamic modeling approach for organic Rankine cycle (ORC) under driving cycle

Organic Rankine cycle (ORC) synergistic multi-objective optimization is the key to obtain the actual waste heat recovery potential under dynamic driving cycle. The ORC operation shows uncertainty and hysteresis under the disturbance of variable high temperature waste heat source. In this paper, a synergistic multi-objective optimization mixed nonlinear dynamic modeling approach is proposed by deeply integrating data selection, feature dimensionality reduction, integrated system, neural network modeling mechanism, ensemble learning mechanism and synergistic multi-objective optimization. Compared with direct modeling, the nonlinear dynamic modeling approach can reduce the data volume by 27.65 % on average. The decision variables and construction time are reduced at least by 69.1 % and 24.26 % on average, respectively. Generalization ability is improved by at least 28.14 % on average. Taking thermodynamic performance, economic performance, thermoeconomic performance and environmental impact as optimization objectives, a synergistic multi-objective optimization of ORC comprehensive performance under driving cycle is carried out. The optimal emissions of CO2 equivalent (ECE) will suppress the optimal power output of per unit heat transfer area (POPA) to a certain extent. A decrease in optimal ECE is accompanied by an increase in optimal electricity production cost. The approach proposed in this paper can provide new ideas and solutions for ORC dynamic modeling and synergistic multi-objective optimization under road conditions.

Advanced exergy analysis on supercritical water gasification of coal compared with conventional O2-H2O and chemical looping coal gasification

Supercritical water gasification (SCWG) that converting coal into hydrogen-rich syngas is a promising cascade utilization technique of coal. Advanced exergy analysis of SCWG is conducted to evaluate avoidable exergy destructions, and results are compared with conventional (CG) and chemical looping gasification (CLG). In the benchmark condition, the exergy efficiency of SCWG process is 68.63%, which is higher than CG and CLG. The biggest irreversibility of gasification process occurs in gasifier caused by gasification reaction, and SCWG gasifier has high avoidable exergy destruction potential. The modified exergy efficiency of SCWG process is 82.38% under unavoidable conditions. However, avoidable exergy destruction portion of syngas self-heating recovery is only 3.55% due to heat transfer mismatch between supercritical water and syngas. Suitable external heat sources should be adopted, such as the variable heat source with constant cp, which can reduce exergy destruction of supercritical water heating to 44.86%. The effects of parameters on SCWG is performed with single factor analysis method. Coal water slurry concentration (CWSC) is the key factor affecting the performance of SCWG. With gasification temperature < 750 °C, gasification pressure > 23 MPa, CWSC > 17% and oxygen-coal ratio < 0.46 kg kg−1, the exergy efficiency of SCWG process is higher than CG and CLG.

Transient thermo-diffusive responses in a nonlocal elastic sphere due to harmonically varying heat sources

Transient thermo-diffusive responses in a nonlocal elastic sphere due to harmonically varying heat sources

Dual Characteristics of Maxwell Hybrid Nanofluid Flow Over a Shrinking Sheet with Variable Heat Source or Sink

Dual Characteristics of Maxwell Hybrid Nanofluid Flow Over a Shrinking Sheet with Variable Heat Source or Sink

Prediction identification method of time-varying internal heat source based on inverse heat transfer problem

Purpose This paper aims to discuss the inverse problems that arise in various practical heat transfer processes. The purpose of this paper is to provide an identification method for predicting the internal boundary conditions for thermal analysis of mechanical structure. A few examples of heat transfer systems are given to illustrate the applicability of the method and the challenges that must be addressed in solving the inverse problem. Design/methodology/approach In this paper, the thermal network method and the finite difference method are used to model the two-dimensional heat conduction inverse problem of the tube structure, and the heat balance equation is arranged into an explicit form for heat load prediction. To solve the matrix ill-conditioned problem in the process of solving the inverse problem, a Tikhonov regularization parameter selection method based on the inverse computation-contrast-adjustment-approach was proposed. Findings The applicability of the proposed method is illustrated by numerical examples for different dynamically varying heat source functions. It is proved that the method can predict dynamic heat source with different complexity. Practical implications The modeling calculation method described in this paper can be used to predict the boundary conditions for the inner wall of the heat transfer tube, where the temperature sensor cannot be placed. Originality/value This paper presents a general method for the direct prediction of heat sources or boundary conditions in mechanical structure. It can directly obtain the time-varying heat flux load and thtemperature field of the machine structure.

The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions. Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications. Mathematical modelling has been widely used in order to better understand the transmission, treatment, and prevention of infectious diseases. Herein, we study the dynamics of a human immunodeficiency virus (HIV) infection model with four variables: S (t), I (t), C (t), and A (t) the susceptible individuals; HIV infected individuals (with no clinical symptoms of AIDS); HIV infected individuals (under ART with a viral load remaining low), and HIV infected individuals (with two different incidence functions (bilinear and saturated incidence functions). A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of the model. The influence of different clinical parameters on the dynamical behavior of S (t), I (t), C (t) and A (t) is described and analyzed. All the results are depicted graphically. On the other hand, we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation, heat flux, hall impact, variable heat source, and nanomaterial. The flow is considered to be 2D, boundary layer, viscous, incompressible, laminar, and unsteady. Sufficient transformations turn governing connected PDEs into ODEs, which are solved using the proposed scheme. To justify the envisaged problem, a comparison of the current work with previous literature is presented.

Numerical Investigation of Suction/Injuction on Triple Diffusive MHD Casson Fluid Flow over a Vertical Stretching Surface

The article examines the characteristics of heat transfer for steady two-dimensional MHD Casson fluid with shear thickening properties in the presence of variable heat source for a vertical stretching sheet. The study considers the thermal radiation’s impact and velocity slip, and uses similarity transformations to convert the governing PDEs and corresponding boundary conditions into ODEs. Numerical solutions are obtained using shooting and R. K-4 methods, and the results presented for both injection and suction cases. The article examines the influence of various neutral parameters on the distribution of temperature, skin friction coefficient, velocity, and local Nusselt number, and presents the findings using tables and graphs. The study reveals that an increase in the Biot number and thermal radiation parameter results in an enhancement of the temperature distribution, while an increase in the suction/injection parameter causes a reduction in the velocity and temperature distributions for both injection and suction cases.

BIE formulation for axisymmetric transient heat conduction applications

Boundary integral equation method is proposed for axisymmetric transient heat transfer applications covering spatially varying heat sources. The radial integral approach using the normalized temperature, thus, eliminating temperature gradients involved, is utilized to switch two-dimensional integrals to the equivalent line-related integrals. The derivative of the temperature is approximated using the finite difference method. To evaluate time-depended equations, the time-marching scheme is adopted. The proposed boundary integral formulation is implemented into axisymmetric applications to assess its accuracy.

About Applications of Deep Learning Operator Networks for Design and Optimization of Advanced Materials and Processes

Abstract The paper explores the possibility of using the novel Deep Operator Networks (DeepONet) for forward analysis of numerically intensive and challenging multiphysics designs and optimizations of advanced materials and processes. As an important step towards that goal, DeepONet networks were devised and trained on GPUs to solve the Poisson equation (heat-conduction equation) with the spatially variable heat source and highly nonlinear stress distributions under plastic deformation with variable loads and material properties. Since DeepONet can learn the parametric solution of various phenomena and processes in science and engineering, it was found that a properly trained DeepONet can instantly and accurately inference thermal and mechanical solutions for new parametric inputs without re-training and transfer learning and several orders of magnitude faster than classical numerical methods.

Model and transient Control strategy design of an Organic Rankine Cycle Plant for waste heat recovery of an Internal Combustion Engine

The multi-sources hybrid polygeneration energy systems are of great interest and topicality as they are one of the most promising technologies in the European’s Green Deal panorama, with the aim of serving users with electrical and thermal energy using a single plant powered by one or more energy sources. In the waste heat recovery field Organic Rankine Cycle (ORC) power plants are becoming increasingly popular, especially for exploiting medium and low temperature heat sources as a micro-small scale power plant. However, the development and diffusion of this technology is still limited due to the high costs and consequently prototype development and experimental assessment of performance is very poor, especially for non-stationary systems. In this work the modelling and validation of a micro-scale waste heat recovery (WHR) plant coupled with a control system is presented. An ORC plant has been modelled through a map-based model approach for the piston pump and the scroll expander while the pipes and the heat exchangers through a 1D thermo-fluid dynamic approach. A preliminary comparison was made between some numerical quantities of the modelled plant and the same experimental quantities in 61 different operating conditions, showing an average error of 50.1%. The model has been calibrated using a vector optimization technique: two calibration parameters of the heat exchangers were calibrated with a genetic algorithm (MOGA II) by reducing the error of 5 quantities obtained from the model with the respective experimental quantities in 15 different operating conditions. The remaining 46 operating conditions were used to evaluate the calibrated model, showing an average error of 3%. Furthermore, in order to provide for the use of the system coupled to highly variable heat sources, such as the exhaust gases of an internal combustion engine, a control strategy has been designed to perform two tasks: leading the ORC performance where the efficiency is higher, acting on the pump speed through a map-based control, implemented by a look-up table control, and protecting the organic fluid from damage caused by high working temperatures through a bypass control system with a PI control, depending on the proportional and integral gains. In order to verify the control strategy behaviour at different thermal transient inputs, a set of simulations has been run, showing a robust and stable manner preserving the organic fluid properties and limiting the superheated steam at expander inlet.

Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources

An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.