Nonlinear Heat Transfer Research Articles

Unsteady nonlinear mixed convective flow of nanofluid over a wedge: Buongiorno model

The article deals with 2D unsteady nanofluid flow past a vertical wedge along with nonlinear mixed convection. Brownian diffusion and thermophoresis effects are considered to model nanofluid flow. Convenient transformations are assumed to change the coupled nonlinear governing PDEs into ODEs. To analyze the problem, the solutions of transformed equations are numerically achieved via ‘bvp4c’, a MATLAB approach. Graphical presentation is adopted to see the impact of various influential parameters. Results reveal that nonlinear temperature and concentration convection parameters exhibit the same impact for velocity, temperature and concentration profile, though nonlinear convection parameter for temperature is more impactful than concentration. Velocity overshoot is observed for assisting flow situations. In nonlinear mixed convection flow, skin-friction coefficient, heat and mass transfer rates prominently change for favorable and adverse pressure gradient conditions.

Differential Transformation Method for Solving Nonlinear Heat Transfer Equations

In this paper, Differential Transformation Method (DTM) is applied for solving the nonlinear differential equations arising in the field of heat transfer. The solution is considered as an infinite series expansion where converges rapidly to the exact solution. The nonlinear convective–radioactive cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples and solutions have been found for each case. Results by DTM with other results calculated by Homotopy Perturbation Method are compatible.

Semianalytical Solution of Transient Heat Transfer for Laminated Structures under Time-Varying Boundary Conditions

In order to solve the transient heat transfer problem of the laminated structure, a semianalytical method based on calculus is adopted. First, the time domain is divided into tiny time segments; the analytical solution of transient heat transfer of laminated structures in the segments is derived by using the method of separation of variables. Then, the semianalytical solution of transient heat transfer in the whole time domain is obtained by circulation. The transient heat transfer of the three-layer structure is analyzed by the semianalytical solution. Three time-varying boundary conditions (a: square wave, b: triangular wave, and c: sinusoidal wave) are applied to the surface of the laminated structure. The influence of some key parameters on the temperature field of the laminated structure is analyzed. It is found that the surface temperature of the laminated structure increases fastest when heated by square wave, and the maximum temperature can reach at 377°C, the temperature rises the most slowly when heated by the triangular wave, and the maximum temperature is 347°C. The novelty of this work is that the analytical method is used to analyze the nonlinear heat transfer problem, which is different from the general numerical method, and this method can be applied to solve the heat transfer problem of general laminated structures.

Experimental study of cooling characteristics to analyse quenching phenomenon of non-heat treatable material with different quenchants

Quenching is one of the commonly used process to improve mechanical properties for any materials. The quality of quenching and efficiency are usually measured by using various quench probes and get the cooling curves. The main parameters which are affecting the cooling characteristics are, geometry, quenchant type and materials grade, etc. A mathematical model that can be employed to get heat flux and cooling curves for a different materials/cooling medium combination. Present model coupled with nonlinear unsteady heat transfer with phase change, which leads to cooling curves for different materials/quenchant. Experiments are conducted in the standard laboratory condition to determine heat flux and surface temperature at the mid-plane of a 10 mm diameter by 70 mm long specimen of Stainless Steel material. InverseSOLVER software is used to analyse the experimental data to obtain cooling curves. This specimen is cooled with different quenching medium, such as, water, vegetable oil and different grade of lubricating oils. The experimental results are analysed for different quenchants using Inverse solver. The experimental results indicated that cooling curves, cooling rate, and the surface heat flux vary with quenchants.

RETRACTED: Analysis of radiative nonlinear heat transfer in a convective flow of dusty fluid by capitalizing a non-Fourier heat flux model

The study is concerned with the heat transfer in a slip flow of a dusty fluid with the impact of a magnetic field and nonlinear thermal radiation. Furthermore, for the heat transfer process the Cattaneo–Christov heat flux model is used. Suitable similarity transformations are used to transform the governing equations. Later, shooting method and the Runge-Kutta Fehlberg's fourth fifth order (RKF-45) process are utilized to solve these reduced system of nonlinear ordinary differential equations. Impact of numerous involved parameters on the flow, thermal fields of both dust and fluid phase, skin friction and rate of heat transfer are visually plotted through graphs and discussed quantitatively. The significant outcomes drawn from the current study are that, the rise in value of the velocity slip parameter decreases the velocity profile but improves the thermal profile of both the phases. The growing values of curvature parameter intensify the flow and the thermal fields of both phases. The cumulative values of magnetic parameter and dust particle mass concentration parameter declines the velocity and thermal gradients of both phases. The thermal relaxation time parameter decays the temperature profile. The heat transfer rate is strengthened with the growing values of the curvature parameter, the velocity slip parameter, and radiation parameter.

Tangent stiffness for nonlinear heat transfer and its application to additive manufacturing

Prediction-correction method is commonly employed in the solution of nonlinear heat transfer equation with temperature dependent thermophysical parameters arising in various engineering problems such as additive manufacturing of metal components. However, the stiffness of such conventional method is secant rather than tangent and thus it only results in suboptimal rate of convergence in Newton's iteration. In this paper, tangent stiffness for nonlinear heat transfer is proposed through the linearization of the weak form and an additional term presents which disappears in the conventional prediction-correction method. Numerical results show that the solution with the proposed tangent stiffness converges much faster than that with secant stiffness and approximately only half of the iteration steps are needed. Especially, in the case that the thermal conductivity varies dramatically with the temperature, the conventional method diverges whereas the tangent stiffness still shows quite good convergence. Application of the proposed method to the modeling of heat transfer in additive manufacturing (AM) process is presented and the obtained temperature results agree quite well with the existing experimental studies. It is worth mentioning that almost half of CPU time is saved due to the application of the proposed tangent stiffness. This saving is of great significance for modeling the AM process of complicated components, which is usually very time-consuming.

Comparative study for magnetized flow of nanofluids between two parallel permeable stretching/shrinking surfaces

The current study intended to discuss a comparative study on the three dimensional Casson nanofluid with nonlinear radiative MHD flow and heat transfer aspects between two parallel stretching/shrinking surfaces. The mathematical models for momentum and temperature are established by employing the boundary layer flow of fluids with spinel-type ferrite MnFe2O4 nanoparticles being distributed in Pure Water/ (H2O) as the base fluid. Remarkable models like Maxwell-Garnett and Patel models are inserted in view of thermal conductivity augmentation. The suitable similarity transformations are adopted for converting the governing non-linear partial differential equations into non-dimensional ODE's and obtaining the relevant parameters for discussion. The major outers of the present study are axial velocity {F′(η)} peters out with amplifying β subject to stretched and shrunk surfaces in relation to both Maxwell-Garnett and Patel models. Growing θw and n exhibits opposite effect on heat transfer rate.

Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer.

In this study, a novel application of neurocomputing technique is presented for solving nonlinear heat transfer and natural convection porous fin problems arising in almost all areas of engineering and technology, especially in mechanical engineering. The mathematical models of the problems are exploited by the intelligent strength of Euler polynomials based Euler neural networks (ENN’s), optimized with a generalized normal distribution optimization (GNDO) algorithm and Interior point algorithm (IPA). In this scheme, ENN’s based differential equation models are constructed in an unsupervised manner, in which the neurons are trained by GNDO as an effective global search technique and IPA, which enhances the local search convergence. Moreover, a temperature distribution of heat transfer and natural convection porous fin are investigated by using an ENN-GNDO-IPA algorithm under the influence of variations in specific heat, thermal conductivity, internal heat generation, and heat transfer rate, respectively. A large number of executions are performed on the proposed technique for different cases to determine the reliability and effectiveness through various performance indicators including Nash–Sutcliffe efficiency (NSE), error in Nash–Sutcliffe efficiency (ENSE), mean absolute error (MAE), and Thiel’s inequality coefficient (TIC). Extensive graphical and statistical analysis shows the dominance of the proposed algorithm with state-of-the-art algorithms and numerical solver RK-4.

A review on the theory of stable dendritic growth.

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented. The sharp interface model and stability criteria for various crystallization conditions and crystalline symmetries met in actual practice are formulated and discussed. The review is also focused on the determination of the main process parameters-the tip velocity and diameter of dendritic crystals as functions of the melt undercooling, which define the structural states and transitions in materials science (e.g. monocrystalline-polycrystalline structures). Selection criteria of stable dendritic growth mode for conductive and convective heat and mass fluxes at the crystal surface are stitched together into a single criterion valid for an arbitrary undercooling. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Multidimensional thermal structures in the singularly perturbed stationary models of heat and mass transfer with a nonlinear thermal diffusion coefficient

A new approach to the study of multidimensional singularly perturbed problems of nonlinear heat conduction is proposed, based on the further development and use of asymptotic analysis methods. We study the question of the existence of classical Lyapunov stable stationary solutions with boundary and internal transition layers (stationary thermal structures) of the nonlinear heat transfer equation. We suggest the efficient algorithm for constructing an asymptotic approximation to the localization surface of the transition layer. To justify the constructed formal asymptotics, we use the principle of comparison.We consider the application of the results of asymptotic analysis to solving inverse problem of reconstructing the temperature dependence of the thermal conductivity coefficient from a known position of the internal layer of thermal structure.

Nonlinear heat transfer analysis of spines using MLPG method

In the current article, an analysis of heat transfer in the spine of different profiles is carried out. A nonlinear differential equation that includes the effect of temperature-dependent thermal conductivity, variable heat transfer coefficient, and surface radiation is solved using a predictor-corrector scheme and the meshless local Petrov-Galerkin (MLPG) method. The moving least square (MLS) method is employed for the approximation of unknown function and the penalty parameter method is used to impose essential boundary conditions. Temperature variation along the length of the spine and rate of heat transfer in steady-state, under convective and convective-radiative environment has been obtained and explained. Performance of the spine under the above conditions is evaluated. Further, the study is extended to calculate volume adjusted performance which presents a comparative thermal performance of different profiles.

Semi-Analytical Solution of a Nonlinear Heat Transfer Model for a Tubular Cocurrent Moving-Bed Reactor With a First-Order Chemical Reaction in the Solid Phase

Abstract The development of mathematical models plays a fundamental role in the design, optimization, and control of processes. Regarding heat transfer in moving bed reactors, the chemical reaction implies the inclusion of a nonhomogeneous and nonlinear term in model equations, making the analytical integration a very difficult task. Up to date, there is not an analytic and/or a semi-analytic solution to a heat transfer model of a moving bed reactor (MBR) with isothermal walls to the distributed parameters in the solid phase. Therefore, starting from analytical solutions of the associated homogeneous (linear) problems and through the spectral expansion of the nonhomogeneous vector, this work presents strategies for determining semi-analytical solutions of nonhomogeneous and nonlinear problems. An MBR with a first-order chemical reaction in the solid phase—kaolinite dehydroxylation in the kaolinite flash calcination process—is selected as the case study; however, the strategies can easily be applied to other nonlinear models. Results for conversion, and fluid and particle temperatures, are given for different parameter values. The solutions perform stable, fast, and accurate. When compared with a hybrid finite difference and finite analytic (FD&FA) numerical method, the solution showed a very good agreement.

Modelling of Applied Magnetic Field and Thermal Radiations Due to the Stretching of Cylinder

In this study, a numerical approach was adopted in order to explore the analysis of magneto fluid in the presence of thermal radiation combined with mixed convective and slip conditions. Using the similarity transformation, the axisymmetric three-dimensional boundary layer equations were reduced to a self-similar form. The shooting technique, combined with the Range–Kutta–Fehlberg method, was used to solve the resulting coupled nonlinear momentum and heat transfer equations numerically. When physically interpreting the data, some important observations were made. The novelty of the present study lies in finding help to control the rate of heat transfer and fluid velocity in any industrial manufacturing processes (such as the cooling of metallic plates). The numerical results revealed that the Nusselt number decrease for larger Prandtl number, curvature, and convective parameters. At the same time, the skin friction coefficient was enhanced with an increase in both slip velocity and convective parameter. The effect of emerging physical parameters on velocity and temperature profiles for a nonlinear stretching cylinder has been thoroughly studied and analyzed using plotted graphs and tables.

Оптимальное управление уравнениями радиационного теплообмена для многокомпонентных сред

An analysis of optimal control problems for nonlinear elliptic equations modeling complex heat transfer with Fresnel conjugation conditions on the discontinuity surfaces of the refractive index is presented. Conditions for the solvability of extremal problems and the nondegeneracy of the optimality system are obtained. For the control problem with boundary observation, the bang-bang property is set.

On the magnetized 3D flow of hybrid nanofluids utilizing nonlinear radiative heat transfer

This article analyzes the heat transfer, non-linear thermal radiation, the Cattaneo-Christov heat flux model and velocity slip effects in hybrid nanofluid flow over a 3D moving sheet. The hybrid type nanoparticles like Ag-Cu and MoS2 and GO are suspended in working liquid. Hybrid nanoliquid is homogeneous-mixture with novel physical and chemical structures making it a promising option for improving thermal efficiency. Hybrid nanoliquids have high ability to absorb and preserve the hydrogen because of their very huge unique surface-area and distinctive and unusual nature of an each nanostructure. Nanostructure carbon atoms like graphite, graphene and few metals like molybdenum and magnesium have recently been found to store hydrogen due to their larger storage-capacity and the higher dehydrogenation and hydrogenation speeds. The system of the mathematical relation in PDEs form is converted to system of ODEs by employing suitable variables. The bvp4c tool available in computational software MATLAB is used for solving the dimensionless ordinary differential system. Furthermore, the flow expectations for each physical flow parameter like are discussed. The physical consequence of flow parameters against subjective flow fields are graphically highlighted with physical justifications. The vitality of prominent parameters against velocity field and temperature distribution is illustrated through graphs. The velocity field diminishes with a larger velocity slip parameter. The velocity field is enhanced by the higher estimations of the Grashof number. The consequence of temperature ratio parameter on thermal field is delineated. By enhancing the thermal relaxation parameter, the thermal field reduces.

Bioconvection transport of magnetized Walter's B nanofluid across a cylindrical disk with nonlinear radiative heat transfer

Nanotechnology plays a crucial role in the main innovation development of the modern age in the latest technology. In recent times, researchers are concentrated to build up various algorithms to increase their heat transfer rate. One of the approaches that have conquered this deficiency is to significantly raise the thermal properties of regular fluids by manifestation of nanoparticles in host fluids. In this article, a numerical study is developed to investigate the bio convective transport of Walter's B nanofluid past a cylindrical disk in the presence of thermophoretic and Brownian diffusions. Additionally, non-linear thermal radiation, variable thermal conductivity and motile microorganisms are also considered. The Buongiorno model is used to explore the nanofluid features with motile microorganisms. The constituted normalized system of modeled flow equations is condensed into dimensionless system of differential form by adopting appropriate similarity variables. The ordinary systems are elucidated through bvp4c technique in MATLAB software. Characteristics of flow parameters against velocity field, temperature distribution, volumetric concentration of species and microorganism's profile are discussed. From the results we observed that velocity field is reduced for larger magnetic parameter. It is noticed that developing values of mixed convection parameter raises the velocity field. It is analyzed that temperature distribution of Walter's B fluid upsurge for variable thermal conductivity parameter. Temperature field intensifies for thermal Biot number. It is perceived that solutal field of species diminishes for larger Brownian motion parameter. The microorganism field is found to decay with Peclet and bioconvective Lewis numbers. The current proposed model is more useful in the field of engineering. The improvement in heat transfer rate is current issue in the world. Nanofluids have high thermal efficiency therefore such fluids are more useful to improve the heat transfer rate.

Importance of bioconvection in 3D viscoelastic nanofluid flow due to exponentially stretching surface with nonlinear radiative heat transfer and variable thermal conductivity

Importance of bioconvection in 3D viscoelastic nanofluid flow due to exponentially stretching surface with nonlinear radiative heat transfer and variable thermal conductivity

Sensitivity analysis of thermal factors affecting the nonlinear freezing process of soil

In the construction of artificial freezing methods and cold region engineering, the determination of the accurate temperature field is the demand of both ensuring the stability of frozen soil and reducing the project investment. Affected by the external environment, phase change latent heat, non-linear thermal parameters, etc., the temperature evolution of the soil freezing process is a non-linear form, and the temperature field evolution will be more complex with the change of different influencing factors. Scientific control and utilization of the influencing factors of the frozen soil temperature field play a vital role in improving the freezing efficiency and accuracy of the soil temperature field. This study aims to analyze the sensitivity of thermal factors on the nonlinear formation process of frozen soil temperature field, and to provide the results for the control of various factors in frozen soil engineering. A freezing model test was designed and implemented, the boundary conditions and temperature evolution in the model were monitored. Meanwhile, the thermal parameters and unfrozen water content of the model soil were tested indoor. Then the theoretical relationship between unfrozen water content and parameters was deduced to determine the variation range of unfrozen water content. The boundary condition values (including the maximum, minimum and average values) and thermal parameters were used in the orthogonal simulation of the freezing model, respectively. The temperature simulation values were compared with the model test values, and the factors affecting the nonlinear heat transfer of frozen soils were analyzed quantitatively by both the range method and variance analysis method. Several suggestions of the vital factors in the soil freezing construction were offered based on this research.

Heat transfer for nonlinear boundary conditions involving radiation for constant and temperature related thermal conductivity material using the MWLS method

The paper presented the heat transfer analysis for nonlinear boundary conditions involving radiation with constant and temperature related thermal conductivity material. For the constant thermal conductivity, linearizing the fourth power of radiation item, solve the temperature distribution through the global iteration coupled with the meshless weighted least squares (MWLS) method. For the temperature related variable thermal conductivity, the Kirchhoff transformation is usually employed to transform the nonlinear heat transfer problem into the linear Laplace's equation. Through the two-step iteration method, the convection and radiation boundary are converted into Dirichlet and Neumann boundary which is the easy-to-program linear condition after the transformation. In the end, the effectiveness and accuracy of the method were illustrated by some numerical examples .

Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange

We propose a model for studying several nonlinear waves for heat transport along a cylindrical system with lateral non-linear heat transfer to the environment. We consider relaxational equations, each with its own relaxation time, for longitudinal heat transfer and for lateral heat transfer across the wall. We consider two kinds of nonlinear lateral heat transport: radiative heat transport, and flux-limited heat transport. This work generalizes our previous studies in which the relaxation time for the lateral heat transfer was considered equal to that of the longitudinal heat flux. We explore the influence of both relaxation times on the propagation speed of linear and nonlinear waves, and on the form of nonlinear waves.