Temperature-dependent Heat Source Research Articles

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

Instability of thermal convection in an inclined fluid layer with temperature-dependent internal heat source

Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources

Abstract Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. This paper presents an enhanced exponential time integrator approach to dynamically simulate non-Newtonian boundary layer flow with spatially and temporally varying heat sources. We propose an explicit scheme with second-order accuracy in time, demonstrated to be stable through Fourier series analysis, for solving time-dependent partial differential equations (PDEs). Utilizing this scheme, we construct and solve dimensionless PDEs representing the flow of Williamson fluid under the influence of space- and temperature-dependent heat sources. The scheme discretizes the continuity equation of incompressible fluid and Navier–Stokes, energy, and concentration equations using the central difference in space. Our analysis illuminates how factors affect velocity, temperature, and concentration profiles. Specifically, we observe a rise in temperature profile with enhanced coefficients of space and temperature terms in the heat source. Non-Newtonian behaviours and geographical/temporal variations in heat sources are critical factors influencing overall dynamics. The novelty of our work lies in developing an explicit exponential integrator approach, offering stability and second-order accuracy, for solving time-dependent PDEs in non-Newtonian boundary layer flow with variable heat sources. Our results provide valuable quantitative insights for understanding and controlling complex fluid dynamics phenomena. By addressing these challenges, our study advances numerical techniques for modelling real-world systems with implications for various engineering and scientific applications.

Prandtl-eyring couple stressed flow within a porous region counting homogeneous and heterogeneous reactions across a stretched porous sheet

The movement of a non-Newtonian incompressible Prandtl-Eyring fluid layer over a stretching/shrinking permeable plate is shown in the current work. The flow is stressed by an additional couple stress, altered by a uniform normal magnetic field, and saturated in a permeable material. Heat transmission is demonstrated using a temperature-dependent heat source, an exponential space-dependent heat source, Joule heating, and viscous dissipations. Momentum, energy, and chemical type concentration equations, coupled with appropriate boundary conditions, support the mathematical structure. The novel aspect of the current work comes from considering species mass transfer using heterogeneous and homogeneous biochemical reactions along with the effects of thermal diffusion in the aforementioned flow. The reaction processes are isothermal with identical coefficients of chemical species. The leading nonlinear partial differential equations are transformed into ordinary differential equations utilizing appropriate similarity transformations. The homotopy perturbation method examines these equations. As a result, the primary objective distributions' analytical solutions are derived, and a graphical representation of them is produced to show the effects of the pertinent physical elements. The heterogeneity reaction serves as a dual role parameter in this diffusion, while the homogeneity reaction has been discovered to be a decreasing factor for particle diffusion. The ability of suction or injection via a permeable surface is observed to reduce the velocity and heat transmission, meanwhile, increasing chemical species condensation.

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid’s fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme.

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Radiation-driven thermoacoustic energy conversion in absorbing media

Thermoacoustic engines rely on an instability that can convert heat into an intense acoustic wave — oscillating pressure and velocity. Being heat-driven, thermoacoustic engines are a promising technology for solar energy conversion, potentially cheap, reliable, and robust, with no moving parts and no exotic materials. Herein, we present an as-yet overlooked mode of triggering a thermoacoustic instability in such engines, driven by radiation. This mode of operation can potentially eliminate much of the viscous losses associated with high-amplitude thermoacoustic energy conversion by eliminating the need for a solid, porous medium with which to mediate heat transfer. A theoretical framework is developed for modeling such devices, with a simplified analysis illustrating that any non-uniform, temperature-dependent heat source has the potential to trigger the thermoacoustic instability. It is then further demonstrated that radiation can indeed drive such instability, with numerical results showing that energy conversion is more substantial when the oscillation period is matched with the characteristic radiative heating time of the gas. A limit-cycle analysis indicates that, for a traveling wave acoustic field, potential efficiencies of up to 90% of Carnot’s efficiency may be achieved, with power densities of up to 5 MW/m3. While several of the assumptions made in the model likely result in lower performance for a real system, the analysis demonstrates the great potential offered by this approach, for future development.

Bioconvective Flow of Tangent Hyperbolic Hybrid Nanofluid Through Different Geometries with Temperature and Concentration Dependent Heat Source: Marangoni Convection

Bioconvective Flow of Tangent Hyperbolic Hybrid Nanofluid Through Different Geometries with Temperature and Concentration Dependent Heat Source: Marangoni Convection

Hydrothermal bioconvective Bödewadt ternary composition nanofluids flow over a stretching rotating disk through a heat generating porous medium

The bioconvective Bödewadt flow of ternary composition nanofluids over a three-dimensional stretched rotating disk is explored. The considered stream layer is filled by a porous medium and the inertia impacts are not neglected. Several physical issues are analyzed such as second order slip, strong magnetic field, thermal radiation, and temperature-dependent heat source. Also, exponential features are assumed for the heat source and Arrhenius activation energy. The components of the ternary nanofluids are spherical Al2O3 nanoparticles, MWCNT cylindrical nanoparticles and platelet graphene nanoparticles and suitable correlations for the thermophysical properties are introduced. The irreversibility properties in all the aforementioned cases are analyzed. The solution methodology depends on transforming the governing system to similar forms then they are solved using 4th order Rung-Kutta method. The obtained results disclosed that the temperature features are higher in case of ternary nanofluids compared to the hybrid and mono nanofluids cases. Also, the given outcomes recommend using the mono nanofluids to obtain lower system irreversibility.

Unsteady MHD flow in a rotating annular region with Homogeneous–Heterogeneous chemical reactions of Walters’ B fluids: Time-periodic boundary criteria

This paper considers the movement of an incompressible non-Newtonian Walters’ B liquid within a rotating annulus. The flow lies within porous media and is magnetized by a uniform normal magnetic field. Mass transmission is included in the arrangements of homogeneous and heterogeneous chemical reactions (HHCR) with a thermal diffusion effect. Heat diffusion is exposed with a temperature- dependent heat source (THS) and an exponential radial-dependent heat source (ERHS), besides Joule heating and viscous dissipations. The mathematical construction is shown by momentum, energy and concentration of chemical materials equations along with time-periodic boundary conditions. The innovation of this study stems from considering mass transfer utilizing HHCR, with thermal diffusion effects in the flow within a rotating annulus, trying to understand the effect of these reactions on the flow and related applications. The principal regulating the structure of nonlinear partial differential equations is transferred by ordinary ones utilizing appropriate similarity analysis. These equations are analyzed by the homotopy perturbation method. Subsequently, the analytical solutions of the main profiles are obtained, and a graphical construction is established to clarify the effects of the relevant physical elements. It is observed that the velocity waves decrease with annulus width enlargement and increase with the wave phase amplitude. With an increase in all significant parameters, heat transmission gets better. Furthermore, as the strength of HHCR is increased, the concentration of molecules decreases. These outcomes are significant in several applications like cancer therapy, biochemical manufacturing purposes through reactors, where biochemical interactions can be regulated by accurate control of various parameters.

Entropy Generation Analysis in Magnetohydrodynamic Couple Stress Nanofluid Flow Through an Oblique Microchannel in a Permeable Medium with Thermal Radiation

The present work examines the flow and thermal energy process in conducting couple stress nanofluid flows through an oblique microchannel. The microchannel is embedded with permeable medium and thermal radiation is implemented. The microchannel boundaries retain the slip boundary conditions. The impact of buoyancy force and magnetic field are incorporated. The temperature dependent heat source effect was also taken into account. The momentum equation has been made by the permeability of the porous medium. The equations are modeled and non-dimensionalized using non-dimensional entities and further solved with the aid of the Runge-Kutta Fehlberg method and the shooting procedure. The detailed discussions about the importance of the effective parameters on entropy generation, the Bejan number have been observed through graphs. The findings of the examination depict that rise in radiation parameter augments the entropy generation and the Bejan number in the channel. The entropy generation and Bejan number diminishes with inflation of the permeability parameter.

Rheological behavior of magnetized ZnO – SAE50 nanolubricant over Riga plate: A theoretical study

[Formula: see text] nanolubricant is one of the most important nanolubricants having widespread uses in heat exchange systems and automobiles. It minimizes friction between moving parts and prevents them from corrosion and scrape, improves durability and performance of the system and also minimizes the consumption of fuel. This work investigates the rheological behavior of magnetized [Formula: see text] nanolubricant over moving/stationary Riga plate with viscous dissipation and nonlinear heat generation. The novel features of the current work are the use of [Formula: see text] nanolubricant as a flow fluid across a Riga plate and the application of the Patel model to boost the thermal conductivity of the nanolubricant. The governing system of equations is transformed to nonlinear ODEs and then treated analytically by using HAM. The augmentation in the velocity of nanolubricant [Formula: see text] is observed due to increasing values of Grashof number. The higher values of nonlinear thermal radiation and nonlinear heat generation parameters upsurge the temperature profile. The value of skin friction increases by increasing modified Hartman number and velocity slip parameter while reverse trend is observed by enhancing magnetic parameter. The radiation parameter, temperature dependent heat source parameter and solid volume fraction tend to augment Nusselt number at the Riga surface.

Heat Transfer of Buoyancy and Radiation on the Free Convection Boundary Layer MHD Flow across a Stretchable Porous Sheet

Theoretical influence of the buoyancy and thermal radiation effects on the MHD (magnetohydrodynamics) flow across a stretchable porous sheet were analyzed in the present study. The Darcy–Forchheimer model and laminar flow were considered for the flow problem that was investigated. The flow was taken to incorporate a temperature-dependent heat source or sink. The study also incorporated the influences of Brownian motion and thermophoresis. The general form of the buoyancy term in the momentum equation for a free convection boundary layer is derived in this study. A favorable comparison with earlier published studies was achieved. Graphs were used to investigate and explain how different physical parameters affect the velocity, the temperature, and the concentration field. Additionally, tables are included in order to discuss the outcomes of the Sherwood number, the Nusselt number, and skin friction. The fundamental governing partial differential equations (PDEs), which are used in the modeling and analysis of the MHD flow problem, were transformed into a collection of ordinary differential equations (ODEs) by utilizing the similarity transformation. A semi-analytical approach homotopy analysis method (HAM) was applied for approximating the solutions of the modeled equations. The model finds several important applications, such as steel rolling, nuclear explosions, cooling of transmission lines, heating of the room by the use of a radiator, cooling the reactor core in nuclear power plants, design of fins, solar power technology, combustion chambers, astrophysical flow, electric transformers, and rectifiers. Among the various outcomes of the study, it was discovered that skin friction surges for 0.3 ≤F1≤ 0.6, 0.1 ≤k1≤ 0.4 and 0.3 ≤M≤ 1.0, snf declines for 1.0 ≤Gr≤ 4.0. Moreover, the Nusselt number augments for 0.5 ≤R≤ 1.5, 0.2 ≤Nt≤ 0.8 and 0.3 ≤Nb≤ 0.9, and declines for 2.5 ≤Pr≤ 5.5. The Sherwood number increases for 0.2 ≤Nt≤ 0.8 and 0.3 ≤Sc≤ 0.9, and decreases for 0.1 ≤Nb≤ 0.7.

A meshless thermal modelling for functionally graded porous materials under the influence of temperature dependent heat sources

In this study, a meshless thermal modeling with meshless local moving kriging interpolation method is presented for analysis of functionally graded porous (FGP) materials under the influence of temperature dependent heat sources. The method is developed based on local collocation with moving kriging shape function. It is truly meshless and having the Kronecker delta property for accurate imposition of boundary conditions. In the proposed model, the weight function is used with correlation parameter treated as the model internal length factor. This produces a local moving kriging method with improved accuracy together with an ease to choose the weight function factor. The method can hence be used in an efficient manner without cumbersome effort for choosing its parameter. The contribution is highlighted in the present study, which is still unexplored in detail in literature. Different forms of porosity are considered to investigate the effect of porosity to heat transfer performance of FGP materials subjected to temperature dependent heat sources. In addition, the method is applied for thermal analysis of FGP materials considering arbitrary geometries, mixed boundary conditions and varied power-law index. Numerical results show the effectiveness and accuracy of the meshless method for thermal modeling and analysis of FGP materials.

Experience of non-uniform heat source/sink on the flow of micropolar nanofluid fluid with heterogeneous and homogenous chemical reaction

Due to the varied applications in industries, chemical reaction has a significant role in the perfect shape and size of the product that is dependent upon the proper cooling of the system. Therefore, the existing analysis reveals the impression of non-uniform heat source/sink on the micropolar nanofluid through a nonlinear vertical stretching surface for the interaction of heterogeneous and homogeneous chemical reactions. Oxide nanoparticle embedding with the traditional water is considered by introducing operational properties such as thermal conductivity and viscosity. The free convective water-based nanofluid past through a permeable medium interacts with the transverse magnetic field and the thermal buoyancy enriches the present discussion. Further, the convective heat transfer condition is useful to enhance the thermal properties as well. Imposing suitable transformations the present problem turned into ordinary and solved by employing the bvp5c built-in MATLAB code. Further, the important results are; inclusion of particle concentration favors for the enhancement in the shear stress as well as the heat transfer rate in conjunction with the resistive forces such as magnetic and porosity but the impact is reversed in case of couple stress coefficient however, retardation in the fluid temperature occurs for the increasing space and temperature dependent heat source.

Analytical Solution of Non Linear DPL Bioheat Transfer Model for Temperature Dependent Metabolic Heat Source During Thermal Therapy

In this research paper, the simulation based modelling of heat transfer in tissue under periodic boundary condition has been considered. The dual phase lag bioheat transfer (DPLBHT) model is implemented for computation of the temperature based thermal therapy treatment. The elements of volumetric heat source such as perfusion of blood, metabolism heat source and external heat source are considered in nonlinear DPL model. In this paper we have taken three cases for metabolic heat source namely, constant, linear and exponential. The combined two numerical methods which are based on finite difference scheme and Runge Kutta (4,5) scheme are exerted to solve the non-linear problem. We compute the exact solution for particular case. Numerical conclusions which are computed by numerical hybrid method are equated with exact result. It has been found that non linear DPL model with exponential metabolic heat source is closed to exact solution. We also expressed the effect of different parameters such as relaxation time, perfusion rate, metabolic heat source parameter, associated blood perfusion heat, heat source because of heat flux and temperature gradient etc.

A Very Simple Procedure for Constructing the Solution of Nonlinear Elliptic PDEs (with Nonlinear Boundary Conditions) Arising from Heat Transfer Problems in Solids

This work presents a procedure for constructing the solution of a second order nonlinear partial differential equation subjected to nonlinear boundary conditions in a very simple and systematic way. The class of equations to be considered here includes, but is not limited to, the partial differential equations which govern the steady-state heat transfer process in bodies with temperature-dependent thermal conductivity and temperature-dependent internal heat source. In addition, it will be considered a large class of nonlinear boundary conditions, especially those arising from the description of the heat exchange process from/to bodies at high temperature levels. Proofs of the solution’s existence and uniqueness are presented.

Characteristics of variable plate conditions on the time-dependent flow of polar fluid over an expanding/contracting surface

The present scenario intended for the flow phenomena of micropolar fluid past an expanding/contracting surface is carried out to reveal the impact of a drag coefficient. Free convection due to the inclusion of the buoyant forces along with the radiative heat energy and non-uniform heat source/sink encourages the flow properties. The novelty of the present investigation is the use of variable plate conditions that affect the flow properties greatly. The transformation of the governing flow phenomena is obtained with the use of suitable similarity transformation and numerical treatment based upon Runge-Kutta fourth-order followed by shooting is imposed to get the solution of this transformed nonlinear system. Further, the simulation of the characterizing parameters is obtained and presented via graphs and tables. The major findings are; the enhancement in the axial velocity is characterized by the non-Newtonian behavior of the fluid and both the space and temperature dependent heat source favors for the augmentation in the fluid temperature.

Activation energy impact on unsteady Bio-convection nanomaterial flow over porous surface

<abstract> <p>Nanofluid is an advanced technology to enhance heat transportation. Additionally, the thermal conductivity of nanofluids is high therefore, they are more useful for heat transportation. Evaluation of entropy generation has been a helpful technique for tackling improvements in thermal features because it provides information that cannot be obtained via energy analysis. For thermodynamic irreversibilities, a good approximation is the rate of entropy generation. As a result of a reduction of entropy production, energy transport infrastructure has become more efficient. This study aims to analyse the bioconvective flow of nanofluid flow through a stretching sheet in the occurence of gyrotactic motile microorganisms. A magnetised nanomaterial model with thermophoretic and Brownian diffusion properties is analysed. The impacts of activation energy, temperature dependent and exponential base heat source are investigated in this analysis. The entropy generation of the system is also observed for nanofluid flow. The mathematical model is developed as partial differential equations. The governing equations are reduced to a dimensionless system of ordinary differential equations by applying similarity transformations. The ODEs are tacked numerically with the aid of shooting scheme in commercial software MATLAB. For graphical and numerical results of flow controlling parameters versus subjective fields, the commercial software MATLAB tool bvp4 is used with the shooting scheme. The novelty of this analysis computes numerical computation of bioconvective nanofluid flow with temperature-dependent and exponential base heat source investigated. Furthermore, the consequence of thermal radiation and entropy of the system is considered. The porous medium with activation energy is also taken into consideration. The results show that the velocity field is reduced with increased bioconvection Rayleigh number. The thermal field is increased via an exponential space-based heat source. The concentration is reduced via Lewis number. the microorganisms profile declines for larger bioconvection Lewis number. The Brinkman number Br, magnetic and permeability characteristics all showed a rising trend when plotted against the entropy production rate.</p> </abstract>

A Temperature-Dependent Heat Source for Simulating Deep Penetration in Selective Laser Melting Process

Numerical methods for simulating selective laser melting (SLM) have been widely carried out to understand the physical behaviors behind the process. Numerical simulation at the macroscale allows the relationship between input parameters (laser power, scanning speed, powder layer thickness, etc.) and output results (distortion, residual stress, etc.) to be investigated. However, the macroscale thermal models solved by the finite element method cannot predict the melt pool depth correctly as they ignore the effect of fluid flow in the melting pool, especially in the case of the presence of deep penetration. To remedy this limitation, an easy-implemented temperature-dependent heat source is proposed. This heat source can adjust its parameters during the simulation to compensate for these neglected thermal effects related to the fluid flow and keyhole, and the heat source’s parameters become fixed once the temperatures of the points of interest become stable. Contrary to the conventional heat source model, parameters of the proposed heat source do not require a calibration with experiments for each process parameter. The proposed model is validated by comparing its results with those of the anisotropic thermal conductivity method and experimental measurements.

MESHLESS SIMULATION OF HEAT CONDUCTION IN FUNCTIONALLY GRADED MATERIALS SUBJECTED TO TEMPERATURE-DEPENDENT HEAT SOURCES

In this paper, an efficient meshless local B-spline based finite difference (FD) method for analysis of functionally graded materials (FGMs) subjected to temperature-dependent heat sources is presented. The favourable properties of B-spline basis functions in having arbitrary degree for resolution of solution, partition of unity and the Kronecker delta properties are combined with high accuracy and low computational effort of differential quadrature method in approximating shape functions and their derivatives. In this study, the FGMs are assumed to have temperature-dependent materials properties that vary as a function of radial distance. The homogenized properties are evaluated with power-law mixture rule. The nonlinearities from material properties and heat source terms are handled by the predictor-corrector method along with the Crank-Nicolson scheme for time integration. Case of nonlinear 2D heat conduction in FGM due to temperature dependentheat sources is examined. The method is shown to be accurate and efficient for complex thermal analysis of FGMs taking into account temperature dependency of material properties and heat sources.