Radiation-conduction Parameter Research Articles

Assessment of temperature distribution on inclined porous rod with a convective and insulated tip

The following work focuses on determining the temperature profile of porous rod using radiative and insulated tip conditions. In addition, graphs are generated to investigate the impact of several non-dimensional attributes on the distribution of temperature for various modes of energy exchange, such as boiling of nucleates and radiative energy exchange, including the convection-conduction parameter, permeability parameter, and radiation-conduction parameter. ND solve technique is applied to solve the generated nonlinear partial differential equation by using MATHEMATICA. The transient thermal response has been visually presented for various key parameters with ranges p=0,2, Nr=1,5,10, Nc=0.3,0.4,0.5, Pe=0.1,0.2,0.3, Q=0.1,0.2,0.3, Bi=1,2,3. The graphical outcome reveals that temperature distribution is a decreasing function of radiation parameter. Exposure time of the rod to the environment gets short for the enhancement in Peclet number. Initially temperature contours are linear, as time progresses the exponential behavior is developed.

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

Transient thermal behavior and efficiency in fully wet porous longitudinal fin: The influence of shape-dependent hybrid nanofluid and internal heat generation

The main focus of this study is to analyze the transient heat transfer characteristics of a convective–radiative longitudinal porous fin fully wetted in hybrid nanofluid along with internal heat generation. The Darcy formulation is considered for analyzing the velocity of the fluid passing through the fin and the Rosseland approximation determines the radiation heat flux. The hybrid nanofluid is obtained by immersing GO and Mo S 2 nanoparticles in the hybrid base fluid C 2 H 6 O 2 ‐ H 2 O . Furthermore, three different shapes of nanoparticles namely spherical, platelet, and blade have been selected for the investigation. The derived nonlinear partial differential equation is nondimensionalized and solved numerically by employing the finite difference method. The effect of shape factor, nanoparticle volume fraction, dimensionless time, wet porous parameter, radiation–conduction parameter, heat generation parameters, and other relevant parameters on the transient thermal analysis of the fin structure has been graphically analyzed and discussed. Furthermore, the transient thermal fin efficiency has been modeled and its variation with the significant parameters has been examined. One of the major outcomes is that efficiency increases with nanoparticle volume fraction. The examination has resulted in a novel outcome that the presence of hybrid nanofluid enhances the fin efficiency and also the high fin efficiency is achieved in the presence of blade-shaped nanoparticles. The findings of the investigation play a prominent role in the heat transfer enhancement of industrial processes.

Thermal analysis of rectangular moving fins with temperature‐variant properties by employing the Galerkin scheme

AbstractIn the present study, the thermal behavior of a longitudinal fin considering three types of heat transfer mechanisms (conduction, convection, and radiation) is investigated. For this research, thermal conductivity, heat source, and heat transfer coefficient are assumed nonindependent. A semianalytical scheme called the Galerkin Method is utilized for solving the dimensionless governing equation. The impacts of important physical variables like Peclet number, gradient of thermal conductivity, thermo‐geometric parameter, and radiation–conduction parameter on temperature profiles are analyzed comprehensively. The obtained results indicate that raising the thermo‐geometric parameter from 0 to 2 leads to a 32% reduction in the temperature profile. Also from the results, it can be found that a 28% increment in the temperature is observed by changing the gradient of thermal conductivity from 0 to 2.

Entropy generation for exact irreversibility analysis in the MHD channel flow of Williamson fluid with combined convective-radiative boundary conditions

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system's entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

Investigation of the lattice Boltzmann method to resolve combined radiation-conduction heat transfer in participating media with curved boundaries

PurposePresent study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.Design/methodology/approachThe numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.FindingsFor the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.Originality/valueThe difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

Analytical and numerical (FEA) solution for steady-state heat transfer in generic FGM cylinder coated with two layers of isotropic material under convective-radiative boundary conditions

An investigation was carried out in order to develop an accurate analytical solution and a numerical (FEA) solution for steady-state heat transfer in a circular sandwich structure incorporated with convective-radiative boundary conditions. The dimensional governing equations and boundary conditions were developed in the form of a 4th order algebraic equation, and then the solution was obtained using Ferrari's method. By solving for the roots of the quartic equation, we were able to determine the dimensionless temperature fields of the FG sandwich composite. The findings obtained utilizing the exact analytical solution for the FG sandwich composite under thermal loads were satisfactorily validated against those data obtained using the Galerkin finite element approximation. The impact of geometric and thermo-physical characteristics, such as Biot number (Bii=1,2), Inner and outer surface thickness ratio (ri=1,2Ro), ambient temperature ratio (θd), radiation-conduction parameter (Nr), and thermal conductivity ratio (λ3λ1) on the efficiency of heat transfer, has also been studied. This study reveals the distinct effect of Biot number on the inner and outer layers of the composite cylinder. It shows that Bi1 has a negligent effect on temperature distribution; on the other hand, the outer surface (Bi2≤1) minimizes temperature variation. However, for design consideration, a thicker inner face sheet is not recommended in high thermal load, as Nr>4 has an insignificant impact on inner surface thickness on top surface temperature. Moreover, the outer surface temperature appears to be more sensitive to θd than the radiation-convection side. Furthermore, the given analytical solution is adequately verified against the proposed FEA method, having an error of less than 1.5%.

Hyperbolic Conduction and Radiation Heat Transfer in Axisymmetric Cylinders with Variable Properties

This work investigates the combined mode of hyperbolic heat conduction and radiation transfer in a one-dimensional axisymmetric cylinder filled with absorbing, emitting, and scattering media. The volumetric radiation is investigated thanks to the semianalytic solution of the matrix formulation of the spherical harmonics equations PN. The governing hyperbolic energy equation is solved using the finite volume method (FVM) with Roe’s correction of interface fluxes in order to enhance the performances of the method, and the lattice Boltzmann method (LBM) has been designed for comparisons. The effects of the parameters such as constant and spatial-dependent scattering albedos, temperature-dependent thermal conductivity, heat-generated sources, extinction, and the conduction–radiation parameter on both the temperature and heat flux distributions for steady and transient states within the medium are examined. The results of the present work are in excellent agreement with those available in the literature. The PN−FVM results are also compared to those obtained with the PN−LBM combination, and excellent agreement is obtained. These results show that the mentioned parameters have a significant effect on both the temperature profiles and the hyperbolic sharp wave front. This study also shows that the proposed layered approach is an efficient, fast, and accurate solution method for radiative analysis in inhomogeneous media, whereas the Roe’s correction of interface fluxes in the FVM is suitable to accommodate a thermal wave front in non-Fourier analysis.

A Semi-Analytical Description of Radiation Coupled with Thermal Wave Conductive Transfer in Inhomogeneous Solid Cylinder

This study presents the analytical layered solution for thermal radiations coupled with non-Fourier conductive heat transfer, formulated from the Cattaneo-Vernotte flux model in inhomogeneous solid cylinder. This solution is built by combining the spherical harmonics for volumetric thermal radiations with the D1Q3 scheme of lattice Boltzmann method (LBM) for hyperbolic energy equation where the gradient of static particle distribution function was discretized at implicit time. The accuracy of the proposed model for dealing with radiation/conduction problems is investigated by considering a semitransparent radiative transfer in a cylinder with temperature dependent thermal conductivity and space dependent scattering albedo. The effects of different parameters, such as scattering albedo, refractive index, thermal conductivity, emissivity, optical thickness, and the conduction-radiation parameter on both radiations and temperature distributions for steady and transient states are studied. Results of the present work are benchmarked against those available in the literature with accuracy greater than 98.9% for a large interval of parameter sets and therefore, excellent agreement has been obtained. It also establishes from this study that the proposed layered approach is an efficient and accurate method for radiative analysis in inhomogeneous media while the D1Q3 scheme is suitable to accommodate thermal wave front in non-Fourier analysis.

Iterative Solutions for the Nonlinear Heat Transfer Equation of a Convective-Radiative Annular Fin with Power Law Temperature-Dependent Thermal Properties

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized in the present investigation. The nonlinear variation of thermal conductivity and heat transfer coefficient governed by the power law is considered. The analytical approximation for the non-dimensional temperature profile is obtained using the differential transform method (DTM)-Pade approximant. The nondimensionalization of the governing energy equation using dimensionless terms yields a nonlinear ordinary differential equation (ODE) with corresponding boundary conditions. The resulting ODE is analytically solved with the assistance of the DTM-Pade approximant procedure. Furthermore, the impact of thermal parameters on the temperature field and thermal stress is elaborated with graphs. The important results of the report divulge that temperature distribution greatly enhances with an augmentation of the heat generation parameter, but it gradually reduces with an increment in the magnitude of the thermogeometric and radiative-conductive parameter.

Backpropagated Neural Network Modeling for the Non-Fourier Thermal Analysis of a Moving Plate

The present article mainly focuses on the transient thermal dispersal within a moving plate using the non-Fourier heat flux model. Furthermore, the innovative, sophisticated artificial neural network strategy with the Levenberg-Marquardt backpropagated scheme (ANNS-LMBS) is proposed for determining the transient temperature in the convective-radiative plate. Using dimensionless terms, the energy model for transient heat exchange is simplified into a non-dimensional form. The arising partial differential equation (PDE) is then numerically tackled using the finite difference method (FDM). A data set for the various scenarios of the thermal parameters influencing the thermal variation through the plate has been generated using the FDM. In addition, the effect of the dimensionless physical variables on the thermal profile of a moving plate has been examined and discussed in detail. Increments in the convection-conduction and radiation-conduction parameters are figured to yield a reduction in the transient thermal dispersion. An upsurge in the Peclet number caused the improvement of thermal dispersal in the plate.

Significance of thermal stress in a convective-radiative annular fin with magnetic field and heat generation: application of DTM and MRPSM

The present paper explains the temperature attribute of a convective-radiative rectangular profiled annular fin with the impact of magnetic field. The effect of thermal radiation, convection, and magnetic field on thermal stress distribution is also studied in this investigation. The governing energy equation representing the steady-state heat conduction, convection, and radiation process is transformed into its dimensionless nonlinear ordinary differential equation (ODE) with corresponding boundary conditions using non-dimensional terms. The obtained ODE is then solved analytically by employing the Pade approximant-differential transform method (DTM) and modified residual power series method (MRPSM). Moreover, the important characteristics of the temperature field, the thermal stress, and the impact of some non-dimensional parameters are inspected graphically, and a physical explanation is provided to aid in comprehension. The significant findings of the investigation reveal that temperature distribution enhances with an increase in the magnitude of the heat generation parameter and thermal conductivity parameter, but it gradually decreases with an increment of convective-conductive parameter, Hartmann number, and radiative-conductive parameter. The thermal stress distribution of the fin varies considerably in the applied magnetic field effect.

Significance of non-Fourier heat conduction in the thermal analysis of a wet semi-spherical fin with internal heat generation

The transient temperature distribution of a wet semi-spherical porous fin with convection, internal heat generation, and radiation is researched using a non-Fourier heat conduction (NFHC) model. A mathematical model for transient heat transfer in a dehumidifying environment is developed from the non-Fourier law and the corresponding governing equation is formulated. This equation is subjected to nondimensionalization using suitable dimensionless terms and is further solved by employing the finite difference method (FDM). A substantial deviation in thermal response by considering non-Fourier law under unsteady heat transmission has been analyzed graphically with the influence of various nondimensional parameters on the dry and wetted fins surface. The examination reveals the notable difference in temperature variation between the dry and wetted fins surfaces. Some important key results of the research analysis include that the transient thermal distribution through the fin decrease as the magnitude of the convective, wet porous and radiation-conduction parameters develop. For higher generating numbers, thermal distribution will be higher. The temperature in the hyperbolic model increases after some time in the existence of relaxation time and the temperature in a non-Fourier model flow in the form of a thermal wave.

Significance of Convection and Internal Heat Generation on the Thermal Distribution of a Porous Dovetail Fin with Radiative Heat Transfer by Spectral Collocation Method.

A variety of methodologies have been used to explore heat transport enhancement, and the fin approach to inspect heat transfer characteristics is one such effective method. In a broad range of industrial applications, including heat exchangers and microchannel heat sinks, fins are often employed to improve heat transfer. Encouraged by this feature, the present research is concerned with the temperature distribution caused by convective and radiative mechanisms in an internal heat-generating porous longitudinal dovetail fin (DF). The Darcy formulation is considered for analyzing the velocity of the fluid passing through the fin, and the Rosseland approximation determines the radiation heat flux. The heat transfer problem of an inverted trapezoidal (dovetail) fin is governed by a second-order ordinary differential equation (ODE), and to simplify it to a dimensionless form, nondimensional terms are utilized. The generated ODE is numerically solved using the spectral collocation method (SCM) via a local linearization approach. The effect of different physical attributes on the dimensionless thermal field and heat flux is graphically illustrated. As a result, the temperature in the dovetail fin transmits in a decreasing manner for growing values of the porosity parameter. For elevated values of heat generation and the radiation-conduction parameter, the thermal profile of the fin displays increasing behavior, whereas an increment in the convection-conduction parameter downsizes the thermal dispersal. It is found that the SCM technique is very effective and more conveniently handles the nonlinear heat transfer equation. Furthermore, the temperature field results from the SCM-based solution are in very close accordance with the outcomes published in the literature.

Performance analysis and optimization of a radiating fin array

Space radiators are used to reject waste heat from power units, electronic devices, and various equipment in space vehicles. It is important that radiators can achieve the heat desired to be dissipated into space with the least mass. With a view to ensuring this aim, the heat transfer calculations that must be performed must be highly accurate. Therefore, the variation of conductivity with temperature should also be taken into account in the mathematical model. This paper presents heat transfer performance and optimization of a fin array consisting of straight fins put axially on a tube and radiating heat into deep space. The mathematical model yields the governing equation as a highly nonlinear integro-differential equation which is solved by the variation of parameters method (VPM). By applying an appropriate optimization procedure, the conduction–radiation parameter, Nc, providing maximum heat transfer is obtained for a given fixed fin profile emissivity, ε, opening angle among the fins, γ, and thermal conductivity parameter describing the variation of thermal conductivity, β. For the range of suitable problem parameters, optimum values of the dimensionless conduction–radiation parameter Nc, which is a combination of thermal and geometric quantities, are expressed in ε and γ for a given β. The correlation equations are expected to provide remarkable benefits to the designer.

A physical depiction of a semi-spherical fin unsteady heat transfer and thermal analysis of a fully wetted convective-radiative semi-spherical fin

The current investigation scrutinizes non-Fourier heat conduction law to describe transient temperature variation through a convective-radiative wetted semi-spherical fin with internal heating. The fin is fully wetted with a hybrid nanofluid containing MnZnFe2O4−NiZnFe2O4 nanoparticles and water or methanol (methyl alcohol (MA)) as base liquids. Dimensionless terms are used to nondimensionalize the energy equation, and the finite difference method (FDM) is used to solve the nonlinear partial differential equation (PDE). In addition, graphs are drawn to explore the impact of several non-dimensional attributes on the temperature gradient, such as radiation-conduction, convection-conduction, and internal heat production parameters for hybrid nanofluid containing MnZnFe2O4 and NiZnFe2O4 nanoparticles with different base liquids. The major findings of the study show that as the magnitude of the wet parameter, and radiation-conduction parameters increases, the transient thermal distribution through the fin drops. Thermal distribution, on the other hand, improves for the parameter of heat generation.

Investigation of Heat Transfer from Convective and Radiative Stretching/Shrinking Rectangular Fins

We study the efficiency of shrinking/stretching radiative fins to improve heat transfer rate. To evaluate the competence of suggested fins, the influence of shrinking/stretching, thermogeometric parameters, surface temperature, convection conduction, radiation conduction, and Peclet number is investigated. The problem is solved numerically using a shooting method. To validate the numerical solution, the results are compared with the solution of a differential transform method. Temperature distribution increases with a rise in convection and radiation conduction parameters when Peclet number, stretching/shrinking, ambience, and surface temperatures are raised. The temperature of the fin’s tip increases as ambient temperature, Peclet number, and surface temperature increase, and decreases for enhanced radiation and convection conduction parameters. Radiation and convection cause the efficiency of the fin to increase for shrinking and decrease for stretching, which shows an important role in heat transfer analysis in mechanical engineering. The formulated model is also studied analytically, and the result is compared to numerical solution, which shows qualitatively good agreement.

Exploration of transient heat transfer through a moving plate with exponentially temperature-dependent thermal properties

The present research examines the transient temperature distribution through a moving plate with exponentially temperature-dependent thermal conductivity and heat transfer coefficient. Further, the internal heat generation, as well as convective boundary condition, is considered. The governing energy equation describing the transient heat transfer is formulated and is transformed into a non-dimensional partial differential equation (PDE) using appropriate non-dimensional terms. The resultant PDE is solved numerically with the assistance of the finite difference method (FDM). The consequence of embedding parameters on the transient thermal profile of a moving plate is explicated through a graphical description. The results reveal that the transient thermal distribution decreases remarkably with an upsurge of convection–conduction parameter and the same trend is perceived for radiation–conduction parameter. The result also manifests that as the plate moves faster, the transient thermal distribution through a moving plate enhances gradually. The higher variation in the thermal distribution is perceived for elevated values of the exponential index of thermal conductivity. Moreover, the nature of transient temperature distribution is compared for linear and exponentially temperature-dependent thermal conductivity.

Effects of diffuse and collimated beam radiation on plume formation in natural convection within a cubical enclosure

In this paper, a comprehensive numerical simulation of coupled natural convection with diffuse and collimated beam irradiation has been performed in a cubic cavity. The cavity is convectively heated from the bottom; all four vertical walls of the cavity are isothermal and the top wall is adiabatic. A semitransparent window is created on the left wall of the cavity and a collimated beam is irradiated on this window at the polar and azimuthal angles of 900 and 1350, respectively. The numerical analysis has been performed for the transparent(τ=0) and the participating (τ=2.5 and 10) media within the cavity and keeping the value of other parameters, like Rayleigh number (Ra=105), Prandtl number (Pr=0.71), conduction-radiation parameter (N=1.5), irradiation (G=1000W/m2) fixed. The results reveal a quadrantal symmetry of fluid flow and heat transfer for various optical thicknesses and the cavity contains four conical vortices where each vortex is occupied in tetrahedron space in case of without collimated irradiation. Moreover, the Q-criterion reveals the formation of a mushroom like fluid-structure inside the cavity. However, with the inclusion of collimated irradiation, the quadrantal symmetry breaks and a bilaterally symmetric nature is established about the plane of the collimated beam. The flow structure becomes much more complex and has been explained by critical flow theory. In addition, the heat transfer characteristics also change in accordance with the dynamics of vortices inside the cavity. The Q-criterion reveals the formation of non-regular fluid structure which is same, however, orientation is opposite in the cavity for transparent and participating media.

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

AbstractThe heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection‐conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat‐generating parameter, thermoelectric, and thermomagnetic fields.