Effect Of Internal Heat Generation Research Articles

Second-grade fluid with carbon nanotubes flowing over an elongated curve surface possessing thermal radiation and internal heat generation effects

Second-grade fluid with carbon nanotubes flowing over an elongated curve surface possessing thermal radiation and internal heat generation effects

Modelling of heat transfer in a molten salt loop using computational fluid dynamics

Compared to the traditional water-based reactor fleet, molten salt reactors (MSRs) operate at significantly higher temperatures. This necessitates the development of experimental as well as modelling and simulation tools that can be used to optimise the design to ensure reactor safety and concept feasibility. Canadian Nuclear Laboratories (CNL) is currently at the stage of conceptually designing a lab-scale MSR loop to provide experimental data to benchmark code predictions. Computational fluid dynamics (CFD) modelling is undertaken within this investigation to understand the natural circulation of fuel salt in a conceptual D-shaped loop with two arms, a riser and a downcomer. The fuel salt used within ORNL MSRE was used within the 3D CFD modelling to execute steady-state analyses, with conjugate heat transfer between moderator and fuel accounted for. An attempt is made to follow CFD best practice guidelines to ensure the numerical accuracy of the CFD results. The effects of internal heat generation on the Rayleigh number, flow and temperature distributions were studied qualitatively within this modelling. Stronger mixing in the downcomer, along with prominent recirculation zones were observed at the connecting regions (arms) of the riser and downcomer, which intensified with the increase in the fuel salt power. Prior to attempting the execution of a detailed experimental test matrix, prediction of the natural circulation within the reactor geometry and the ability to understand the flow patterns as a result of varying a range of numerical parameters is required. It is expected that this initial modelling study to adopt the paradigm of CFD-informed experimentation will aid in developing an MSR flow loop at CNL by reducing the number of design iterations, thus shortening the loop design and commission time.

Transient hygrothermal response of an infinite solid cylinder with internal heat generation

This paper aims to study the effect of internal heat generation in a transient infinitely long solid cylinder subjected to hygrothermal loadings. The linear dependence theory of moisture and temperature is derived, based on Dufour and Soret effect. The meticulous solutions of temperature, moisture, and thermal stresses are procured by using the Hankel transform technique. The influence of the internal heat source on the radial aspect is examined for coupled and uncoupled cases. In the present study, the composite material T300/5208 is considered and the coupled and uncoupled cases are analyzed. The results obtained are computed numerically and illustrated graphically. The study presented here is purely hypothetical and entirely based on mathematical principles.

Effect of Internal Heat Generation on Mixed Convection Flow from a Vertical Plate to a Fluid with Nonlinear Thermal Radiation

Effect of Internal Heat Generation on Mixed Convection Flow from a Vertical Plate to a Fluid with Nonlinear Thermal Radiation

A novel analysis for heat transfer enhancement in a trapezoidal fin wetted by MoS2 + Fe3O4 + NiZnFe2O4- methanol based ternary hybrid nanofluid

Nanofluids have grasped the attention of numerous researchers due to their enhanced thermal properties and heat transport performance. Recently, the mixture of ternary nanoparticles is exploited to synthesize a unique nanofluid that has superior thermal features. In this regard, the effects of internal heat generation, thermal radiation, and convection on a steady heat transfer mechanism in a trapezoidal fin wetted with ternary hybrid nanofluid are scrutinized in this investigation. Additionally, this research explores the comparative assessment of thermal and heat energy variations in both dry and wet conditions. The non-dimensional transformations result in the governing differential equation and boundary conditions being reduced to dimensionless expressions of an ordinary differential equation (ODE). A numerical method Runge–Kutta-Fehlberg's fourth-fifth is employed to solve the yielded differential equation of temperature. In addition, the effects of pertinent thermal variables on the thermal profile of the fin are explored graphically. The outcomes reveal that improving the surface radiation variable lowers the thermal profile, and the same behavior is detected for the surface convection parameter. Furthermore, the fluids comprising ternary nanoparticles have the greatest thermal variation. Also, the longitudinal trapezoidal fin has the optimum performance, and higher heat transfer characteristics compared to the typical straight fin.

Thermosensitive Response of a Functionally Graded Cylinder with Fractional Order Derivative

The present paper deals with thermal behaviour analysis of an axisymmetric functionally graded thermosensitive hollow cylinder. The system of coordinates are expressed in cylindrical-polar form. The heat conduction equation is of time-fractional order <i>0</i> < α ≤ <i>2</i>, subjected to the effect of internal heat generation. Convective boundary conditions are applied to inner and outer curved surfaces whereas heat dissipates following Newton’s law of cooling. The lower surface is subjected to heat flux, whereas the upper surface is thermally insulated. Kirchhoff’s transformation is used to remove the nonlinearity of the heat equation and further it is solved to find temperature and associated stresses by applying integral transformation method. For numerical analysis a ceramic-metal-based functionally graded material is considered and the obtained results of temperature distribution and associated stresses are presented graphically.

Homotopy perturbation approach for Ohmic dissipation and mixed convection effects on non-Newtonian nanofluid flow between two co-axial tubes with peristalsis

In this study, the effects of internal heat generation and mixed convection with thermal radiation on peristaltic motion of a non-Newtonian fluid are investigated. The fluid used is third-grade model. The flow is through the gap between two co-axial vertical tubes under the effect of radially varying magnetic field. The outer tube is flexible with sinusoidal deformations. The problem is modulated mathematically by a system of partial differential equations which describes the equations of momentum, heat transfer and nanoparticles concentration which are simplified by using long wave length and low-Reynolds number assumptions. The closed solutions of fluid temperature and nanoparticle concentration are obtained, and the solution of velocity is obtained by using the homotopy perturbation method (HPM). The radially varying magnetic field effect on the axial velocity is discussed and it is shown that the increase of magnetic field parameter tends to reduce the fluid flow.

Internal heat generation impact on MHD natural convection of dusty hybrid nanomaterials within a porous cavity

AbstractThe numerical contribution of the natural heat flow of dusty hybrid nanofluid due to a square cavity filled with a porous medium with the effects of internal heat generation and the magnetic field is presented in this paper. The system of the problem equations is divided into hybrid nanofluid (Al2O3–Cu) phase equations and dusty phase equations, which are converted to a dimensionless form to be suitable for solving them numerically using the finite difference method. The results manifest in the streamlines, isotherms contours for both hybrid nanofluid phase and dust phase as well in local and average Nusselt numbers profiles. The numerical computations are performed and presented via graphs and tables due to the influence of governing physical parameters like , , , (0 ≤ Σ ≤ /2), , , , and . The results indicate that increasing of fluid–particle interaction parameter for velocity leads to increment of the streamlines and isotherms of both the dust and hybrid nanofluid phases. A notable enhancement is found in the streamlines of the hybrid nanofluid phase and dust phase for high values of the Rayleigh number. The average Nusslet number ameliorates due to suspended dust particles in the hybrid nanofluid while deteriorates with increasing nanoparticle volume fraction. Furthermore, rising values of Hartmann number lead to reducing streamlines of the hybrid nanofluid and dust phases but an increase occurs with an increment of the inclined angle of the magnetic field. A notable agreement is obtained between the data of the present study and other previously published work.

Effect of internal heat generation or absorption on conjugate thermal-free convection of a suspension of hybrid nanofluid in a partitioned circular annulus

This study aims to explain the impact of the presence of a solid conductive partition on the thermal-free convective motion mechanism and heat transmission process within a concentric circular annulus filled with a water-based hybrid nanoliquid containing Copper (Cu) and Alumina (Al2O3) nanoparticles. The thermal natural convective flow is formed within the annulus due to the temperature difference which is externally imposed between the internal heated cylinder and the external cooled one and internally generated by the interior heat generation/absorption (IHG/A) phenomenon. The technique of finite volume is applied to discretize and approximately solve the non-dimensional conservation equations. The influence of selected factors such as the nanoparticles concentration, Rayleigh number, fluid/solid heat conductivity ratio, and the IHG/A parameter on the thermo-hydrodynamic behavior and heat exchange rate is interpreted. The findings show that, in the presence of a conductive solid partition, the combined effects of the IHG/A phenomenon and the combined nanoparticles considerably modify the flow and heat exchange behaviors within the annulus. We also employed a new correlation to predict the mean heat exchange rate in the defined input parameter range.

Optimal Homotopy Asymptotic Method for Investigation of Effects of Thermal Radiation, Internal Heat Generation, and Buoyancy on Velocity and Heat Transfer in the Blasius Flow

In this study, analytical examination of effects of internal heat generation, thermal radiation, and buoyancy force on flow and heat transfer in the Blasius flow over flat plate has been presented. The governing nonlinear partial differential equations of the problem are transformed into a set of coupled nonlinear third-order ordinary differential equations by the similarity variable method and have been systematically solved using the optimal homotopy asymptotic method. The main aim of the present study is to inspect the effects of various physical parameters in the flow model on velocity and heat transfer in steady two-dimensional laminar boundary layer flow with convective boundary conditions. The influences of the Grashof number, internal heat generation, the Biot number, radiation parameter, and the Prandtl number on the skin-friction coefficient, the fluid velocity profile, and temperature distribution have been determined and discussed in detail through several plots. The finding revealed that the fluid velocity and temperature delivery upsurge with snowballing in the values of the Biot number and internal heat generation parameters. The temperature profile of the fluid declines contrary to the value of the Grashof number and the Prandtl number but increases with thermal radiation. Moreover, it is found that the skin-friction coefficient and the rate of heat intensify with the Grashof number, internal heat generation, the Biot number, and thermal radiation parameter. The obtained result is likened with the previously published numerical results in a limited case of the problem and shows an excellent agreement.

Analytical Assessment of (Al2O3–Ag/H2O) Hybrid Nanofluid Influenced by Induced Magnetic Field for Second Law Analysis with Mixed Convection, Viscous Dissipation and Heat Generation

The current study is an attempt to analytically characterize the second law analysis and mixed convective rheology of the (Al2O3–Ag/H2O) hybrid nanofluid flow influenced by magnetic induction effects towards a stretching sheet. Viscous dissipation and internal heat generation effects are encountered in the analysis as well. The mathematical model of partial differential equations is fabricated by employing boundary-layer approximation. The transformed system of nonlinear ordinary differential equations is solved using the homotopy analysis method. The entropy generation number is formulated in terms of fluid friction, heat transfer and Joule heating. The effects of dimensionless parameters on flow variables and entropy generation number are examined using graphs and tables. Further, the convergence of HAM solutions is examined in terms of defined physical quantities up to 20th iterations, and confirmed. It is observed that large λ1 upgrades velocity, entropy generation and heat transfer rate, and drops the temperature. High values of δ enlarge velocity and temperature while reducing heat transport and entropy generation number. Viscous dissipation strongly influences an increase in flow and heat transfer rate caused by a no-slip condition on the sheet.

About influence of differential rotation in convection zone of gaseous or fluid giant planet (Uranus) onto the parameters of orbits of satellites

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. We suggest in the current research to take into consideration the additional well-known effect of differential rotation which obviously takes place in the gaseous or fluid convection zone of primary giant Planet (indeed, the aforementioned effect exists even not depending on the orbital evolution of satellites around host Planet). Nevertheless, estimations for the contribution of the aforementioned effect of differential rotation in the Uranus system (including all its most massive satellites) let us exclude using such effect from calculations of mutual evolution of the eccentricity e along with the semi-major axis a for all satellites of Uranus (Planet of ice-type). It means that the Uranus can be considered in the analytic exploration of governing equations as to be the appropriate candidate for applying the modern ansatz [Efroimsky, 2015] (tidal dissipation effect depending on the tidal-flexure frequency) in regard to estimations of eccentricity e along with semi-major axis a for satellites of Uranus. We can see from the results of calculations in Section 3 that the combined system of governing equations (in the sense of combined contributions to the tidal dissipation from Uranus + from satellite) yields the really observed magnitudes of decelerations for semi-major axises of all the satellites of Uranus. Meanwhile, internal heat generation effects in the satellites (due to tidal dissipation effect) are much more than those which definitely take place in the Uranus, excepting the case of Ariel.

Unsteady anisotropic heat conduction in heterogeneous composite conical shells with temperature-dependent thermal conductivities: an analytical study

The present study proposes an exact analysis for unsteady anisotropic conduction heat transfer in heterogeneous composite conical shells. The fibers in the composite conical shell are wound in arbitrary directions so that a defined fiber angle changes between 0° and 90°. The cone’s base is considered to have a general linear boundary condition, while the effects of internal heat generation, thermal convection, and external radiation heat flux on the temperature distribution are investigated. The heterogeneity of the heat transfer problem is caused by a linear dependence of conduction coefficients on the temperature. To solve the governing equations, first, the Kirchhoff transformation followed by an appropriate finite integral transform is applied. The resulting nonhomogeneous equation is then separated into two equations, i.e., steady equation and unsteady equation. The solution of the steady case is derived using Green’s function, while the separation of variables method is utilized to solve the unsteady part. Eventually, the temperature distribution is achieved by applying the inverse transforms on the subsequent solutions. The verification of this solution is based on the comparison between the present analytical results and numerical computations with a second-order finite difference code. Applicability of the present solution is evaluated for resolving an industrial case problem.

The Effects of Internal Heat Generation or Absorption on Mixed Convection in a Lid-Driven Rectangular Cavity using Finite Volume Method

Mixed convection heat transfer in cavities is a significant phenomenon in numerous engineering fields, such as nuclear reactors, solar energy storage, and heat exchangers. Despite acknowledging that a square is a basic shape found in these systems, not all the figures are geometrical. Less attention was given to the rectangle cavity even though it could be found in these systems. Various internal reactions could occur inside the systems, especially in geothermal heat exchangers. Therefore, this research aims to analyze the effect of internal heat generation or absorption in a two-dimensional (2D) horizontal cavity to the fluid flow and heat transfer process numerically. The vertical walls are well insulated. Meanwhile, the top and bottom walls are kept at and , respectively, where . The top wall moves at a constant speed from left to right. The finite volume method (FEM) and SIMPLE algorithm are employed to discretize the governing equations. Next, the algebraic equations are solved iteratively using the tri-diagonal matrix algorithm (TDMA). The influences of heat generation or absorption parameters are investigated in terms of the flow, heat transfer, and Nusselt number. The numerical results are plotted in the form of streamlines and isotherms. It is found that the presence of heat generation or absorption has a significant effect on the fluid flow and heat transfer process in the horizontal cavity. Overall, for internal heat generation, the heat transfer rate decreases, while the opposite pattern can be observed for the case of internal heat absorption. However, for Ri = 10.0, as the heat generation's value increases from 2 to 4, the heat transfer rate is the same.

Effects of internal heat generation and Lorentz force on unsteady hybrid nanoliquid flow and heat transfer along a moving plate with nonuniform temperature

AbstractThe aim of the studyThis study aims to explore the transient magnetohydrodynamics (MHD) boundary layer thermal convective flow of a hybrid nanoliquid past a moving vertical plate under the influence of internal heat generation and variable surface temperature.The research methodologyThe problem is modeled by coupled nonlinear partial differential equations with relevant boundary conditions. Formulated control equations are worked out using the robust implicit finite‐difference technique. The current work is validated with existing literature for special cases of the problem. The impact of important characteristics on hydrodynamic and thermal patterns, accompanied by skin friction parameter and Nusselt number, is scrutinized graphically.The major conclusion of the studyImpacts of MHD, inner thermal generation, and variable surface temperature on nanoliquid circulation and energy transport are studied. It has been found that velocity, temperature, and skin friction coefficient increase with the increase in the heat generation parameter, whereas the Nusselt number reduces with such parameter.The significance of the studyObtained results can be used in different engineering devices, including heat exchangers, solar collectors, and chemical reactors.

Cross Diffusion and Internal Heat Generation Effects on Mixed Convection of Non-Newtonian Fluids Flow Adjacent to a Vertical VHF/VMF Wedge in Porous Media: the Entire Regime

The problem of cross diffusion (Soret/Dufour) and internal heat generation effects on combined convection flow of non-Newtonian fluids flow over the vertical wedge in a saturated porous medium with the entire regime is solved numerically. The internal heat generation is assumed to be an exponential decaying form. The power law model of Ostwald-de-Waele for non-Newtonian fluids is considered here. The entire regime of the combined convection is included, as the combined convection parameter varies from 0 (pure free convection) to 1 (pure forced convection). The transformed equations are obtained by using a suitable coordinate transformation and then Keller box method (KBM) is utilized to solve the non-similar equations for the variable heat flux and variable mass flux (VHF/VMF) conditions. Comparisons with the previously published article are performed and the good agreement is achieved. The main numerical results for the dimensionless temperature and concentration distributions, the local Nusselt and Sherwood numbers are obtained.

Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects

We present a mathematical and numerical study of the transient Marangoni thermo-convection flow of an electrically conducting Newtonian fluid in an isotropic Darcy porous rectangular semiconductor melt enclosure with buoyancy and internal heat generation effects, in an (x, y) coordinate system. The governing equations comprising the mass conservation, x-direction momentum, y-direction momentum and energy equation are formulated subject to a quartet of boundary conditions at the four walls of the enclosure. The upper enclosure wall is assumed to be “free” with an appropriate surface tension dynamic boundary condition. A series of transformations are implemented to render the mathematical model dimensionless and into a vorticity form. The governing thermophysical parameters are shown to be the Marangoni number for surface tension (thermocapillary) effects (Ma), Prandtl number (Pr), Grashof number for buoyancy effects (Gr), enclosure aspect ratio (A), Hartmann hydromagnetic number (Ha), Darcy number for bulk porous resistance (Da), and the internal heat generation parameter (Γ) the latter being a function of the internal (RaI) and global Rayleigh numbers (Ra). An efficient finite difference numerical method is employed to solve the boundary value problem. Validations with earlier purely fluid solutions (Da → ∞) are included. A mesh-independence test is included with further validation with other published studies. Isotherms and isovels (streamlines) are computed as are Nusselt numbers at selected boundaries. Solutions for the case of Pr = 0.054 (semiconductor melt) are also compared with earlier studies showing excellent correlation. The model finds applications in the bulk crystal growth of semiconductors, electromagnetic materials processing control and also hybrid fuel cells.

A Study on the Effects of Internal Heat Generation on the Thermal Performance of Solid and Porous Fins using Differential Transformation Method

In this study, the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method. The parametric studies reveal that porosity enhances the finheat dissipating capacity but the internal heat generation decreases the heatenhancement capacity of extended surface. Also, it is established that whenthe internal heat parameter increases to some certain values, some negativeeffects are recorded where the fin stores heat rather than dissipating it. Thisscenario defeats the prime purpose of the cooling fin. Additionally, it is established in the present study that the limiting value of porosity parameterfor thermal stability for the passive device increases as internal heat parameter increases. This shows that although the internal heat parameter canhelp assist higher range and value of thermal stability of the fin, it producesnegative effect which greatly defeats the ultimate purpose of the fin. Theresults in the work will help in fin design for industrial applications whereinternal heat generation is involved.

Effect of Internal Heat Generation on Solidification of Molten Fuel Droplet during its Interaction with Coolant in a Nuclear Reactor

One of the important issues in safety analysis of severe accidents in fast reactors is Molten Fuel Coolant Interaction (MFCI). MFCI is the phenomenon in which fragmentation of the molten fuel takes place when it comes in direct contact with liquid sodium coolant. For complete understanding of MFCI, we need to study the solidification of the molten fuel happening along with fragmentation. Solidification / melting of any material initially held at its melting temperature is the classic Stefan’s problem. In the case of a severe reactor accident the molten fuel might have a significant amount of decay heat, even though nuclear fission reactions have been stopped by reactor shut down systems. The presence of decay heat in this case, makes the transient Stefan problem more difficult to solve analytically. Here, an investigation of this special case of Stefan’s problem with internal heat generation in nuclear materials has been carried out considering a typical droplet size of 4 mm diameter. The numerical heat transfer analysis has been carried out using the commercial software Fluent. The validation of the problem is done with the steady state analytical solution available for the position of phase change front. Parametric studies have been carried out by varying internal heat generation rates and convective heat transfer coefficient at the surface of the droplet. Temperature profiles and liquid fraction are obtained at different instants. Solidification time and final equilibrium temperature are estimated from the results. It is observed that there is significant increase in drop solidification time for heat generation rates (HG) greater than 100 MW/m3 for the drop size of 4 mm. The maximum HG which is tolerated by the droplet without reaching its boiling point is about 6 GW/m3 when the heat transfer coefficient from its surface is fixed at h=56000W/m2K.

The Effect of Internal Heat Generation of a Reactive Hydromagnetic (MHD) Fluid Flow through a Vertical Plate

In this study, we discussed the flow of an electrically conducting fluid with internal heat generation over a vertical plate on a reactive MHD fluid. We obtained the semi analytical solutions of the dimensionless equations governing the fluid flow using the method of weighted residual by the collocation method. The parameters with their effect on velocity and temperature fields are discussed graphically using Mapple 17 computer software. We showed that the internal heat generation, magnetic field intensityand the reactive rate have significant effects on the velocity profiles and temperature distributions.