Types Of Thermal Boundary Conditions Research Articles

Magnetohydrodynamic study of Micropolar fluid flow in the porous walled channel with variable viscosity and thermal conductivity: HAM Solution

This article examines the production of entropy and the heat transfer rate in the passage of micropolar fluid through a channel. The micropolar fluid takes place through the porous walled channel under the presence of an external magnetic field acting in the perpendicular direction of the flow. In this work, the thermal conductivity and viscosity of the fluid is considered variable and are the function of the temperature. Here, we consider two-dimensional creeping flow with two different forms of temperature boundary conditions, namely, Newtonian heating (NH) boundary constraints and specified surface temperature (SST) boundary conditions. The flow of the micropolar fluid in the proposed problem is governed by the coupled non-linear PDEs. These PDEs are first transformed into the ODEs by the use of some suitable similarity transformations and then obtained ODEs are further solved by using the semi-analytic Homotopy Analysis Method (HAM). This article shows the effect of various flow parameters on the fluid’s velocity, heat transfer rate, temperature of the fluid, and entropy production for both types of thermal boundary conditions. Through this article, it is concluded that the entropy production is minimal for Newtonian heating (NH) boundary conditions as compared to specified surface temperature (SST) boundary conditions. This result suggests that the NH boundary condition is more suitable for electrical appliances as compared to the SST boundary condition. This type of model is applicable in nuclear reactors, engineering appliances, heat reservoirs, etc.

Research on temperature field of dry clutch assembly based on inverse analysis of thermal boundary conditions

The clutch temperature field is critical for the clutch design and lifetime analysis. In this paper, a new approach for reconstructing the temperature field of the clutch assembly based on the inverse analysis of thermal boundary conditions is present. Three typical types of thermal boundary conditions during the clutch operation were analyzed and integrated into a numerical model with several coefficients assumed. The optimal coefficients are obtained by optimizing the derivation between temperature simulation and rig test based on the reverse problem analysis. The NLPQL optimization algorithm, coupled with the Kriging response surface model, is utilized to improve the computation efficiency. Finally, the optimum parameter combination is conducted and the effectiveness of the proposed method is validated by the rig test data under the continuous engagement and disengagement condition. The results indicate that the clutch temperature distribution and the dynamic mechanism of the clutch contact status using the approach proposed agrees very well with the test data of the rig test. The temperature deviations between the model corrected and the rig test data are within 10 °C, with over 80% of the temperature deviations being less than 5 °C. This study establishes a new clutch temperature field simulation method based on reverse problem analysis and gives a significant insight and foundation for improving the prediction of the temperature distribution of the clutch.

Modeling of Heat Transfer in Composite Bodies Reinforced with Tubes with Swirlers Through Which a Twisted Liquid Heat Carrier Moves in the Turbulent Mode. II. Model Problem

For a model problem, we compute the velocity form-parameters of the flows of heat carrier in tubes and the temperature fields in concrete cylindrical shells longitudinally and spirally reinforced with steel tubes filled with air pumped through these tubes. We compared the results obtained in the cases of reinforcement of these structures with smooth tubes and tubes with swirlers. It is shown that the application of tubes with swirlers significantly intensifies the process of heat removal from the structure as compared with the tubes with smooth inner surfaces if all other conditions are identical. It was discovered that, for some types of thermal boundary conditions, the efficiency of heat removal from the structure strongly depends on the direction of pumping of the heat carrier through the tubes. We also studied the influence of the parameters of reinforcement, the cross-sectional sizes of the tubes, and the velocity of motion of the heat carrier in the tubes on the temperature field formed in the shell. It was shown that the variations of these parameters make it possible to control, to a significant degree, the intensity of heat removal from the composite body. It is also demonstrated that some well-pronounced temperature edge effects may appear in the vicinities of edges of the reinforced-concrete shell.

Hydro-dynamically and thermally fully developed flow analysis of magneto-hydrodynamic fluid through annular duct

A hydro-dynamic thermal fully developed forced convective heat transfer analysis of magneto-hydrodynamics fluid flow through an annular sector duct is presented in this paper. Two types of thermal boundary conditions i.e., axially uniform heat flux along with peripherally uniform temperature (known as H1-condition) and, axially and peripherally uniform temperature (known as T condition), have been considered to carry out the thermal analysis of fluid. The velocity components along r and [Formula: see text] direction are transformed into algebraic form by using power law discretized scheme, whereas cross-sectional pressure [Formula: see text] is estimated with the help of well know technique [Formula: see text]. The governing partial differential equations are solved by numerically with the help of [Formula: see text] code. Furthermore, simulated results have been compared with the existing results of literature to validate the results. From the results, it is noted that hydro-dynamically and thermally impacts relate directly by increasing the Hartman number, (M). It is further reported that the effect of magnetic field becomes insignificant for the higher number of fins, N. The findings of the present analysis will be applicable in various types of thermal systems.

NUMERICAL INVESTIGATION OF FORCED CONVECTION HEAT TRANSFER AROUND AND THROUGH AN ELLIPTICAL POROUS CYLINDER

Convection heat transfer from a heated elliptical porous cylinder in the incompressible and laminar cross-flow is studied numerically. The effects of Darcy number (10<sup>-6</sup> ≤ Da ≤ 10<sup>-2</sup>), aspect ratio (0.2 ≤ AR ≤ 5), Prandtl number (0.7 ≤ Pr ≤ 70), Reynolds number (10 ≤ Re ≤ 40), on the average Nusselt number (Nu), as well as the lift and the drag coefficients are investigated. Two types of thermal boundary conditions for porous cylinder are investigated: uniformly distributed heat source and constant temperature. The fluid flow in the porous medium is numerically simulated by the superficial velocity model. Additionally, the energy equation in the porous medium is simplified by the local thermal equilibrium (LTE) hypothesis. It is concluded that the aspect ratio of the elliptical cylinder has a great influence on the heat transfer and fluid flow characteristics of this problem. Results show that increasing the Darcy number increases the Nusselt number and decreases the drag coefficient of the porous cylinder. Moreover, values of Da smaller than 10<sup>-4</sup> resemble the fluid flow and heat transfer characteristics of the impermeable solid cylinder.

Equivalence of three thermal boundary conditions in compressible turbulent channel flows.

In this paper, direct numerical simulations have been performed to explore the equivalence of different thermal boundary conditions in compressible turbulent channel flows at fixed Re=6000,Ma=1.5. Three canonical types of thermal boundary conditions will be investigated at almost equivalent setups, including the first boundary condition with fixed wall temperature T_{w} (constant Dirichlet boundary condition), the second boundary condition with fixed wall heat-flux q_{w} (constant Neumann boundary condition), and the third boundary condition (Robin boundary condition). The turbulent statistics of the temperature and velocity fields, including mean profiles, root-mean-square values, second-order statistics, and normalized probability density functions, temperature stripes near the wall and the budget of internal energy have been analyzed in detail to clarify the differences caused by the different thermal boundary conditions. The results show that the three thermal boundary conditions have almost negligible effect on the velocity field, whereas some discernible deviations can be observed for the temperature field in the near-wall region with y^{+}≲30. Furthermore, the statistics from the second and third thermal boundary conditions are very close, enabling the usage of the second boundary condition to mimic the more complex third boundary conditions.

On the choice of thermal boundary conditions for microstructure modelling of additive processes

Advanced phase-field modelling of LPBF should consider both melting and solidification, because microstructure quantities like the primary dendrite spacing as well as grain orientations typically are inherited across successive layers. This cannot be achieved by considering constant cooling conditions, which however still is state of the art by now. In this work, two different types of thermal boundary conditions that both allow taking the transition between melting and solidification into account have been implemented and compared. For a given set of laser process parameters, the melting and solidification dynamics, melting depth, dendritic microstructure and grain selection have been simulated in 2d for the multicomponent Ni-base alloy ABD®-900AM. It is demonstrated that latent heat release has a significant impact on the thermal conditions at the dendrite tips, and thus on microstructure. The simulation results are discussed by comparison with analytical heat source models, heat balance considerations and experimental results.

Diffusion-thermo and heat source effects on the unsteady radiative MHD boundary layer slip flow past an infinite vertical porous plate

The heat and mass transfer characteristics of the nonlinear, unsteady, radiative MHD boundary layer slip flow of a chemically reacting fluid past an infinite vertical porous plate are taken into account in this study. The effect of physical parameters are accounted for two distinct types of thermal boundary conditions namely prescribed uniform wall temperature thermal boundary condition and prescribed heat flux thermal boundary condition. Exact solution of the governing equations for the fluid velocity, temperature and concentration are obtained by using two term perturbation technique subject to physically appropriate boundary conditions. The expressions of skin friction, Nusselt number and Sherwood number are also derived. The numerical values of fluid velocity, temperature and concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. Results are compared with the literature in the limiting case.

Thermoelastic damping in nonlocal rod using three-phase lag heat conduction model

This manuscript studies thermoelastic damping of a longitudinally vibrating nanorod at small-scale. The heat conduction in the present work is constructed based on the three phase-lag heat conduction model and the elastic effects are modeled using nonlocal elasticity. Isothermal and adiabatic type of thermal boundary conditions are considered in the numerical analysis. It is found that the thermoelastic damping of the present resonator under adiabatic thermal boundary conditions is higher than that of the isothermal boundary conditions. The nonlocal elasticity gives higher thermoelastic damping than the classical elasticity. The present results are in good agreement with those of the available literature. Thermoelastic damping for clamped-clamped nanorod vibrating in longitudinal mode is 83% higher than that of the clamped-free nanorod for both adiabatic and isothermal boundary conditions. The critical length of nanorod at which the thermoelastic damping is maximum, is lower for the adiabatic condition than isothermal condition. The energy dissipation occurs at very fast rate at higher values of thermal relaxation parameters and more clearly this effect is seen for nanorod with less than 100 nm length. The numerical results presented in this work are useful for the design of the next generation nanoscale devices based on longitudinal resonators.

Effect of General Thermal Boundary Conditions on the Dynamic and Buckling of Polymeric Hybrid Nanocomposite Beam with Variable Thickness

This paper deals with the effect of general thermal boundary conditions on the dynamic and buckling of polymeric hybrid nanocomposite beam. The Timoshenko beam with variable thickness is made of a polymer matrix reinforced with a combination of carbon nanotubes (CNT) and nanoclay (NC) particles. The thermal and mechanical properties of the hybrid nanocomposite beam are obtained by Halpin–Tsai micromechanical method. The governing equations are derived through using Hamilton's principle and then solved by using the differential quadrature method (DQM). In this work, for the first time, the general thermal boundary conditions are applied to hybrid nanocomposite beam with variable thickness. The numerical results of dynamic response are obtained for different thermal and mechanical boundary conditions. Besides the effects of the amount as well as shape factor of the nanofiller, and different types of thermal boundary conditions on the natural frequencies and critical buckling load are investigated. The results show that the dynamic response of the beam with uniform thickness is more affected by changes in the amount of nanoclay, while beam with non-uniform thickness is more sensitive to changes in the amount of CNT. In addition, thermal boundary conditions involving a constant heat flux on one side have different responses with the increase of CNT value.

Numerical Investigation of Effect of Temperature Profile Imposed on the Crucible Surface on Oxygen Incorporated at the Crystal Melt Interface for 450 mm Diameter Silicon Single Crystal Growth in Presence of CUSP Magnetic Field Using Czochralski Technique

Numerical investigation has been carried out to study the effect of thermal boundary condition on turbulent melt flow and oxygen transfer inside a crucible used to grow 450 mm diameter silicon single crystal using Czochralski method. Two types of thermal boundary conditions, namely, isothermal crucible surface and experimentally measured temperatures on the crucible surface have been imposed on the crucible wall and crucible bottom. Melt motion owing to buoyancy, surface tension variation at the free melt surface as well as crystal and crucible rotation has been considered. Effect of CUSP magnetic field has also been investigated. Melt having aspect ratio of 1 and 0.5, representing high and moderate level of melt inside the crucible have been considered. K-epsilon turbulent model with low Reynolds number formulation has been used for turbulence modelling. Melt motion governed by natural convection, Marangoni convection and crystal as well as crucible rotation shows higher oxygen concentration at melt crystal interface for aspect ratio of 1, when experimental temperature profile is imposed at the crucible wall. For melt aspect ratio of 0.5, natural convection and Marangoni convection dependent melt show higher oxygen concentration for isothermal crucible wall boundary condition. Marangoni convection in absence of rotation of crystal and crucible leads to low oxygen concentration zone near the crystal outer surface, the size of which is larger for melt aspect ratio of 0.5. Maximum turbulent viscosity values for aspect ratio of 1, in case of experimental temperature at the crucible are higher compared to isothermal case, which is just the opposite of the trend for aspect ratio of 0.5. Imposing a CUSP magnetic field leads to similar distribution of turbulent viscosity for both types of thermal boundary conditions, irrespective of the type of thermal boundary condition. Oxygen concentration at the melt crystal interface is found to be higher in presence of CUSP magnetic field. Value of maximum turbulent viscosity for the two boundary condition are similar for melt aspect ratio of 1.0. Crucible surface temperature profile for aspect ratio of 1, on actual melt aspect ratio of 0.5 predicts lower oxygen concentration at melt crystal interface. Values and distribution of turbulent viscosity is however the same for both temperature profiles.

MHD free convection in a porous non-uniformly heated triangle cavity equipped with a circular obstacle subjected to various thermal configurations

This study numerically investigates the magnetohydrodynamic (MHD) free convection of a fluid in a porous triangle cavity containing a circular obstacle subjected to various thermal configurations. The investigation is conducted using a penalty finite element technique. The inclined side walls are non-uniformly heated while the bottom is maintained cold isothermal. Three types of thermal configurations are considered at the obstacle boundary. The effects of various physical parameters on the MHD free convection have been studied. The temperature field, fluid flow and heat transfer are strongly dependent on the type of thermal boundary condition of the circular obstacle, Prandtl number and magnetic induction. The obtained results are verified with a grid sensitivity study and validated using existing results in literature. A comparison between the present results and ones existing in literature illustrates the reliability and dependability of this study.

Graphene and CNT impact on heat transfer response of nanocomposite cylinders

AbstractReinforcing polymers with nanofillers is an advanced approach to improve and manage the thermal behaviors of polymeric nanocomposite materials. Among the proposed nanofillers, graphene and carbon nanotube (CNT) with superior thermal conductivity are two advanced nanofillers, which have extensively been utilized to enhance the heat transfer responses of host polymeric materials. In this work, the impacts of randomly oriented graphene and CNT to steady state and transient heat transfer behaviors of functionally graded (FG) nanocomposite cylinders have been investigated using an axisymmetric model. Nanocomposite cylinders have been assumed to be under heat fluxes, heat convections or temperatures as different types of thermal boundary conditions. The thermal properties of the resulted nanocomposite materials are estimated by micromechanical model. Moreover, the governing thermal equations of axisymmetric cylinders have been analyzed using a highly consistent and reliable developed mesh-free method. This numerical method predicts temperature fields via MLS shape functions and imposes essential boundary conditions with transformation approach. The effects of nanofiller content and distribution as well as thermal boundary conditions on the heat transfer responses of nanocomposite cylinders are studied. The results indicated that the use of nanofiller resulted in shorter stationary times and higher temperature gradients in FG nanocomposite cylinders. Moreover, the use of graphene in nanocomposites had stronger impact on thermal response than CNT.

The influence of thermal boundary conditions on turbulent forced convection pipe flow at two Prandtl numbers

Different types of thermal boundary conditions are conceivable in numerical simulations of convective heat transfer problems. Isoflux, isothermal and a mixed-type boundary condition are compared by means of direct numerical simulations (for the lowest Reynolds number) and well-resolved large-eddy simulations of a turbulent forced convection pipe flow over a range of bulk Reynolds numbers from Reb=5300 to Reb=37700, at two Prandtl numbers, i.e. Pr=0.71 and Pr=0.025. It is found that, while for Pr=0.71 the Nusselt number is hardly affected by the type of thermal boundary condition, for Pr=0.025 the isothermal boundary condition yields ≈20% lower Nusselt numbers compared to isoflux and mixed-type over the whole range of Reynolds numbers. A decomposition of the Nusselt number is derived. In particular, we decompose it into four contributions: laminar, radial and streamwise turbulent heat flux as well as a contribution due to the turbulent velocity field. For Pr=0.71 the contribution due to the radial turbulent heat flux is dominant, whereas for Pr=0.025 the contribution due to the turbulent velocity field is dominant. Only at a moderately high Reynolds number, such as Reb=37700, both turbulent contributions are of similar magnitude. A comparison of first- and second-order thermal statistics between the different types of thermal boundary conditions shows that the statistics are not only influenced in the near-wall region but also in the core region of the flow. Power spectral densities illustrate large thermal structures in low-Prandtl-number fluids as well as thermal structures located right at the wall, only present for the isoflux boundary condition.A database including the first- and second-order statistics together with individual contributions to the budget equations of the temperature variance and turbulent heat fluxes is hosted in the open access repository KITopen (DOI:https://doi.org/10.5445/IR/1000096346).

Convective Heat Transfer Utilizing Magnetic Nanoparticles in the Presence of a Sloping Magnetic Field Inside a Square Enclosure

Unsteady natural convection flow and heat transfer utilizing magnetic nanoparticles in the presence of a sloping magnetic field inside a square enclosure are simulated numerically following nonhomogeneous dynamic model. Four different thermal boundary conditions: constant, parabolic in space, sinusoidally in space, and time for the bottom hot wall are considered. The top wall of the enclosure is cold while the vertical walls are thermally insulated. Galerkin weighted residual finite element method is used to solve the governing nondimensional partial differential equations. For simulations, 12 types of nanofluids consisting magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn–Zn ferrite (Mn–ZnFe2O4), and silicon dioxide (SiO2) nanoparticles along with water, engine oil, and kerosene as base fluids are used. The effects of the important model parameters such as Hartmann number, magnetic field sloping angle, and thermal Rayleigh number on the flow fields are investigated. The results show that the average Nusselt number, shear rate, as well as the nanofluid velocity decreases as the Hartmann number intensifies. Moreover, the rate of heat transfer in nanofluid exaggerates with the increase of the thermal Rayleigh number and the magnetic field sloping angle. Sinusoidally varied in space thermal boundary condition at the bottom wall provides the highest average Nusselt number and the shear rate compared to the other types of thermal boundary conditions studied here. For this case, the highest average Nusselt number is obtained for the Mn–ZnFe2O4–Ke nanofluid. On the other hand, Fe3O4–H2O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

Nonlinear Vibration Behavior of Rapidly Heated Temperature-Dependent FGM Shallow Spherical Shells

In the present research, thermally induced vibration of shallow spherical shells made of functionally graded materials is investigated. The thermomechanical properties of the FGM media are assumed to be temperature dependent. Based on the uncoupled thermoelasticity theory, the one-dimensional heat conduction equation is established. The top and bottom surfaces of the shell are subjected to several types of rapid heating boundary condition. Because of the temperature dependency of the material properties, solution of nonlinear heat conduction equation needs a numerical method. In the first step, generalized differential quadrature method (GDQM) is applied to discretize the heat conduction equation across the shell thickness. Afterward, the governing system of time-dependent ordinary differential equations is solved using the successive Crank–Nicolson scheme. The obtained thermal force and thermal moment resultants at each time step are applied to the equations of motion. The axisymmetric equations of motion, using the first-order shear deformation theory (FSDT) based on the Kármán type of geometrical nonlinearity, are derived with the aid of the Hamilton principle. Using the harmonic differential quadrature method, shell domain is divided into a number of nodal points, and differential equations are turned into a system of ordinary differential equations. To obtain the displacement components at any time, time marching scheme based on the Newmark method is implemented. The obtained highly nonlinear algebraic equations are solved by means of the Newton–Raphson method. Comparison studies are performed to validate the formulation and solution method of the present research. Various examples are illustrated to discuss the influences of effective parameters such as power law index in the FGM formulation, thickness of the shell, temperature dependency, shell opening angle, in-plane boundary conditions, type of thermal boundary conditions, and geometrical nonlinearity on thermally induced response of the FGM shell under thermal shock.

New Closed-Form Thermal Boundary Layer Solutions in Shear Flow With Power-Law Velocity

The forced convection problem for a developing thermal boundary layer in a parallel shear flow is studied. If the shear flow has a power-law velocity profile, exact similarity thermal boundary layer solutions in terms of Gamma functions can be found. Specifically, three types of thermal boundary conditions are considered: a step temperature change, a step flux change, and a concentrated heat source. The latter is also analogous to mass diffusion form an isolated source. The mixing index for mass diffusion is found exactly.

Effect of Power-Law Fluid Behavior on Nusselt Number of a Circular Disk in the Forced Convection Regime

Forced convection heat transfer is investigated from a thin disk in power-law fluids over wide range of conditions such as: Reynolds number, 1 ≤ Re ≤ 100, Prandtl number, 1 ≤ Pr ≤ 100, power-law index, 0.4 ≤ n ≤ 1.8, and disk thickness to diameter ratio, t/D = 0.01, 0.025, 0.05, and 0.075. The wide range of values of the power-law index spanned here covers both shear-thinning as well as shear-thickening fluid behavior. These results also elucidate the influence of the type of thermal boundary conditions, i.e., constant wall temperature condition (CWT) and constant heat flux condition (CHF) prescribed on the disk surface. Extensive results are presented in terms of the local and average Nusselt numbers to delineate the effect of each of the influencing parameters, Re, Pr, n, t/D for each thermal boundary condition. Limited results are also included here at vanishingly small values of the Peclet number to understand the behavior in the creeping flow condition. Finally, the present numerical results on the average Nusselt number have been consolidated in the form of a predictive equation to facilitate the interpolation of the present data for intermediate values of the parameters and/or a priori estimation of the average Nusselt number in a new application.

Згинні коливання в'якопружних плас- тин в рамках моделі Кірхгофа-Лява

Within the framework of the hypotheses of the classical Kirchhoff-Love theory, complete systems of resolving equations are constructed to determine the stress-strain state and the temperature of dissipative heating under steady transverse vibrations of plates made of a linear viscoelastic material, the properties of which depend on the frequency of external excitation and temperature. The equations were obtained without any preliminary suggestions about the law of temperature variation over the plate thickness. This law is determined in the process of solving the problem. The unrelated problem of vibrational bending of viscoelastic plates for complicated way of fixing a contour and different types of thermal boundary conditions is considered. Mathematical models of problems on the steady-state transverse vibrations of plates made of a linear viscoelastic material, the properties of which depend on temperature for an arbitrary law of its change over the thickness of the object. If the material characteristics depend on temperature, investigation of the influence of temperature of dissipative heating is reduced to solution of complicated non-linear systems of differential equations.

The effect of acoustic wave on the stability of stationary convective flow of binary fluid in a horizontal layer subjected to horizontal temperature and concentration gradients

The effect of acoustic wave propagating in the direction of temperature gradient on a stability of stationary plane-parallel flow of binary fluid, generated by horizontal temperature and concentration gradients in a horizontal layer is investigated for two types of thermal boundary conditions: perfectly conductive and adiabatic boundaries. The study is performed analytically for the longwave perturbations and numerically for finite-wavelength perturbations. Stability maps for fixed Prandtl number value Pr=0.01 and different values of Schmidt number and acoustic Reynolds number are obtained. The most dangerous instability modes and critical perturbation structure are discussed. Comparison with the case where acoustic wave is absent is performed. It is shown, that longwave perturbations are always stabilized by acoustic wave. Numerical investigation demonstrates, that acoustic wave also stabilizes the flow with respect to finite-wavelength perturbations when negative concentrational Grashof number is higher in modulus than certain value depending on acoustic wave intensity.