Dimensional Heat Research Articles

3-Dimensional Heat Transfer Modeling for Laser Powder Bed Fusion Additive Manufacturing Using Parallel Computing and Adaptive Mesh

3-Dimensional Heat Transfer Modeling for Laser Powder Bed Fusion Additive Manufacturing Using Parallel Computing and Adaptive Mesh

An analytical study on sublimation process in the presence of convection effect with heat and mass transfer in porous medium

The mathematical study of one dimensional heat and mass transfer phenomena is investigated. A Stefan like phenomena is defined as a heat and mass transfer problem with presence of convection in vapour region for heat and moisture flow and convective term due to mass transfer of the water vapour in frozen region. The sublimation process considered in two region: (i) In frozen region, s(t)<x<∞, there is no effect of moisture in this region. (ii) In vapour region, 0<x<s(t), there is an effect of heat and moisture flows. The thermo-physical properties of each region are constant, but may be differ for different region. The analytical solutions are obtained for the temperature and moisture profile and moving sublimation interface by using the similarity transformation procedure. The effect of some parameters included in the sublimation process with various enclosures, i.e. dimensionless quantity l0, Peclet number Pe, Luikov number Lu, KT, a21 and other constant parameters are comprehensively investigated and represented graphically.

An Experimental Investigation to Determine the Effect of Tube Material on the Tubeside Heat Transfer Performance of the Enhanced 1EHT Three Dimensional Heat Transfer Tube

Condensation heat transfer characteristics were experimentally investigated over a wide range of operating conditions in order to determine the heat transfer performance inside horizontal, smooth and enhanced heat transfer tubes; using R410A in tubes produced of copper and stainless steel. Experimental data was verified and results were compared to the performance measured in a smooth tube. Results indicate that the condensation heat transfer coefficient (HTC) enhancement ratio is in the range from 1.15 to 2.05 for the 1EHT tube and for the HX tube it ranged from 1.18 to 1.69. Smooth tube heat transfer performance was slightly affected by the thermal conductivity of the tube; however, larger enhancements are found in the enhanced tubes.Heat transfer coefficients increase with an increase of mass velocities. When the mass flux increases, the liquid flow becomes more turbulent and the liquid film becomes thinner; this reduces the thermal resistance and enhances the heat transfer. Heat transfer performance for low mass velocities rise slowly, showing only a small difference in magnitude. Performance increase is larger at high mass flux rates than that those found at low mass fluxes. The influence of thermal conductivity on the condensation heat transfer of the enhanced horizontal tubes was discussed. Better heat transfer performance occurs in tubes produced of a higher thermal conductivity material (copper) or in tubes with a smaller diameter.

Prediction of 3-dimensional heat treatment model during the friction stir spot welding of AA 6061

In this research work, a die steel tool was used to join the two aluminium sheets together on a radial drill machine. For this, a cylindrical-shaped tool was fabricated. This tool is then clamped into the drill machine tool post. This rotating tool is then inserted/indented into the workpiece thus generating heat due to friction. The of the deformation of aluminium starts near the vicinity of the die steel tool impression. The tool transferred the soft material from the tip to the plunger. The plunger is in contact with the Aluminum sheet. Soften material is forged on the sheet with the help of a plunger and thus creating a solid phase joint between the Aluminum sheets. Three-dimensional numerical modelings were performed on Ansys software. A 3-D heat transfer model was used to solve the problem of friction stir spot welding (FSSW). This model was solved by applying the energy conservation equation. This model involves the heat generated at the boundary of the workpiece (AA) and the rotating tool and for study, the problem, steady-state heat transfer equation was used. The numerically computed and the measured values are compared to validate the results.

Hexagonal Grid Computation of the Derivatives of the Solution to the Heat Equation by Using Fourth-Order Accurate Two-Stage Implicit Methods

We give fourth-order accurate implicit methods for the computation of the first-order spatial derivatives and second-order mixed derivatives involving the time derivative of the solution of first type boundary value problem of two dimensional heat equation. The methods are constructed based on two stages: At the first stage of the methods, the solution and its derivative with respect to time variable are approximated by using the implicit scheme in Buranay and Arshad in 2020. Therefore, Oh4+τ of convergence on constructed hexagonal grids is obtained that the step sizes in the space variables x1, x2 and in time variable are indicated by h, 32h and τ, respectively. Special difference boundary value problems on hexagonal grids are constructed at the second stages to approximate the first order spatial derivatives and the second order mixed derivatives of the solution. Further, Oh4+τ order of uniform convergence of these schemes are shown for r=ωτh2≥116, ω&gt;0. Additionally, the methods are applied on two sample problems.

Homotopy perturbation and numerical solutions for MHD flow of PTT fluid through a channel embedded in a porous medium

An analysis is made of the steady one dimensional flow and heat transfer of an incompressible viscoelastic electrically conducting fluid (PTT model) in a channel embedded in a saturated porous medium. The pressure driven flow is subjected to a transverse magnetic field of constant magnetic induction (field strength). The heat transfer accounts for the viscous dissipation. The governing equation (a non-linear ordinary differential equation) is solved analytically (Homotopy Perturbation Method) and numerically (Runge-Kutta method with shooting technique) providing the consistency of the result. The role of Deborah number substantiates both Newtonian and non-Newtonian aspects of the flow model. The inclusion of two body forces affects rheological property of the flow model considered. Temperature distribution in the boundary layer is shown when the channel surfaces are held at constant temperatures. A novel result of the analysis is that the contribution of viscous dissipation is found to be negligible as the variation of temperature is almost linear across the flow field in the present PTT fluid model indicating preservation of thermal energy loss.

Modulation of piezoelectric properties in electrospun PLLA nanofibers for application-specific self-powered stem cell culture platforms

There is an increasing effort to utilize piezoelectric materials as a self-powered platform to electrically stimulate cells/tissues in regenerative medicine and tissue engineering applications. Poly(l-lactic acid) (PLLA) holds great potential for biological applications due to its biodegradability, especially in a nanofibrous form prepared by electrospinning. However, the mechanism underlying its realization and transformation of piezoelectricity is not well understood. In this study, a design-of-experiment approach was employed to systematically dissect the effects of dimensional control and heat treatment on the piezoelectric performance of electrospun PLLA nanofibers. Specifically, we revealed that the fiber diameter- and heat treatment-dependent phase content change between electrospinning-induced amorphous and crystalline α/α’ phases was responsible for the piezoelectric performance in the transverse and longitudinal directions. Such modulation of piezoelectric properties in PLLA nanofibers was critical in determining the differentiation efficiency of stem cells in a phenotype-specific manner, where neurogenesis and osteogenesis were enhanced by orthogonal and shear piezoelectricity, respectively. Overall, our findings highlight the potential of electrospun PLLA nanofibers with precisely controlled piezoelectric properties through a systematic approach for self-powered stem cell engineering platforms, specific to target tissues.

Visualization Of Thermal Distribution During Machining of Dental Implants

Dental implants used are usually metallic. One of the most widely used materials for the same is Titanium-based alloy like Ti-6Al-4V, which suffers difficulty processing and machining due to its thermo-physical properties. The thermo-physical property of the material plays a significant role in the biocompatibility and safety to use them as dental implants. Due to its hardness and difficult-to-machine characteristics, a large amount of heat gets generated while machining, creating dimensional error. Hence before assembly of parts, they must be processed so that stress deformation of the assembly due to heat can be avoided. During machining of Ti-6Al-4V, the cooling strategy needs prior information on the thermal field, and hence, the distribution of temperature in the material is an essential domain to study. To understand the thermal distribution in the material during machining, 3-dimensional heat diffusion equations have been solved using a Finite Difference scheme coupled with the Liebmann method to generate the thermal distribution in the material. An efficient parallelized code for the same has been written in MATLAB and utilized in this numerical study. This study reveals the variation of the temperature gradient with time and space, all along with the three orthogonal directions, which will be helpful for the scientists, engineers, and surgeons to ascertain the sustainability [1, 2], suitability, and longevity of the implants.

Fractional Order Model of the Two Dimensional Heat Transfer Process

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

Global solvability of 2D MHD boundary layer equations in analytic function spaces

In this paper we are concerned with the global well-posedness of solutions to magnetohydrodynamics (MHD) boundary layer equations in analytic function spaces. When the initial data is a small perturbation around a selected profile, and such a profile is governed by an one dimensional heat equation with a source term, we establish the global in time existence and uniqueness of analytic solutions to the two dimensional (2D) MHD boundary layer equations. It is noted that the far-field state of velocity is not required to be small initially, but decays to zero as time tends to infinity with suitable decay rates. The whole analysis is divided into two parts: When the initial far-field states are not small, we reformulate the original problem into a small perturbation problem by extracting a suitable background profile which is governed by a heat equation, then we prove a long-time existence of solutions, and the lower bound of lifespan of solutions is given in term of the small parameter of initial perturbation; After establishing the long-time existence, combining the decay properties of far-field state and the properties of solutions to the heat equation, it is shown that both the solution obtained in the first part and the background profile indeed satisfy some smallness requirements when time goes to the lower bound of lifespan of solutions. Then we can show the global existence of solutions after this moment.

Three dimensional heat transfer in the Carreau-Yasuda hybrid nanofluid with Hall and ion slip effects

For enhancement of heat and mass transfer, the use of hybrid nano-particles in shear rate-dependent viscous fluid is of great significance given applications. In this study, we have considered the impacts of Hall and ion-slip currents on the three-dimensional (3D) flow of shear rate-dependent viscous fluid. The shear rate-dependent rheology is characterized by the Carreau-Yasuda model. Ethylene glycol is found in plasma and rheological characteristics are best described by the power-law constitutive model which is a special case of the Carreau-Yasuda rheological model, Therefore, the most generalized model is considered to examine the rheological characteristics. Further, Al 2 O 3 − ethylene glycol and TiC − Al 2 O 3 − ethylene glycol are termed as Carreau-Yasuda nanofluid and Carreau-Yasuda hybrid nanofluids respectively. Specifically, here in the considered problem, Titanium carbide and aluminum oxide (TiC and Al 2 O 3) hybrid nano-particles which are source materials for MXenes, are dispersed in the Ethylene glycol (C 2 H 6 O 2) as a base fluid. The finite element method (FEM) is implemented to find the numerical solution of the boundary value problems. The thermal performance of both types of fluids is analyzed under the influence of related parameters. The thermal performance of both types of fluids is compared. Hall and ion-slip currents are induced to the ion and electron collisions and cause Hall and ion-slip forces which have the opposite direction to the magnetic force induced due to the magnetic field interaction. Thus Hall and ion-slip forces are favorable forces and result in to increase in momentum boundary layer thickness (MBLT). It is also discovered that the Hall and ion-slip forces in TiC − Al 2 O 3 − ethylene glycol flow are greater than those in Al 2 O 3 − ethylene glycol flow. Furthermore, Hall and ion-slip currents play an important role in decreasing Ohmic dissipation, which has a negative impact on the thermal performance of the working fluid. The role of generative chemical reaction on the transport of mass is opposite to the role of the destructive chemical reaction. Joule heating (Ohmic dissipation) directly affects the temperature of fluid particles and their kinetic energy increases and hence thermal boundary layer thickness (TBLT) becomes wider. Thus Ohmic dissipation has adverse effects on thermal performance. Thus fluids with no dissipation behave better as coolants.

3D heat flow effects in the imaging of subsurface graphical features in semi-transparent media by pulsed thermography

Pulsed thermography has proven to be a useful tool to detect subsurface features in ancient bookbindings and, in particular, to provide the IR image of texts buried beneath the end-leaves of the books. In this paper the theory is presented to analyze the influence of the geometrical and physical parameters involved in the processes leading to the distortion in the IR image of the detected buried graphical features. The distortion is mainly due to the lateral diffusion of the heat generated at the ink feature after the absorption of an excitation light. A comprehensive analysis taking into account the three dimensional heat diffusion process, in an optically semi-transparent medium, is considered. Numerical results are reported showing the behavior of the contrast and of a distortion parameter of the buried inked feature detected by the IR imaging in the various considered cases.

Two Dimensional Biomagnetic Fluid Flow and Heat Transfer over a Nonlinear Stretching Sheet with Temperature Dependent Viscosity

This investigated the flow and heat transfer of two dimensional biomagnetic fluid (blood) flow over a non-linear stretching sheet in the presence of magnetic dipole. It is assumed that the magnetic field is sufficiently strong enough to saturate the ferrofluid and variation of magnetization with temperature can be approximated by a linear function of temperature difference. The fluid viscosity is assumed to vary as an inverse linear function of the temperature. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformation. Numerical solutions are obtained by using bvp4c function technique in MATLAB software. The acquired results are shown graphically and were examined for several values of the dimensionless parameters. It is observed that for different values of ferromagnetic interaction parameter and variable viscosity parameter, the velocity distribution decreases while temperature distribution increases. The magnitude of skin friction coefficient and the rate of heat transfer decrease with the increasing values of radiation parameter and Prandtl number. The results are also compared for specific values of the parameters with others documented in literature.

Numerical Modelling on the Influence of Source in the Heat Transformation: An Application in the Metal Heating for Blacksmithing

Many physical problems, such as heat transfer and wave transfer, are modeled in the real world using partial differential equations (PDEs). When the domain of such modeled problems is irregular in shape, computing analytic solution becomes difficult, if not impossible. In such a case, numerical methods can be used to compute the solution of such PDEs. The Finite difference method (FDM) is one of the numerical methods used to compute the solutions of PDEs by discretizing the domain into a finite number of regions. We used FDMs to compute the numerical solutions of the one dimensional heat equation with different position initial conditions and multiple initial conditions. Blacksmiths fashioned different metals into the desired shape by heating the objects with different temperatures and at different position. The numerical technique applied here can be used to solve heat equations observed in the field of science and engineering.

Extended symmetry analysis of two-dimensional degenerate Burgers equation

We carry out the extended symmetry analysis of a two-dimensional degenerate Burgers equation. Its complete point-symmetry group is found using the algebraic method, and all its generalized symmetries are proved equivalent to its Lie symmetries. We also prove that the space of conservation laws of this equation is infinite-dimensional and is naturally isomorphic to the solution space of the (1+1)-dimensional backward linear heat equation. Lie reductions of the two-dimensional degenerate Burgers equation are comprehensively studied in the optimal way and new Lie invariant solutions are constructed. We additionally consider solutions that also satisfy an analogous nondegenerate Burgers equation. In total, we construct four families of solutions of two-dimensional degenerate Burgers equation that are expressed in terms of arbitrary (nonzero) solutions of the (1+1)-dimensional linear heat equation. Various kinds of hidden symmetries and hidden conservation laws (local and potential ones) are discussed as well. As a by-product, we exhaustively describe generalized symmetries, cosymmetries and conservation laws of the transport equation, also called the inviscid Burgers equation, and construct new invariant solutions of the nonlinear diffusion and diffusion–convection equations with power nonlinearities of degree −1/2.

Measuring dimensional and morphological heat alterations of dismemberment-related toolmarks with an optical roughness metre.

This experimental study provides a further understanding of the post-burning nature of sharp force trauma. The main objective is to analyse the distortion that fire may inflict on the length, width, roughness, and floor shape morphology of toolmarks induced by four different implements. To this end, four fresh juvenile pig long bones were cut with a bread knife, a serrated knife, a butcher machete, and a saw. A total of 120 toolmarks were induced and the bone samples were thus burnt in a chamber furnace. The lesions were analysed with a 3D optical surface roughness metre before and after the burning process. Afterwards, descriptive statistics and correlation tests (Student's t-test and analysis of variance) were performed. The results show that fire exposure can distort the signatures of sharp force trauma, but they remain recognisable and identifiable. The length decreased in size and the roughness increased in a consistent manner. The width did not vary for the saw, serrated knife, or machete toolmarks, while the bread knife lesions slightly shrunk. The floor shape morphology varied after burning, and this change became more noticeable for the three knives. It was also observed that the metrics of the serrated knife and machete cut marks showed no significant variations. Our results demonstrate that there is a variation in the toolmark characteristics after burning. This distortion is dependent on multiple factors that influence their dimensional and morphological changes, and the preservation of class features is directly reliant upon the weapon employed, the trauma caused, and the burning process conditions.

Derivation of Second Order Partial Differential Equation Indicating Wave and Heat Equation through the Use of the Navier Stoke’s Equation for Unsteady and Incompressible Flow

In this paper, we have tried to approach the concepts of two-dimensional wave equation and one dimensional heat equation through the means of the Navier Stoke’s equation for unsteady and incompressible flow. Our pursuit to do so has been supported with ample justifications and analytic discussions. The strong relation shared by the fluid dynamics, wave mechanics and heat flow has been brought to light through our attempts.

Sensitivity Analysis on Thermal Performance of Gas Heater with Finned and Finless Tubes using Characteristics-based Method

Natural gas must be preheated to prevent phase change and gas hydrate in pressure reduction stations. This paper aims to investigate the effect of the fins of gas tubes and their configuration, arrangement, and shape on the heat transfer and thermal efficiency of gas. To conduct a parametric study, two tube cases with fins and without fins, and in the finned case for the fin’s configuration, two longitudinal and circular arrangements, and the formation of the fins, two solid and interrupted forms were analyzed. Also, three types of cross-sections, including rectangular, convergent parabolic, and divergent parabolic, for the shape of the fins have been studied. For this simulation, the three-dimensional, incompressible, and steady flow was considered, and for analysis and discretization of convective heat equations, the characteristic-based method was applied. FORTRAN software was also used to implement and solve the equations. The results show that in solid and interrupted fins and increasing the number of fins in parallel, the dimensionless heat transfer coefficient increases. Also, the dimensional heat transfer coefficient decreases with increasing the ratio of fin height to the tube’s diameter. Also, the most significant heat transfer improvement was related to the divergent parabolic cross-section.

Contribution of joule heating and viscous dissipation on three dimensional flow of Casson model comprising temperature dependent conductance utilizing shooting method

This report examines the flow of non-Newtonian fluids down a bilateral surface under the influence of a magneto-hydrodynamic effect that is applied in many fields seen in the applied sciences and has received the attention of researchers because of its vast usage. It is assumed that the movement of particles generated fluid due to the movement of walls in the light of horizontal and vertical directions. Thermal study is carried out by employing the contribution of Joule heating, viscous dissipation and radiation. The phenomena of variable thermal conductivity and mass diffusion coefficient are also used in the modeling of the law of conservation of energy transport and species. The contribution of Brownian thermocouple and diffusion is captured by using the Buongrino model. The impact of various impact parameters was sketched. The involvement of the various parameters is measured in terms of dimensional stress, heat rate and mass. The limitation case of the current investigation is compared with the case of the published publications and an excellent arrangement is noted. The rate of transfer of thermal energy at wall of hot surface has gained using large values of Prandtl number because of large values of Prandtl number results reduction in thermal boundary layer while ratio between momentum and thermal boundary layers called Prandtl number. Hence, reduction in thermal boundary layer (TBL) results maximum production in rate of transfer of thermal energy.

Unsteady three dimensional radiative-convective flow and heat transfer of dusty nanofluid within porous cubic enclosures

Study of the convective transport of the dusty nanofluid is germane to dust ladder air, fluidization, gas cooling systems to enhance heat transfer process, environmental pollution, dust collection, sedimentation, and petroleum industry. Therefore, we aim in this article to deal with the transient three dimensional (3 D) radiative-convective flows and heat transfer of dusty nanofluid within porous cubic enclosures. Two systems of the differential equations are formulated for the nanofluid and dusty phases and two SIMPLE (Semi Implicit Method for Pressure Linked Equation) techniques are carried out for the distributions of the nanofluid and dusty pressures. The porous elements are the glass balls and the non-Darcy model is applied for the porous medium. All the porous properties are constants and taken into account during all the computations. The radiation flux is assumed in the normal direction and components of the system are in the thermal equilibrium state. The mixture is consisting of water as a host fluid and alumina as nanoparticles. The main findings revealed that the dusty parameters have significantly impacts on the heat transfer and hence they are important factors in such types of flows. Also, the increase in the nanoparticles volume fraction from 0% to 10% gives an enhancement in the average Nusselt number up to 12.88%.