scholarly journals Thermal Load and Heat Transfer in Dental Titanium Implants: an Exact Analytical Solution to the ‘Heat Equation’

2021 ◽  
Author(s):  
Ziyad S. Haidar
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exposure Time ◽  
Thermal Load ◽  
Exact Analytical Solution ◽  
Titanium Implants ◽  
Surrounding Tissue ◽  
Temperature Changes

Introduction: Heat is a kinetic process whereby energy flows from between two systems; hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and -drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury; this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants upon hot-liquid intake. Materials and Methods: We investigate the impact of the material, the location point along implant length, and the exposure time of the thermal load on temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability and success rates, whether for immediate or delayed loading strategies.

scholarly journals Modeling methodology of locally non-equilibrium heat conductivity processes

Vestnik IGEU ◽  
2020 ◽  
pp. 65-71
Author(s):  
A.V. Eremin
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exact Analytical Solution ◽  
Separation Of Variables ◽  
Infinite Plate ◽  
Transfer Processes ◽  
Non Equilibrium

With the development of laser technologies and the ability to carry out processing steps under extreme conditions (ul-trahigh temperatures, pressures and their gradients), the interest in studying the processes that occur under locally non-equilibrium conditions has grown significantly. The key directions for the description of locally non-equilibrium pro-cesses include thermodynamic, kinetic and phenomenological ones. The locally non-equilibrium transfer equations can also be derived from the Boltzmann equation by using the theory of random walks and molecular-kinetic methods. It should be noted that some options of locally non-equilibrium processes lead to conflicting results. This study aims to develop a method for mathematical modeling of locally nonequilibrium heat conduction processes in solids, which allows determining their temperature with high accuracy during fast and high-intensity heat transfer processes. As applied to heat transfer processes in solids, a generalized heat equation that takes into account the relaxation properties of materials is formulated. The exact analytical solution is obtained using the Fourier method of separation of variables. The methodology for mathematical modeling of locally non-equilibrium transfer processes based on modified conservation laws has been developed. The generalized differential heat equation which allows performing N-fold relaxation of the heat flow and temperature in the modified heat balance equation has been formulated. For the first time, an exact analytical solution to the unsteady heat conduction problem for an infinite plate was obtained taking into account many-fold relaxation. The analysis of the solution to the boundary value problem of locally nonequilibrium heat conduction enabled to conclude that it is impossible to instantly has establish a boundary condition of the first kind. It has been demonstrated that each of the following terms in the relaxed heat equation has an ever smaller effect on the heat transfer process. The obtained results can be used by the scientific and technical personnel of organizations and higher educational institutions in the study of fuel ignition processes, the development of laser processing of materials, the design of highly efficient heat transfer equipment and the description of fast-flowing heat transfer processes.

Transient Heat Transfer between a Plate and a Fluid whose Temperature Varies Periodically with Time

1980 ◽  
Vol 102 (1) ◽  
pp. 126-131 ◽  
Author(s):  
J. Sucec
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Forced Convection ◽  
General Problem ◽  
Laplace Transformation ◽  
Exact Analytical Solution ◽  
Transient Heat Transfer ◽  
Convection Problem ◽  
Complex Temperature

Using the method of complex temperature in conjunction with the Laplace transformation, an exact analytical solution is found for the transient, conjugate, forced convection problem consisting of a plate, whose base is insulated, interacting with a fluid, moving in a steady slug fashion, whose temperature, at points far from the plate, varies sinusoidally with time. Simple quasi-steady results are derived for comparison. Also presented is a method for determining the qualitative conditions under which one might expect a quasi-steady analysis to be valid in a general problem.

A New Exact-Analytical Solution for Convective Heat Transfer of Nanofluids Flow in Isothermal Pipes

2017 ◽  
Vol 35 (02) ◽  
pp. 233-242 ◽  
Author(s):  
P. Akbarzadeh
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Exact Analytical Solution ◽  
Perturbation Technique ◽  
Particle Diameter ◽  
Whittaker Function ◽  
Surface Mass

ABSTRACTThis study presents a new exact-analytical solution for convective heat transfer of thermally fully-developed laminar nanofluid flows in a circular tube for the first time. In this problem, the pipe wall is exposed to a constant temperature. The solution is based on the Whittaker function and perturbation technique. In the nanofluid model, it is assumed that nanoparticles and base-fluid behave as a single-phase with average properties. In this study, the effects of Reynolds number, volume fraction of the particles, Peclet number, and particle diameter are investigated on the average heat transfer coefficient, surface mass transfer, and Nusselt number.

Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
A. Amiri Delouei ◽  
M. Norouzi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Laplace Transformation ◽  
Exact Analytical Solution ◽  
Function Technique ◽  
Conductive Heat ◽  
Fiber Reinforced ◽  
Legendre Series

The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier–Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.

Heat Transfer and Thermal Load Analysis of Exhaust Manifold

2012 ◽  
Vol 226-228 ◽  
pp. 2240-2244 ◽  
Author(s):  
Shi Long Xu ◽  
Yan Shi ◽  
Shou Cheng Li
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Alloy Steel ◽  
Thermal Load ◽  
Convective Heat Transfer Coefficient ◽  
Heat Transfer Analysis ◽  
Nonlinear Material ◽  
Joint Analysis ◽  
Deformation Analysis ◽  
Exhaust Manifold

With the appearance of high temperature resistance alloy steel and the requirement of light weight for vehicles, more and more exhaust manifolds are made from newly developed alloy steel. The changing of material directly affects the design and manufacturing process. To estimate the thermal load of the tight-coupled exhaust manifold, the joint analysis methods of CFD and FEM are put forward to predict the temperature distribution, thermal stress and deformation. Using Computational Fluid Dynamics (CFD) method, gas temperature and convective heat transfer coefficient, adjoining the inside and outside surfaces of the exhaust manifold, are estimated firstly in this paper. Then these results are mapped to the finite element mesh of exhaust manifold, which are created for the heat transfer analysis. At last, thermal stress and thermal deformation analysis are presented by taking nonlinear material properties into account, which provide some reference to evaluate the cooling capacity and structure design of exhaust manifold.

An Inverse Method for Determining Thermal Load History Which Reduces Transient Thermal Stress

2006 ◽  
Author(s):  
Takuya Ishizaka ◽  
Shiro Kubo ◽  
Seiji Ioka
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Temperature Distribution ◽  
Thermal Load ◽  
Inverse Method ◽  
Temperature History ◽  
Load History ◽  
Transient Thermal Stress ◽  
Inner Surface ◽  
Transient Thermal

When high temperature fluid flows into a pipe, a temperature distribution in the pipe induces a thermal stress. It is important to reduce the thermal stress for managing and extending the lives of plants. In this problem heat conduction, elastic deformation, heat transfer, liquid flow should be considered, and therefore the problem is of multidisciplinary nature. In this paper an inverse method is proposed for determining the optimum thermal load history which reduces transient thermal stress considering the multidisciplinary physics. As a typical problem, transient thermal stress in a thin pipe during start-up was treated. It was assumed that the inner surface was heated by liquid flow and the outer surface was insulated for simplicity. The multidisciplinary complex problem was decomposed into a heat conduction problem with given internal wall temperature history, thermal stress problem with given temperature distribution, and heat transfer problem with given heat flux on an inner surface. An analytical solution of the temperature distribution of the radial thickness and the thermal hoop stress distribution was obtained. The maximum inner hoop tensile stress was minimized for the case where inner surface temperature Ts(t) was expressed in terms of the 3rd order polynomial function of time t. Finally, from the temperature distributions, the optimum fluid temperature history was obtained for reducing the transient thermal tensile stress.

An exact analytical solution for convective heat transfer in rectangular ducts

2012 ◽  
Vol 13 (10) ◽  
pp. 768-781 ◽  
Author(s):  
Mohammad Mohsen Shahmardan ◽  
Mahmood Norouzi ◽  
Mohammad Hassan Kayhani ◽  
Amin Amiri Delouei
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Exact Analytical Solution
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