scholarly journals A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Heat Capacity ◽  
Phase Change ◽  
Temperature Profile ◽  
Series Solution ◽  
Thermal Loading ◽  
Heat Conduction Problem ◽  
Finite Thickness ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Transform Method

A two-dimensional differential transform method is applied to solve one-dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other. In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature. A series solution is derived for the temperature profile in the melting or solidifying slab with temperature-dependent thermal conductivity and volumetric heat capacity. The latent heat effect of the phase change is incorporated into the temperature-dependent heat capacity. Numerical results demonstrate the effects of the temperature-dependent parameters on the transient temperature profile of the slab.

Approximate Analytical Method to Stefan Problem for Spheres with Wide Temperature Range of Phase Transition

2014 ◽  
Vol 627 ◽  
pp. 145-148 ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Phase Change ◽  
Temperature Profile ◽  
Solid Sphere ◽  
Transient Temperature ◽  
Transform Method ◽  
Differential Transform ◽  
Apparent Specific Heat ◽  
Heat Method ◽  
The One ◽  
Analytical Series

The two-dimensional differential transform method is applied to solve the one-dimensional phase change problem for a solid sphere with time-dependent boundary temperature. The problem assumes that the phase change occurs over a range of temperatures and the initial temperature of the sphere is an arbitrary constant. An approximate analytical (series) solution is derived for the temperature profile in the melting or solidifying sphere. The solution is based on the apparent specific heat method. Numerical results illustrate the effects of the Stefan number, which is the ratio of sensible heat to latent heat, on the transient temperature profile in the sphere.

Clamp Load Decay in Preloaded Dissimilar Lightweight-Material Joints due to Cyclic Temperature

2014 ◽  
Author(s):  
Sayed A. Nassar ◽  
Amir Kazemi ◽  
Mohamad Dyab
Keyword(s):  
Finite Element ◽  
Temperature Profile ◽  
Thermal Loading ◽  
Dissimilar Materials ◽  
Temperature Dependent ◽  
Element Analysis ◽  
Temperature Load ◽  
Cyclic Temperature ◽  
Material Creep ◽  
Aluminum And Magnesium Alloys

Experimental and Finite Element methods are used for investigating the effect of cyclic thermal loading on the clamp load decay in preloaded single-lap bolted joints that are made of dissimilar-materials. Joint material combinations include steel and lightweight materials such as aluminum and magnesium alloys, with various different thicknesses. The range of cyclic temperature profile varies between −20°C and +150°C. A computer-controlled environmental chamber is used for generating the desired cyclic temperature profile and duration. Real time clamp load data is collected using high-temperature load cells. Percent clamp load decay is investigated for various combinations of joint materials, initial preload level, and test specimen thicknesses. Thermal and material creep finite element analysis is performed using temperature-dependent mechanical properties. FEA result has provided insight into interesting experimental observations regarding model predictions and the experimental data is discussed.

Application of a Differential Transform Method to the Transient Natural Convection Problem in a Vertical Tube with Variable Fluid Properties

2016 ◽  
Vol 71 (2) ◽  
pp. 185-193
Author(s):  
Ryoichi Chiba
Keyword(s):  
Natural Convection ◽  
Special Functions ◽  
Vertical Tube ◽  
Differential Transform Method ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Transform Method ◽  
Recursive Procedure ◽  
Transient Natural Convection ◽  
Differential Transform

AbstractThe transient natural convection of a viscous fluid in a heated vertical tube is studied using the two-dimensional differential transform method (DTM). A time-dependent Dirichlet boundary condition is imposed for tube wall temperature. The partial differential equations for the velocity and temperature fields within the tube are solved by the DTM while considering temperature-dependent viscosity and thermal conductivity of the fluid. As a result, tractable solutions in double-series form are derived for the temperature and flow velocity. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results illustrate the effects of temperature-dependent properties on transient temperature and flow behaviour, including the Nusselt number and volumetric flow rate. The DTM gives accurate series solutions without any special functions for nonlinear transient heat transfer problems which are advantageous in finding the derivative or integral.

Effects of thermal material properties on precision of transient temperatures in pulsed laser welding of Ti6Al4V alloy

2018 ◽  
Vol 233 (9) ◽  
pp. 3170-3181
Author(s):  
Massab Junaid ◽  
Taqi Ahmad Cheema ◽  
Hani Haleem ◽  
Saad-ul-Fatah ◽  
Khalid Rahman ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Specific Heat ◽  
Temperature Profile ◽  
Material Properties ◽  
Pulsed Laser ◽  
Ti6al4v Alloy ◽  
Transient Temperature ◽  
Constant Density ◽  
Temperature Dependent ◽  
Temperature Distributions

This study investigates the effect of temperature-dependent material properties on the precision of a simulation in pulsed laser beam welding of Ti6Al4V alloy. Ti6Al4V is one of the most extensively used titanium alloys. The precision in transient temperature distributions developed in the thermal modeling part of a sequentially coupled thermo-mechanical simulation is crucial to the end results of structural mechanics. The temperature profile obtained by a finite element model at two distinct locations is validated by experimental results using temperature-dependent material properties. Then, the effect of assuming constant room temperature values for thermal conductivity, specific heat, and density on the temperature distribution is studied at different welding speeds. Temperature distributions are unaffected by the constant density assumption. The constant thermal conductivity assumption underestimates the peak temperatures far from the weld region, whereas the constant specific heat assumption overestimates these temperatures. This effect becomes prominent at low welding speeds. The temperature profile when conductivity and specific heat are assumed to be constant is nearly similar to that in the case of constant conductivity when conductivity and specific heat are assumed constant. Therefore, conductivity is the dominant variable. The constant conductivity assumption also restricts the heat flow from the weld to the edge region, thus increasing the size of the weld pool. This effect also becomes increasingly prominent at low welding speeds.

scholarly journals Axisymmetric stationary heat conduction problem for half-space with temperature-dependent properties

2020 ◽  
Vol 24 (3 Part B) ◽  
pp. 2137-2150
Author(s):  
Dariusz Perkowski ◽  
Piotr Sebestianiuk ◽  
Jakub Augustyniak
Keyword(s):  
Heat Conduction ◽  
Half Space ◽  
Heat Conduction Problem ◽  
Hankel Transform ◽  
Heating Zone ◽  
Temperature Dependent ◽  
Transform Method ◽  
Special Cases ◽  
Temperature Dependent Properties ◽  
Method Model

The study examines problems of heat conduction in a half-space with a thermal conductivity coefficient that is dependent on temperature. A boundary plane is heated locally in a circle zone at a given temperature as a function of radius. A solution is obtained for any function that describes temperature in the heating zone. Two special cases are investigated in detail, namely Case 1 with given constant temperature in the circle zone and Case 2 with temperature given as a function of radius, r. The temperature of the boundary on the exterior of the heating zone is assumed as zero. The Hankel transform method is applied to obtain a solution for the formulated problem. The effect of thermal properties on temperature distributions in the considered body is investigated. The obtained results were compared with finite element method model.

scholarly journals Analysis of Transient Thermal Distribution in a Convective–Radiative Moving Rod Using Two-Dimensional Differential Transform Method with Multivariate Pade Approximant

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1793
Author(s):  
Ganeshappa Sowmya ◽  
Ioannis E. Sarris ◽  
Chandra Sen Vishalakshi ◽  
Ravikumar Shashikala Varun Kumar ◽  
Ballajja Chandrappa Prasannakumara
Keyword(s):  
Heat Generation ◽  
Padé Approximant ◽  
Differential Transform Method ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
Transform Method ◽  
Pade Approximant ◽  
Differential Transform ◽  
Transient Thermal

The transient temperature distribution through a convective-radiative moving rod with temperature-dependent internal heat generation and non-linearly varying temperature-dependent thermal conductivity is elaborated in this investigation. Symmetries are intrinsic and fundamental features of the differential equations of mathematical physics. The governing energy equation subjected to corresponding initial and boundary conditions is non-dimensionalized into a non-linear partial differential equation (PDE) with the assistance of relevant non-dimensional terms. Then the resultant non-dimensionalized PDE is solved analytically using the two-dimensional differential transform method (2D DTM) and multivariate Pade approximant. The consequential impact of non-dimensional parameters such as heat generation, radiative, temperature ratio, and conductive parameters on dimensionless transient temperature profiles has been scrutinized through graphical elucidation. Furthermore, these graphs indicate the deviations in transient thermal profile for both finite difference method (FDM) and 2D DTM-multivariate Pade approximant by considering the forced convective and nucleate boiling heat transfer mode. The results reveal that the transient temperature profile of the moving rod upsurges with the change in time, and it improves for heat generation parameter. It enriches for the rise in the magnitude of Peclet number but drops significantly for greater values of the convective-radiative and convective-conductive parameters.

Transient Temperature Fields in Crossflow Heat Exchangers With Finite Wall Capacitance

1988 ◽  
Vol 110 (1) ◽  
pp. 49-53 ◽  
Author(s):  
M. Spiga ◽  
G. Spiga
Keyword(s):  
Heat Capacity ◽  
Heat Exchangers ◽  
Green's Functions ◽  
Green’S Functions ◽  
Temperature Fields ◽  
Transient Temperature ◽  
Inlet Temperature ◽  
Transform Method ◽  
Transfer Resistance ◽  
Primary Fluid

Solutions are provided in nondimensional form for the transient analysis of direct-transfer crossflow heat exchangers, with both fluids unmixed and finite wall heat capacity. The two-dimensional transient temperature distributions of core wall and both fluids are determined by analytical methods for any externally applied variation of the primary fluid inlet temperature. The general solutions are derived by the local energy balance equations, and are presented as simple integrals of the Green’s functions, which represent the pulse response following a deltalike perturbation in the inlet temperature of the primary fluid, and are deduced using the Laplace transform method. The Green’s functions are expressed as integrals of modified Bessel functions, in terms of the heat capacity ratios, number of transfer units, heat transfer resistance and flow capacitance ratios.

Numerical Solution of the General Two-Dimensional Inverse Heat Conduction Problem (IHCP)

1997 ◽  
Vol 119 (1) ◽  
pp. 38-45 ◽  
Author(s):  
A. M. Osman ◽  
K. J. Dowding ◽  
J. V. Beck
Keyword(s):  
Experimental Data ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Simulated Data ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Temperature Dependent

This paper presents a method for calculating the heat flux at the surface of a body from experimentally measured transient temperature data, which has been called the inverse heat conduction problem (IHCP). The analysis allows for two-dimensional heat flow in an arbitrarily shaped body and orthotropic temperature dependent thermal properties. A combined function specification and regularization method is used to solve the IHCP with a sequential-in-time concept used to improve the computational efficiency. To enhance the accuracy, the future information used in the sequential-in-time method and the regularization parameter are variable during the analysis. An example using numerically simulated data is presented to demonstrate the application of the method. Finally, a case using actual experimental data is presented. For this case, the boundary condition was experimentally measured and hence, it was known. A good comparison is demonstrated between the known and estimated boundary conditions for the analysis of the numerical, as well as the experimental data.

Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities

2014 ◽  
Vol 3 (4) ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Moisture Transfer ◽  
Sudden Change ◽  
Moisture Diffusivity ◽  
Diffusion Problem ◽  
Transient Temperature ◽  
Temperature Dependent ◽  
Transform Method ◽  
Recursive Procedure ◽  
Heat And Moisture ◽  
Moisture Profiles

AbstractThe two-dimensional differential transform method (DTM) is applied to solve the one-dimensional coupled heat and moisture diffusion problem for a slab with temperature-dependent thermal and moisture diffusivities, which are expressed by a linear function and an exponential function of temperature, respectively. One surface of the slab is subjected to convective hygrothermal loading and the other has constant prescribed temperature and moisture. Approximate analytical (series) solutions for the temperature and moisture profiles in the slab are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results for a slab subjected to a sudden change in surface temperature illustrate the effects of temperature-dependent diffusivities on the transient temperature and moisture profiles of the slab. The results indicate that the nonlinear effect originating from the varying moisture diffusivity is not negligible for resin composites. The DTMis a useful new analytical method for solving nonlinear coupled transient problems.

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