scholarly journals Semi-derivative integral method (SDIM) to transient heat conduction: Time-dependent (power-law) temperature boundary conditions

2021 ◽  
pp. 143-143
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Power Law ◽  
Integral Method ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Time Dependent ◽  
Conduction Time ◽  
Parabolic Profile ◽  
Temperature Boundary

Transient heat conduction in semi-infinite medium with a power-law time-dependent boundary conditions has been solved by an integral-balance integral method applying to a semi-derivative approach. Two versions of the integral-balance method have been applied: Goodman?s method with a generalized parabolic profile and Zien?s method with exponential (original and modified) profile.

scholarly journals Semi-derivative integral method to transient heat conduction time-dependent heat flux boundary conditions

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 303-308
Author(s):  
Jordan Hristov
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Heat Conduction ◽  
Power Law ◽  
Integral Method ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Time Dependent ◽  
Conduction Time ◽  
Flux Boundary Conditions

Transient heat conduction in semi-infinite medium with a time dependent heat flux as boundary condition has been solved by a semi-derivative integral-balance method. Two versions boundary fluxes have been considered: power-law and exponential.

scholarly journals Analytic Solutions for Heat Conduction in Functionally Graded Circular Hollow Cylinders with Time-Dependent Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sen-Yung Lee ◽  
Chih-Cheng Huang
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Integral Transformation ◽  
Transient Heat Conduction ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Time Dependent ◽  
Power Functions ◽  
Hollow Cylinders

An analytic solution method, without integral transformation, is developed to find the exact solutions for transient heat conduction in functionally graded (FG) circular hollow cylinders with time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order regular singular differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. The exact solution of the system with thermal conductivity and specific heat in power functions with different orders is developed. Finally, limiting studies and numerical analyses are given to illustrate the efficiency and the accuracy of the analysis.

scholarly journals Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 377-389
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Surface Temperature ◽  
Integral Method ◽  
Infinite Medium ◽  
Surface Heating ◽  
Integration Technique ◽  
Solution Approach ◽  
Linear Heat ◽  
Thermal Penetration Depth ◽  
Non Linear

Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach. The thermal penetration depth and solution behaviours with finite speeds have been analyzed.

Transient Conduction From Parallel Isothermal Cylinders

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Rajai S. Alassar
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Energy Equation ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Basis Functions ◽  
Cylindrical Coordinates ◽  
Transient Conduction ◽  
Isothermal Cylinders

The transient heat conduction from two parallel isothermal cylinders is studied using the naturally fit bipolar cylindrical coordinates system. The energy equation is expanded in a Fourier series using appropriate basis functions to eliminate one of the physical coordinates. The resulting modes of the expansion are solved using a finite difference scheme. It is shown that, as is the case with a single isothermal cylinder in an infinite medium, steady states for two isothermal cylinders are not possible and heat transfer changes indefinitely with time.

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Partner Ndlovu ◽  
Rasselo Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Conservation Laws ◽  
Linear Function ◽  
Power Law ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Lie Point Symmetries ◽  
Transient Heat Conduction Problem

AbstractSome new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

scholarly journals Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
R. T. Al-Khairy ◽  
Z. M. AL-Ofey
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Closed Form Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.

Sign in / Sign up

Export Citation Format

Share Document