Related Experiment Video
Updated: Mar 17, 2026

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
Published on: July 5, 2024
Exact Analytical Solution for 3D Time-Dependent Heat Conduction in a Multilayer Sphere with Heat Sources Using
1Department of Mechanical Engineering, Salmas Branch, Islamic Azad University, Salmas, Iran.
Abstract:
An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed.
More Related Videos
10:23Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
Published on: December 1, 2023
08:52Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
Published on: April 30, 2018
Related Concept Videos
Conduction, Convection and Radiation: Problem Solving
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Heat Flow and Specific Heat
Differential Form of Maxwell's Equations
Mechanisms of Heat Transfer II
Thermal expansion and Thermal stress: Problem Solving
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55...