Finite element solution to transient asymmetric heat conduction in multilayer annulus Research
This study investigate the heat transfer and thermal stresses for the time-dependent asymmetric heat conduction in a multilayer annulus by using finite element method. The realistic problem of isotropic multilayer annulus subjected to heat flux with internal heat generation and initial temperature is solved. The results of temperature and thermal stress have been computed numerically, illustrated graphically and interpreted technically. These results may be used in many engineering problem like combustion chamber, electric generator, compressor, hydraulic pumps etc. MSC: 35G30 • 35K20 • 74S05 • 80A20 • 80M10
Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions
Abstract The separation of variables ( SOV ) method has recently been applied to solve time-dependent heat conduction problem in a multilayer annulus. It is observed that the transverse (radial) eigenvalues for the solution in polar ( r - θ ) coordinate system are always real numbers (unlike in the case of similar multidimensional Cartesian problems where they may be imaginary ) allowing one to obtain the solution analytically. However, the SOV method cannot be applied when the boundary conditions and/or the source terms are time-dependent, for example, in a nuclear fuel rod subjected to time-dependent boundaries or heat sources. In this paper, we present an alternative approach using the finite integral transform method to solve the asymmetric heat conduction problem in a multilayer annulus with time-dependent boundary conditions and/or heat sources. An eigenfunction expansion approach satisfying periodic boundary condition in the angular direction is used. After integral transformation and subsequent weighted summation over the radial layers, partial derivative with respect to r -variable is eliminated and, first order ordinary differential equations ( ODEs ) are formed for the transformed temperatures. Solutions of ODEs are then inverted to obtain the temperature distribution in each layer. Since the proposed solution requires the same eigenfunctions as those in the similar problem with time-independent sources and/or boundary conditions—a problem solved using the SOV method—it is also “free” from imaginary eigenvalues.
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.