Analytical solutions for three-dimensional steady and transient heat conduction problems of a double-layer plate with a local heat source

An equivalent temperature model of 3-D steady heat conduction analysis for a fiber metal laminated plate coated with a thermal barrier

“…, and ( 1,2,3) i ki = represent the thermal conductivities of the CFML structure along x , y and z directions, respectively.…”

“…For the composited structure coated with thermal barrier which subjected to high-temperature environment, we have obtained analytical solutions of three-dimensional steady temperature field and three-dimensional steady thermodynamic analysis in previous work [3,4]. Bhowmick et al [5] studied friction and wear behavior of tetrahedral amorphous carbon and fluorinated ta-C coatings in the temperature range between 25°C and 500°C.…”

A semi-analytical solution of 3-D transient temperature field for a uniform plate subjected to Gaussian-distribution laser heat source

“…Considering the cooling effect caused by free or forced convection in the ambient gas, Brockman et al [37] calculated a two-dimensional temperature field in a sheet moving slice heated with a laser beam, and a two-dimensional integral Fourier transform on the space coordinates was used by them to solve the problem as well as the analytical solution of the problem in Fourier space was obtained. Jiang and Dai [38] solved the three-dimensional steady heat conduction problem of a double-layer plate by using the Poisson method and the layer wise approach, where the double-layer structure including a coating layer and FGM layer, in addition, the separation of variables method and the layer wise approach were used to solve the three-dimensional transient thermal conduction problem. Taking into consideration the solid-liquid-vapor phase-change process [39] and the simply supported conditions [40] respectively, Jiang et al solved the three-dimensional transient temperature field of a high strength and low alloy rectangular steel plate under laser shock processing by the separate variable method.…”

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

“…Jiang and Dai 17 studied the 3D heat conduction involving two‐layered composite using the Poisson method and layer‐wise scheme (LWS). The transient problem was also solved using the LWS and separation of variables.…”