Analytical Solution of Three-Dimensional Stable Conduction Heat Transfer on a Composite Plate with Internal Energy Generation


  • Mansour Mustafaoğlu


Analytical Solution Method, Composite Materials, Conductive Heat Transfer , Energy Generation


In this study, an analytical solution is presented for the conductive heat transfer of a plate made of composite materials at stable conditions with energy generation and radiation flux within the composite plate. The proposed exact solution is useful for studying heat transfer in tanks and composite panels. In addition, the coefficient of thermal conductivity tensor for composite materials is introduced and a method for determining the coefficient based on the properties of the matrix is introduced. The heat transfer equation in the Cartesian coordinate system for composite materials is obtained when the fibers in each layer are wrapped around the plate. Then, using the method of separating the variables, an exact solution for this equation is presented under certain boundary conditions.


Hearmon RF. Equations for transforming elastic and piezoelectric constants of crystals. Acta Crystallographica (1957) 10(2):121–124.

Huntington HB. The elastic constants of crystals. Solid state physics (1958) 7:213–351.

Diffusion through laminated orthotropic cylinders: Begel House Inc. (1974).

Golovchan VT, Artemenko, AG. Heat conduction of orthogonally reinforced composite material. Journal of engineering physics (1986) 51(2):944–949.

Shi-qiang D, Jia-chun L. Homogenized equations for steady heat conduction in composite materials with dilutely-distributed impurities. Applied Mathematics and Mechanics (1983) 4(2):167–173.

Greengard L, Lee J-Y. Electrostatics and heat conduction in high contrast composite materials. Journal of Computational Physics (2006) 211(1):64–76.

Newnham P, Abrate S. Finite element analysis of heat transfer in anisotropic solids: application to manufacturing problems. Journal of reinforced plastics and composites (1993) 12(8):854–864.

Sun Y, Wichman IS. On transient heat conduction in a one-dimensional composite slab. International Journal of Heat and Mass Transfer (2004) 47(6-7):1555–1559.

Onyejekwe OO. Heat conduction in composite media: a boundary integral approach. Computers & chemical engineering (2002) 26(11):1621–1632.

Lu X, Tervola P, Viljanen M. Transient analytical solution to heat conduction in composite circular cylinder. International Journal of Heat and Mass Transfer (2006) 49(1-2):341–348.

Halpin JC. Primer on Composite Materials Analysis, (Revised): CRC Press (1992).

Amiri Delouei A, Norouzi M. Exact analytical solution for unsteady heat conduction in fiber-reinforced spherical composites under the general boundary conditions. Journal of Heat Transfer (2015) 137(10).




How to Cite

Analytical Solution of Three-Dimensional Stable Conduction Heat Transfer on a Composite Plate with Internal Energy Generation. (2023). International Journal of Innovative Research and Reviews, 7(1), 12-16.

Most read articles by the same author(s)

<< < 1 2 3 4 5 6 7 8 9 10 > >>