State space approach to thermoelectric fluid with fractional order heat transfer

A new mathematical model for electromagnetic thermofluid equation heat transfer with thermoelectric properties using the methodology of fractional calculus is constructed. The governing coupled equations in the frame 11 of the boundary layer model are applied to variety problems. Laplace transforms and state space techniques (Ezzat Can J Phys Rev 86:1241–1250 in 2008) are used to get the solution of a thermal shock problem, a layer problem and a problem for the semi-infinite space in the presence of heat sources. According to the numerical results and its graphs, a parametric study of time-fractional order 0 < α ≤ 1, on temperature and the thermoelectric figure of merit are conducted.