In this paper, we present a Kane-Mele model in the presence of magnetic field and next nearest neighbors hopping amplitudes for investigations of the electronic and transport properties of monolayer phosphorene. We have also considered the effects of uniaxial and biaxial in-plane strain on the electronic behavior of phosphorene layer. Moreover the impact of out-of-plane strain on density of states of phosphorene layer has been studied. Specially, the temperature dependence of static thermal conductivity of phosphorene layer has been studied due to magnetic field, spin-orbit coupling and strain effects. The Kane Mele model Hamiltonian has been applied for describing the electron dynamics. We have exploited the linear response theory and Green's function approach to obtain the temperature behavior of thermal conductivity, electrical conductivity, Seebeck coefficient and figure of merit. Our numerical results indicate, thermal conductivity increases upon increasing the temperature in the low amounts region. This fact comes from the increasing of thermal energy of charge carriers and excitation of them to the conduction bands. The temperature dependence of seebeck coefficient show the thermopower gets negative sign at high temperatures in the presence of spin-orbit coupling and strain effects. The effects of both spin orbit coupling, magnetic field factors on temperature behavior of electrical conductivity of phosphorene monolayer have been investigated in details. Moreover the effects of both in-plane uniaxial and biaxial strains on transport properties of single layer phosphorene have been addressed.
