The thermal rectifier is an analog of the electrical rectifier, in which heat flux in a forward direction is larger than that in the reverse direction. Owing to the controllability of the heat flux, the solid-state thermal rectifier is promising from both theoretical and applicational points of view. In this paper, we examine analytical expressions of thermal-rectification coefficients R for thermal rectifiers with typical linear and nonlinear model functions as nonuniform thermal conductivities against temperature T. For the thermal rectifier with linear (quadratic) temperature-dependent thermal conductivity, a maximum value of R is calculated to be 3 (≃14). With use of a structural-phase-transition material, a maximum value of R is found to ideally reach to κ_{2}/κ_{1}, where κ_{1} (κ_{2}) is the minimum (maximum) value of its κ(T). Values of R for the thermal rectifiers with an inverse T-dependent function and an exponential function of κ are also analytically examined.