Abstract: In ref. [1], V. E. Najenov studied the conditions that when the viscosity of the liquid is on exponential function of temperature, the pipe flow, hoving sleady heat transfer, is one-dimensional and with nonuniform temperature. For plane canal and circular pipe he still studied the velocity and the temper turefields.In thispaper, the author presents two new methodsfor solving the same problem. The method as in ref. [1] may be regarded as the natural branch of the methods of this paper. One of our new methods only can solve the same problem as in ref.[1] and the complex degree of its computing process is nearly the same as that in ref. [1]. But the other can go beyond the studying scope of ref. [1], namely, for the case ihal the curvatures of circumference of the cross section of the pipe are not equivalent everywhere, the problem may also be solved.

Key words: viscoelastic plate, dynamic stability, von Kármán’s hypothesis, Galerkin method, chaos, Hopf bifurcation