APPROXIMATE SOLUTION OF NONLINEAR TRANSIENT HEAT-CONDUCTION IN CYLINDRICAL GEOMETRY

The applicability of the Heat Balance Integral method (HBI) using hybrid profiles (HP(n)) for heat diffusion problems in cylindrical geometry is studied. Three test problems are taken to validate the method, namely, TP1 - long hollow cylinder, inner boundary is supplied with constant heat flux and the outer boundary is at infinity, TP2 - the same geometry with the inner boundary at constant temperature, TP3 - the same geometry with convection at the boundary. It is found that HBI in combination with HP(n) gives much better solutions as compared to the HBI-polynomial (P(n)) combinations. This method is applied to non-linear cases like temperature dependent thermal conductivity, boiling or condensation at the boundary. For assessment of accuracy Root Mean Square Residual (E(rms)) is defined. The residual minimization technique is used to select the parameter beta in the HP(n) profile. It is shown that this procedure yields solutions which are in excellent agreement with the available exact solutions in the case of the three test problems. In the case of nonlinear problems, the value of E(rms) which is comparable to the values in the test cases, shows that the HBI-HP(n) is a very good combination for all problems.