inverse estimation of the wall temperature in stagnation region of impinging flow on the cylinder with uniform transpiration

In this paper, for the first time, a numerical code based on the levenberg–marquardt method is presented to solve the inverse heat transfer problem of an annular jet on a cylinder with uniform transpiration and estimate the time-dependent wall temperature using temperature distribution at a point. also, the effect of noisy data on the final result is studied. for this purpose, the immediate task is to solve the temperature with no dimensions and convection heat transfer in a cylinder with a radial incompressible flow numerically. the free stream is steady, and the initial strain rate of flow is . the equations of momentum and energy are transformed into semi-similar equations using similarity variables. after discretizing the new equation system using the finite difference technique, it is solved by using the tri-diagonal matrix algorithm. after that, the wall temperature is calculated throughout using the levenberg–marquardt approach. this is a collaborative technique aimed at minimizing the least-square summation of the error values, where the error indicates the difference between the predicted and observed temperatures. this method exhibits considerable stability for noisy input data. in most cases, surface blowing decreases the prediction accuracy by displacement of the boundary layers from the surface, whereas suction acts vice versa. the main reason for this study is that in many industrial applications, it is not possible to insert the sensor on the wall to measure the temperature of the wall the sensor can be inserted in another place and the wall temperature distribution can be obtained by inverse analysis (determining of unknown boundary condition).