I'm in the need of fundamental information about free-jet flames. I'd like to calculate the heat transfer from a oxygen-hydrogen flame to a polymer plate. Are there any approximation equations for such a problem or do I have to go the hard way with differential equ. ?

(1). From the text book, you should be able to find the flame temperature. (I would guess, it's around several thousand degree.) (2). Then you need to know the wall temperature of the plate and its original temperature, in order to compute the heat conduction in the plate. Here we are assuming that the flame temperature and the wall temperature are independent of the heat conduction in the plate. (3). You can assume several wall temperatures to simulate the actual case. (depends on the relative position of the flame and the plate, I guess) (4). You can assume that the jet is a round one. So, the problem can be made 2-D axisymmetric heat conduction (in x-r coordinates, x is normal to the wall, r is from the center of the jet). I am assuming that the jet is aiming at the plate. (5). Now you have a transient heat conduction problem to solve, with the temperature as a function of x and time. Look into the heat conduction handbook first for the existing transient solutions. (6). You can also make it more complicated by assuming a wall temperature distribution, as a function of r. Even in this case, you should be able to write a program to solve the temperature distribution as a function of time and r. (it is going to be difficult to deal with heat transfer problems without knowing how to solve heat conduction problem.)