Several parameters need to be checked, for example surface roughness, wind speed, air temperature near the surface, surface temperature, air density, specific heat capacity of air depends..................................... Q/A=p*cp*(Tair-Tsurface) /ra. The ra parameter is obtained from the attached file.
This type of relationship is experimental and I saw that they used it in several articles...
The total flux radiated by the lamp is 60 W, most of it in the infrared, and a part in the visible range. This flux could be assumed as isotropic, hence radiated in 4·pi steradians (pi=3.14159...). If anisotropic, the irradiance diagram of the lamp should be known and taken into account.
The solid angle under which the lamp sees your area is 1/d², where d is the distance between the lamp and the 1 m² surface, supposed to be perpendicular to the radiation.
Therefore, if your surface absorbs all the radiation, it receives 60·4·pi/d² W/m² if the assumptions mentioned above are correct.
The mentioned heat flux is caused by the temperature difference (sensible heat transfer) and you must also calculate the heat flux caused by radiation. heat flux due to radiation is obtained from the sum of short wave radiation and long wave radiation.
Yes, the answer I gave relates to the radiative transfer only, assuming a perfect absorption by the surface. If the medium between the lamp and the area is not the vacuum, heat transfer by convection and conduction should also be taken into account.