The Fay-Riddel equation is, I gather, an equation that gives the heat flux through, for example, the nose-cone of a space vehicle during re-entry.

I've been given a simplified version of this equation which looks as follows:

From my understanding, these are the variables and their units:

Where m is metre, s is second, W is watt, K is kelvin, kg is kilogram.

Clearly it can't be homogeneous because there's a kelvin on the RHS, and none on the LHS...

Can anybody shed some light on this equation I've been given? Is it erroneous?