Heat is generated in the medium at rate g{x,y,z,t) per unit time and per unit volume. What is the mathematical formulation of this ?

Consider a physical  involving a plate with width a and thickness A, which moves horizontally along the x direction with a constant velocity u. Assume constant physical properties. Also, suppose the plate to be infinitely long in the axial (x) direction. The plate looses heat by convection through its lateral surfaces, at y = 0 and y = o, to an ambient at temperature with a heat transfer coefficient h. The bottom surface at z = 0 is supposed insulated, while a transient heat flux with distribution qix,y,t) is supplied at the top surface z = A, in the region x > 0. The initial temperature in the medium is F\x,y,z) and the plate enters into the heated zone (x > 0) with a uniform temperature To at x = 0. Heat is generated in the medium at rate g{x,y,z,t) per unit time and per unit volume. What is the mathematical formulation of this ?

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