The correct answer is option 'C' - heat flux.

Heat transfer is the process by which thermal energy is exchanged between objects or systems due to a temperature difference. The rate at which heat is transferred per unit area is known as the heat flux.

Heat flux is a measure of how much heat is transferred through a given area in a given amount of time. It is expressed in units of watts per square meter (W/m²) or calories per square centimeter per second (cal/cm²/s).

Now let's break down the options and understand why heat flux is the correct answer:

a) Temperature gradient: The temperature gradient refers to the change in temperature per unit length or distance. It represents how temperature changes with respect to position. While temperature gradient is related to heat transfer, it does not directly measure the rate of heat transfer per unit area.

b) Thermal conductivity: Thermal conductivity is a property of a material that describes how well it conducts heat. It is the measure of the ability of a material to conduct heat through it. While thermal conductivity is important in determining the rate of heat transfer, it is not the rate of heat transfer per unit area itself.

c) Heat flux: Heat flux is the rate of heat transfer per unit area. It quantifies the amount of heat energy transferred across a given surface area in a given time. It represents the flow of heat through a surface and is directly related to the temperature difference across the surface and the thermal conductivity of the material.

d) Specific heat: Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by a certain amount. It is an intrinsic property of a substance and is not directly related to the rate of heat transfer per unit area.

In summary, the rate of heat transfer per unit area is called heat flux. It represents the flow of heat through a surface and is determined by the temperature difference and thermal conductivity.