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Which of these terms represent the rate of heat addition to the system due to heat transfer?

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Which of these terms represent the rate of heat addition to the system due to heat transfer?

(a) -k gradT

(b) k gradT

(c) ∇.(k gradT)

(d) ∇.(k gradT)

The question was asked in homework.

The above asked question is from Energy Equation in chapter Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

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Correct choice is (c) ∇.(k gradT)

Easy explanation: Rate of heat addition is

q=-k gradT

The total rate of heat added to the system is

-div(q)=∇.(k gradT).

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