Question
The heat current is written as $\frac{\triangle\text{Q}}{\triangle\text{t}}.$ Why don't we write $\frac{\text{dQ}}{\text{dt}}?$
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Answer
The amount of heat crossing through any cross-section of a slab in time $\triangle\text{t}$ is called heat current.
It is written as $\frac{\triangle\text{Q}}{\triangle\text{t}}$ and not as complete derivative $\frac{\text{dQ}}{\text{dt}}.$
This is because the amount of heat crossing through any cross section is a function of many variables like temperature difference, area of cross-section, etc.
So, we cannot write it as a complete derivative with respect to time.
It is written as $\frac{\triangle\text{Q}}{\triangle\text{t}}$ and not as complete derivative $\frac{\text{dQ}}{\text{dt}}.$
This is because the amount of heat crossing through any cross section is a function of many variables like temperature difference, area of cross-section, etc.
So, we cannot write it as a complete derivative with respect to time.
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