if the old radiator is replaced with a new one that has longer tubes made of the same material and same thickness as those in the old unit, what should the total surface area available for heat exchange be in the new radiator to achieve the necessary heat exchange rate at the recommended temperature gradient?

The rate of heat transfer between two things is related to the temperature difference between them. Internal heat must be moved from the different organs and tissues to the colder body surface for the subsequent thermal loss. Internal heat transport describes the movement of heat from the bodily core to the shell.

Briefing:

we will use this relation

[tex]K=\frac{Q d}{A * c h a n g e i n T}[/tex]

change throughout T = ΔT ,

consequently New Area (A) = 3/2 * Old Radiator Area

Considering that the heat conductivity of something like the new and old radiators is the same.

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The complete question is-

The radiator of a car is a type of heat exchanger. Hot fluid coming from the car engine, called the coolant, flows through aluminum radiator tubes of thickness d that release heat to the outside air by conduction. The average temperature gradient between the coolant and the outside air is about 130 K/mm . The term ΔT/d is called the temperature gradient which is the temperature difference ΔT between coolant inside and the air outside per unit thickness of tube.