Question

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 the heat exchange be in the new radiator to achieve the desired cooling temperature gradient?
Please, explain me

Answer 1

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 \(\dfrac{\triangle T}{d}\) is called the temperature gradient, which is the temperature difference \(\triangle T\) between the coolant inside and the air outside per unit thickness of tube.
The radiator of an old car is no longer performing satisfactorily. The average temperature gradient between the coolant flowing through its tubes and the outside air is 195 K/mm, causing the engine to overheat.
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 the heat exchange be in the new radiator to achieve the desired cooling temperature gradient?

Answer 2

my answer is 3/2 of the old unit, am I right?
the logic is \[-k A_{old}*~(old)\frac{\triangle T}{d} = -kA_{new}*~~(new)\frac{\triangle T}{d}\]
\[\rightarrow A_{new}= A_{old} \frac{195}{130}= \frac{3}{2}A_{old}\]