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 deltaT/dis called the temperature gradient which is the temperature difference deltaT between x coolant inside and the air outside per unit thickness of tube.
Cooling temperature gradient?
A) twice that of the old unit
B) three halves that of the old unit
C) same as that of the old unit
D) two third that of the old unit
E) one-half that of the old unit
Part B
If the old radiator is replaced with anew one made of a material that has twice the thermal conductivity of the material of the old radiator what should the total surface area available for heat exchange in the new radiator be to achieve the desired temperature gradient ?
Assume that the tubes of the new radiator are as thick as tubes in older unit.
A) twice that of the old unit
B) three halves that of the old unit
C) same as that of the old unit
D) two third that of the old unit
E) one-half that of the old unit

The temperature difference between deltaT between x coolant inside and the air outside per unit thickness of the tube will be three halves that of the old unit.

The total surface area that is available for heat exchange in the new radiator in order to achieve the desired temperature gradient is three fourth that of the old unit.

Based on the information given, the temperature difference will be:

K = Qd/AΔT

Anew = 3/2 A(old)

For the second statement, this will be:

K¹ = 2K(old)

= 3/2 ÷ 2

= 3/2 × 1/2 = 3/4

Therefore, it's three fourth that of the old unit.

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