Question

Which of the following equation is known as Newton’s law of cooling?

• A. Q = hA (Tw – To)
• B. Q = [ kA (Tw-To) ] L
• C. Q = mcp (Tw – To)
• D. Q = UA (Tw – To)

Hint:

Newton's Law of Cooling is the governing equation for convective heat transfer, defined by $Q = hA \Delta T$, where $h$ is the convection coefficient.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Convection is the transfer of heat between a solid surface and a moving fluid in contact with it.
The rate of convective heat transfer is described mathematically by Newton's Law of Cooling.

Step 2: Detailed Explanation:
Newton's Law of Cooling states that the rate of convective heat transfer from a surface is directly proportional to the surface area and the temperature difference between the surface and the fluid.
The mathematical equation is represented as:
\[ Q = hA(T_w - T_o) \]
Where:
$Q$ is the rate of heat transfer,
$h$ is the convective heat transfer coefficient,
$A$ is the heat transfer surface area,
$T_w$ is the temperature of the solid surface, and
$T_o$ is the temperature of the surrounding fluid.
Option B represents Fourier's law of conduction.
Option C represents sensible heat change in a substance of mass $m$ and specific heat $c_p$.
Option D represents the overall heat transfer equation using the overall heat transfer coefficient ($U$).
Therefore, Option A is the correct representation of Newton's law of cooling.

Step 3: Final Answer
The correct option is (A).