Question

Consider a heat exchanger in which both fluids have the same specific heats but different mass flow rates. Which fluid will experience a larger temperature change: the one with the lower or higher mass flow rate?

Short answer

Answer: The fluid with the lower mass flow rate will experience a larger temperature change than the one with the higher mass flow rate.

Step-by-step solution

Understand the concept of heat transfer in a heat exchanger

A heat exchanger is a device used to transfer heat between two or more fluids. The fluids in the heat exchanger have different temperatures, and heat transfer occurs from the hotter fluid to the cooler fluid until the temperature of the two fluids equalizes. In the given exercise, we are considering two fluids with the same specific heats but different mass flow rates.

Define the heat transfer equation

The heat transfer equation (Q) for a fluid can be expressed as: Q = m*c_p*ΔT Where, Q = heat transfer (J) m = mass flow rate of the fluid (kg/s) c_p = specific heat of the fluid (J/kg*K) ΔT = temperature change of the fluid (K)

Set up equations for both fluids in the heat exchanger

Let the mass flow rates be m1 and m2 for fluid 1 and fluid 2, respectively, with m1 ≠ m2. Let ΔT1 and ΔT2 be the temperature changes for fluid 1 and fluid 2. Since the heat transferred from fluid 1 to fluid 2 must be the same (assuming no heat loss to the surroundings and no heat stored in the heat exchanger itself), we can set the heat transfer equations for both fluids equal to each other: m1 * c_p * ΔT1 = m2 * c_p * ΔT2

Eliminate common terms and solve for temperature change

We can cancel out the common term c_p from both sides of the equation: m1 * ΔT1 = m2 * ΔT2 Now, we can divide both sides by m1 * m2: ΔT1 / m1 = ΔT2 / m2

Analyze the relationship between mass flow rate and temperature change

From the above equation, we can see that the temperature change of a fluid is inversely proportional to its mass flow rate, given the same heat transfer. Therefore, the fluid with the lower mass flow rate will experience a larger temperature change, while the fluid with the higher mass flow rate will experience a smaller temperature change. So, the fluid with the lower mass flow rate will experience a larger temperature change than the one with the higher mass flow rate.