Question

A heat exchanger is to cool oil $\left(c_{p}=2200 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\( at a rate of \)10 \mathrm{~kg} / \mathrm{s}$ from \(120^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\) by air. Determine the heat transfer rating of the heat exchanger and propose a suitable type.

Short answer

Answer: The heat transfer rating of the heat exchanger is 1760 kW, and a suitable type of heat exchanger for cooling oil at the given conditions is the shell and tube heat exchanger.

Step-by-step solution

Identify the known parameters and formula for heat transfer

We are given the following information: - The specific heat capacity of oil: \(c_{p} = 2200 \mathrm{~J} / \mathrm{kg \cdot K}\) - The mass flow rate of oil: \(\dot{m} = 10 \mathrm{~kg} / \mathrm{s}\) - The initial temperature of oil: \(T_{1} = 120^{\circ} \mathrm{C}\) - The final temperature of oil: \(T_{2} = 40^{\circ} \mathrm{C}\) We can find the heat transfer rating using the formula: \(q = \dot{m} \cdot c_{p} \cdot \Delta T\) where \(q\) is the heat transfer rating \(\dot{m}\) is the mass flow rate \(c_{p}\) is the specific heat capacity \(\Delta T\) is the temperature difference

Calculate the temperature difference and heat transfer rating

First, determine the temperature difference: \(\Delta T = T_{1} - T_{2} = 120^{\circ} \mathrm{C} - 40^{\circ} \mathrm{C} = 80 \mathrm{K}\) Now, we can calculate the heat transfer rating: \(q = \dot{m} \cdot c_{p} \cdot \Delta T = 10 \mathrm{~kg} / \mathrm{s} \cdot 2200 \mathrm{~J} / \mathrm{kg \cdot K} \cdot 80 \mathrm{K}\) \(q = 1760000 \mathrm{~W}\) or \(1760 \mathrm{kW}\)

Propose a suitable type of heat exchanger

There are different types of heat exchangers, such as shell and tube, plate, and finned tube. For cooling oil, a plate or shell and tube heat exchanger is typically used due to their efficiency and ability to handle a large temperature difference. In this case, since the temperature difference is 80 K and we need high efficiency for cooling, a shell and tube heat exchanger could be a suitable choice. To summarize: Heat transfer rating of the heat exchanger: \(1760 \mathrm{kW}\) Proposed type of heat exchanger: Shell and tube heat exchanger