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2. A 5 cm-thick beef steak is being frozen in a -30°C room. The product has 73% moisture content, a density of 970 kg/m 3, and thermal conductivity (frozen) of 1.1 W/(m K). Estimate the freezing time using Plank's equation. The product has an initial freezing temperature of -75°C, and the movement of air in the freezing room provides a convective heat-transfer coefficient of 5 W/(m 2 K).

2. A 5 cm-thick beef steak is being frozen in a -30°C room. The product has 73% moisture content, a density of 970 kg/m 3, and thermal conductivity (frozen) of 1.1 W/(m K). Estimate the freezing time using Plank's equation. The product has an initial freezing temperature of -75°C, and the movement of air in the freezing room provides a convective heat-transfer coefficient of 5 W/(m 2 K).

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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**Problem Statement:** A 5 cm-thick beef steak is being frozen in a -30°C room. The product has 73% moisture content, a density of 970 kg/m³, and a thermal conductivity (frozen) of 1.1 W/(m·K). Estimate the freezing time using Plank’s equation. The product has an initial freezing temperature of -75°C, and the movement of air in the freezing room provides a convective heat-transfer coefficient of 5 W/(m²·K). **Solution Approach:** To solve this problem, we will use Plank’s equation, which is commonly applied in food processing to estimate the freezing time of products. We need to calculate the time required to freeze the given beef steak based on its properties and the environmental conditions provided. 1. **Assumptions:** - The steak is uniformly 5 cm thick. - The freezer has a constant temperature of -30°C. - The properties provided (density, thermal conductivity, and moisture content) remain constant during the process. 2. **Variables:** - Thickness (L) = 5 cm = 0.05 m - Temperature of the room (T_r) = -30°C - Initial freezing temperature (T_i) = -75°C - Density (ρ) = 970 kg/m³ - Thermal conductivity (k) = 1.1 W/(m·K) - Moisture content = 73% - Convective heat-transfer coefficient (h) = 5 W/(m²·K) 3. **Plank’s Freezing Time Equation:** - Plank’s equation will be applied, which generally includes the properties and dimensions of the product, along with the temperature difference and cooling conditions. The goal is to substitute the known values into Plank’s equation and calculate the freezing time, ensuring all units are consistent.
Transcribed Image Text:**Problem Statement:** A 5 cm-thick beef steak is being frozen in a -30°C room. The product has 73% moisture content, a density of 970 kg/m³, and a thermal conductivity (frozen) of 1.1 W/(m·K). Estimate the freezing time using Plank’s equation. The product has an initial freezing temperature of -75°C, and the movement of air in the freezing room provides a convective heat-transfer coefficient of 5 W/(m²·K). **Solution Approach:** To solve this problem, we will use Plank’s equation, which is commonly applied in food processing to estimate the freezing time of products. We need to calculate the time required to freeze the given beef steak based on its properties and the environmental conditions provided. 1. **Assumptions:** - The steak is uniformly 5 cm thick. - The freezer has a constant temperature of -30°C. - The properties provided (density, thermal conductivity, and moisture content) remain constant during the process. 2. **Variables:** - Thickness (L) = 5 cm = 0.05 m - Temperature of the room (T_r) = -30°C - Initial freezing temperature (T_i) = -75°C - Density (ρ) = 970 kg/m³ - Thermal conductivity (k) = 1.1 W/(m·K) - Moisture content = 73% - Convective heat-transfer coefficient (h) = 5 W/(m²·K) 3. **Plank’s Freezing Time Equation:** - Plank’s equation will be applied, which generally includes the properties and dimensions of the product, along with the temperature difference and cooling conditions. The goal is to substitute the known values into Plank’s equation and calculate the freezing time, ensuring all units are consistent.
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