1. 1 Mathematical Modeling and Engineering Problem Solving Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis Applied Numerical Method for Engineers Tutorial 1

2. 2 P. 1.1 Water accounts for roughly 60% of total body weight. Assuming it can be categorized into six regions, the percentages go as follows. Plasma claims 4.5% of the body weight and is 7.5% of total body water. Dense connective tissue and cartilage occupies 4.5% of the total body weight and 7.5% of the total body water. Interstitial lymph is 12% of the body weight, which is 20% of the total body water and 4.5% total body weight. If intracellular water is 33% of the total body weight and transcellular water is 2.5% of the body water, What percent of total body weight must the transcellular water be? What percent must the transcellular water be?

3. 3 Solution 1.1 ComponentsTotal Body WeightTotal Body Water 1Plasma4.5%7.5% 2Dense4.5%7.5% 3Interstitial12%20% 4Inaccessible4.5%7.5% 5Intracellular33%? 6Trancellular?2.5% Total60%100% 1.5 % 55 %

4. 4 P. 1.2 A group of 30 students attend a class in a room that measures 10 m by 8 m by 3 m. Each student takes up about 0.075 m 3 and gives out about 80W of heat (1W = 1J/s). Calculate the air temperature rise during the first 15 minutes of the class if the room is completely sealed and insulated.

5. 5 Notes Assume the heat capacity, C v, for air is 0.718 kJ/(kg K) Assume air is an ideal gas at 20 ̊C and 101.325 kPa. The heat absorbed by the air Q is related to the mass of the air, m, the heat capacity, and the change in temperature by the following relationship: The mass of air can be obtained from the ideal gas law: Mwt: 28.97 kg/kmol (air) R: 8.314 kPa m 3 /(kmol K)

6. 6 Solution 1.2 Compute total heat absorbed Q of students Computer the mass Compute change of temperature

7. 7 Solution 1.2 The temperature rise after 15 minutes: T = (20 ̊C +273.15) + 10.50615 T = 303.65615 K or T = 30.50615 ̊C