1. Chemical Engineering Mathematics 1

2. Presentation Contents Chemical Engineering Mathematics2  Partial Differentiation Equation in long non-uniform rod  Partial Differentiation Equation Diffusion equation in one dimension  Newton's Law of Cooling and Applications  Applications of Separation of Variables  Growth and Decay  Laplace transform and Applications

3. Partial Differential Equation Chemical Engineering Mathematics3

4. Partial Differentiation Equation in long non-uniform rod Chemical Engineering Mathematics4

5. Contd…. 5

6. Contd…. 6 of the rod are insulated and only the ends may be exposed. Also assume there is no heat source within the rod. Consider an arbitrary thin slice of the rod of width Δx between x and x+ Δx. The slice is so thin that the temperature throughout the slice is u (x,t). Fig 1 taken from https://en.wikiversity.org/wiki /Nonlinear_finite_elements/A xial_bar_strong_form

7. Diffusion equation in one dimension Chemical Engineering Mathematics7

8. Ordinary Differential Equation (ODE) Chemical Engineering Mathematics8 An ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions Application 1. Cooling/Warming Law 2. Population Growth and Decay 3. Radio-Active Decay and Carbon Dating 4. Mixture of Two Salt Solutions 5. Series Circuits 6. Draining a tank

9. Newton's Law of Cooling Chemical Engineering Mathematics9

10. Applications Newton's Law of Cooling Chemical Engineering Mathematics10 1. To predict how long it takes for a hot object to cool down at a certain temperature. 2. To find the temperature of a soda placed in a refrigerator by a certain amount of time. 3. It helps to indicate the time of death given the probable body temperature at the time of death and current body temperature.

11. Applications of Separation of Variables Chemical Engineering Mathematics11

12. Growth and Decay Chemical Engineering Mathematics12

13. Laplace Transform Chemical Engineering Mathematics13

14. Applications Laplace Transform Chemical Engineering Mathematics14 To solve the problem related to communication and network analysis. To make a equation in simple form from hard equation like vibration of spring. To solve Mixing Problem Involving Two Tanks