Answer Happy

i need the numerical solution
THERMMAL PHYSICS NEWTON'S LAW OF COOLING (Forward Differentiation) 1. Description of the problem The nature of the thermal energy transferred from one place at a higher temperature to another place of lower temperature is complicated and in general involves the processes of conduction, convection and radiation. However, if this temperature difference is not too large, the rate of change of temperature can be approximated using Newton's law of Cooling. Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surrounding environment). Mathematically Newton's Law of Cooling can be written as a first order ordinary differential equation AT(1) --R(T(t)-7) dt T: instantaneous temperature of the object [°C] t: times ] R: cooling constant (depends on the thermal energy transfer mechanism, the contact area with its surroundings and the thermal properties of the object [min] Teny: ambient temperature of the surrounding environment (assumed constant) [°C] Newton's Law of Cooling given by the above equation can be solved analytically or numerically when the system's initial temperature is To

II. The required Work Based on the input parameters: R = 0.05 rate constant expressed in minutes tmax = 60 length of simulation time in minutes T(t=0) = 100 initial temperature of system in °C Teny = 0 surrounding environmental temperature in °C 1. Calculate the analytical solution by integrating both sides of equation. 2. A standard technique for the numerical solution of differential equations involves converting the differential equation into a finite difference equation. Use the Forward Differentiation to solve this equation: a) With N=500, N= number of time steps (h=(tmax-tó)/N) b) With N=10. 3. Plot in the same figure: • The analytical Solution • The numerical solution (N=500) • The numerical solution (N=10)