Please write a matlab code. If possible avoid using syms in code as it slows down the code. Thank you in advance.

In heat transfer one of the important concepts is "Heat Transfer from Extended Surfaces." One of the most common application of this concept is when we use an extended surface specifically to enhance the heat transfer between a solid and an adjoining fluid. Such an extended surface is termed as Fin. Steady-state heat balance equation results in the following ODE: 1 da dT d2T dr 1 h dA, -) (T-T.) = 0 A d dx A kdx For a fin with uniform cross-sectional area, Ac is constant. A is the surface area measured from the base to x and P is the fin perimeter (As = Px). The fin is attached to a base surface x O) of temperature Tv and extends into a fluid of temperature Tax Convective heat transfer takes place at the tip of the fin (x = L). The rate at which energy is transferred to the fluid by convection from the tip must equal the rate at which energy reaches the tip by conduction through the fin. The energy balance is given as below: dT hA (T|x=L-T.) = -KA, + dx XEL Heat transfer rate (q) can be obtained by applying the Fourier's Law at the fin base, as follows: dT 41 = 4b = -kAc ds! dx 0 Fin effectiveness (is defined as the ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin. 9f f hAc(T) -To) The thermal performance of the fin is provided by the fin efficiency (1, as follows. 4 = nf= 478 4f hAf(T) -T.) x Analytical solution for the above system is given as follows: 6 Temperature distribution: cosli m (L-x)+sinli m (L-x) mak co so m L+ sinh mL Ob sinh W L +) sh ml. Heat transfer rate: qr=M co sh 1 + sinh m. nuk @ = T - TO 0o = To - To mar m= M = kAc Given parameters: h=Convection heat transfer coefficient = 100 W/ mK k=Thermal conductivity = 180 W/mk d=Diameter = 0.005 m L = Length of fin=0.05 m T.= 25 C For a Pin fin: Td2 Ac=Cross-sectionalarea= 4 P = Perimeter = nd Au= Surface area = ndL Develop a code in MATLAB to solve the above ODE using finite difference algorithm Obtain the temperature distribution as a function of position (X). Evaluate the rate of heat transfer and performance of the fin in terms of effectiveness and efficiency