Having problem of how to find tm and Tm

Problem 4:

Heat Transfer coefficient estimation in a quenching experiment simulation

with the aid of MATLAB

You are required to compute the estimated heat transfer coefficient (h)

data for an Inconel thermocouple mounted at the center face of a cylindrical

probe. The hot probe is dunked into a quench tank containing Canola Oil at a

temperature of Ts

Key data for the probe:

Material: Inconel

Density (ρ) = 8470 kg/m3

Diameter = 15 mm

Length = 45 mm

Specific heat capacity (cp) = 4184 J/kg oC

Temperature of the Canola oil in the quench tank is Ts = 21 oC

Important relationships to incorporate in your computations

Heat lost by the probe = qA = h*A*(Tm-Ts)

Decrease in internal energy of the probe = qm = - *V*cp*cr

Under equilibrium conditions qA = qm. Solve for h as a function of time, time

being the midstep time, tm

Where:

h = heat transfer coefficient

cr = the cooling rate determined as delT/delt

A = the surface area of the probe.

V = volume of the probe

4 | P a g e

Please follow these steps in completing this exercise and submit the

materials requested.

 Read the Canola Oil sheet from the RDData.xlsx file from the data

folder of D2L

 Assign the first column to ‘t’, and the second column to ‘T’

 Create new arrays ‘delt’ and ‘delT’ as the mid-step values computed

from ‘t’ as delt = (t(n)-t(n-1)) and delT = (T(n)-T(n-1)). As a check, delt

will have positive values and delT will be negative values. With

negative delT values, the negative sign in the qm term will be flipped to

a positive one, resulting in positive values for h. ‘n’ is a subscript that

you could use to keep track entries of the time and temperature

arrays.

 You will need to use ‘delt’; and delT’ in computing and visualizing ‘h’

 Create a cooling rate array cr = delT/delt

 Create array tm and Tm corresponding to the midpoints of t and T

Temperature steps

 Code the equation for computing h

 Generate a plot of T versus t

 Generate a plot of h versus tm

[Walter Roberson]

This looks to be an elaboration of https://www.mathworks.com/matlabcentral/answers/491824-create-array-tm-and-tm-corresponding-to-the-midpoints-of-t-and-t-temperature-steps . You should probably be editing the details into that Question instead of opening a new one.