The boundary value and initial value statement are,
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].
What is Initial Value Problem?
In multivariable calculus, an initial value problem is an ordinary differential equation that also includes an initial condition that identifies the value of the unknown function at a specific location in the domain. An initial value problem is frequently solved when modelling a system in physics or another scientific field.
Consider a cylindrical potato, sliced into thin slices with thickness L = 1 cm, much smaller than the diameter slices.
Initial temperature [tex]T_i = 20^o[/tex]
Final temperature = [tex]T_f = 75^o[/tex]
Now we have to solve the given cases.
Consider the heat equation,
q = k(∂T / ∂x) ..(1)
(a) Now we have to find the boundary value
Boundary Value:
[tex]T_i = 20^oc, T_f = 75^oc\\[/tex]
⇒ ΔT = [75 - 20]
⇒ΔT = 55°c
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex]
Hence, the boundary value and initial value statement are,
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].
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Complete question:
Complete question is attached below,
