Question

For heat transfer

1. how would one calculate the temperature of a probe at a distance X from wall.

Thermal conductivity is known

Diameter is known

Extenernal ambient temperature is known

Surface heat transfer coefficient is known

Gas temperature is known

Radiative heat transfer is negligible

2. How would one calculate rate at which energy is gained by convection to the probe (using above information)

3. How to determine minimum length of probe to be considered thermally infinite

Answer 1

1.

you can solve this Type of problems step by step

first write down given data

Here we are provided with

thermal conductivity (k),

Diameter of probe (D),

External ambient temp. ,

distance of probe from wall =X,

surface heat transfer coefficient (h),

radiant heat transfer is negligible

the problem which have combination of convection & conduction heat transfer total resistance to system is provided by these two

where U is overall heat transfer coefficient & 1/U gives overall resistance to the system

h is heat transfer coefficient

& 1/h is resistence to HT

similarly k is conductivity of material

x is distance across which temperature variation is observed

now finally the heat transfer problem can be solved by using

Q =U A

= log mean temperature = (T2-T1)/ln(T2/T1)

we can get area , overall HT coefficient from data also we have ambient temp now we can calculate probe temp

simply by putting all other values in equation & solving it .

always problems will be provided with all other data & by combination of formulaes we can solve our question .

2.

if you are asked for convection the you just simply need to use below formula

Q = hA

where A is heat transfer area .

similarly if we asked to solve for conduction the just use Q = k*A *dT/dX

3.

how to determine minimum length of probe to be consider thermally infinite

where is ambient temp. & Tx is temp at x distance from heated end

at which x

that length x can be considered as thermally infinite .

we can write it as

lim