1. C.K. PITHAWALA COLLAGE OF ENGINEERING AND TECHNOLOGY
Sub:- Heat Transfer
Topic:- Critical radius of insulation
Guided by :-Sonal madam,Digvijay sir
Batch :-A4

2. Prepared by:- Name Enrollment No. Roll No. Vanasiwala Krunal
Vasavada Jenish
Patel Vivekkumar
Wankawala Dhruv

3. What is Thermal Insulation?
Thermal insulation is the reduction of heat transfer (the transfer of thermal energy between objects of differing temperature) between objects in thermal contact or in range of radiative influence. 
The insulating capability of a material is measured with thermal conductivity (k). Low thermal conductivity is equivalent to high insulating capability (R-value),means offers higher resistance to heat flow.

4. Low thermal conductivity (k) materials reduce heat fluxes
Low thermal conductivity (k) materials reduce heat fluxes. The smaller the k value, the larger the corresponding thermal resistance (R) value. As the thickness of insulating material increases, the thermal resistance—or R-value—also increases & heat flow rate decreases. 
But for the case of cylinder & Sphere,the thermal resistance decreases as the Insulation thickness increases up to certain limits. And beyond this limit thermal resistance Also increase as thickness of insulation increase.
This limiting radius is known as critical radius of insulation for which max heat flow occurs.

5. Critical radius of insulation for cylinder:-
Consider a wire of radius r1 & surface temperature T1.The pipe is insulated with the insulation with the thermal conductivity Ki & outer radius r2.
In this case hest is conducted first through the insulation & then it is convected to the environment. Which is at temperature T ,heat transfer co-efficient h.
As we increase the radius of insulation(r2),the conductive resistance increase & convective resistance decrease .

6. To find the value of outer radius r2 for which heat transfer rate is maximum.

7. For

9. The value of R2 for which the heat transfer rate is maximum is called critical radius of insulation

10. Experiment carried out on:- Inside Material-Copper [K=385W/m K],
Insulation Asbestos [K=0.15W/m K]
We found following result

13. Critical radius of insulation for sphere:-
Consider a hollow sphere of outer radius r1 is covered with a layer of insulation With outer radius r2 having constant thermal conductivity K. the sphere is exposed to environment Where air is at temperature of Tair & hair is heat transfer co-efficient of air.

14. The heat flow rate can be expressed as:-
For

17. Thank You