A plastic sleeve of outer radius $${r_0} = 1\,\,mm$$ covers a wire (radius $$r = 0.5$$ $$mm$$) carrying electric current. Thermal conductivity of the plastic is $$0.15\,\,W/m$$-$$K$$. The heat transfer coefficient on the outer surface of the sleeve exposed to air is $$25$$ $$W/{m^2}$$-$$K$$. Due to the addition of the plastic cover, the heat transfer from the wire to the ambient will

If a foam insulation is added to a $$4cm$$ outer diameter pipe as shown as figure, the critical radius of insulation (in $$cm$$) is ________.

Consider a long cylindrical tube of inner and outer radii, $${r_i}$$ and $${r_0}$$ , respectively, length, $$L$$ and thermal conductivity, $$k.$$ Its inner and outer surfaces are maintained at $${T_i}$$ and $${T_0}$$ , respectively $$\left( {{T_i}\,\,\, > \,\,\,{T_0}} \right).$$ Assuming one-dimensional steady state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

As the temperature increases, the thermal conductivity of a gas