A hollow tube has a length l, inner radius `R_(1)` and outer radius `R_(2)` . The material has a thermal conductivity K. Find the heat flowing through the walls of the tube if (a) the flat ends are maintained at temperature `T_(1)` and `T_(2)`(T_(2)gtT_(1)` (b) the inside of the tube is maintained at temperature `T_(1)` and the outside is maintained at `T_(2)` .

Find the heat current through the frustum of a cone shown in figure-4.20. Temperature of its two ends are maintained at T_(1) and T_(2) (T_(2)>T_(1)) respectively and the thermal conductivity of the material is k.

A spherical shell of inner radius R_(1) and outer radius R_(2) is having variable Where 'r' is the distance from the centre Two surface of the shell are maintained at temperature T_(1) respectively (T_(1) ltT_(2)) The heat current flowing through the shell would be .

A rod of length L with sides fully insulated is made of a material whose thermal conductivity K varies with temperature as K=(alpha)/(T) where alpha is constant. The ends of rod are at temperature T_(1) and T_(2)(T_(2)gtT_(1)) Find the rate of heat flow per unit area of rod .

A rod of length L with sides fully insulated is made of a material whose thermal conductivity K varies with temperature as K=(alpha)/(T) where alpha is constant. The ends of rod are at temperature T_(1) and T_(2)(T_(2)gtT_(1)) Find the rate of heat flow per unit area of rod .

A hollow sphere of inner radius r_(0) and outer radius 2r_(0) is made of a uniform material of constant thermal conductivity K. The temperature with in the ball is maintained at 2T_(0) and outside the ball is T_(0) . If temperature at distance (3r_(0))/(2) from centre is (pT_(0))/(3) , then find the value of p.

A thick spherical shell of inner and outer radii r and R respectively has thermal conductivity k = (rho)/(x^(n)) , where rho is a constant and x is distance from the centre of the shell. The inner and outer walls are maintained at temperature T_(1) and T_(2) (lt T_(1)) (a) Find the value of number n (call it n_(0) ) for which the temperature gradient remains constant throughout the thickness of the shell. (b) For n=n_(0) , find the value of x at which the temperature is (T_(1)+T_(2))/(2) (c) For n = n_(0) , calculate the rate of flow of heat through the shell.

A rod of length l and cross-section area A has a variable thermal conductivity given by K = alpha T, where alpha is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperature T_(1) and T_(2) (T_(1)gtT_(2)) . Heat current flowing through the rod will be

A rod of length l and cross-section area A has a variable thermal conductivity given by K = alpha T, where alpha is a positive constant and T is temperature in kelvin. Two ends of the rod are maintained at temperature T_(1) and T_(2) (T_(1)gtT_(2)) . Heat current flowing through the rod will be