Fin Design and Transient Heat Conduction · Heat Transfer · GATE ME

The heat loss from a fin is $$6W.$$ The effectiveness of the fin are $$3$$ and $$0.75,$$ respectively. The heat loss (in $$W$$) from the fin, keeping the entire fin surface at base temperature, is ___________________

Biot number signifies the ratio of

Which one of the following configurations has the highest fin effectiveness?

The value of Biot number is very small (less than $$0.1$$), when

Lumped heat transfer analysis of a solid object suddenly exposed to a fluid medium at a different temp is valid when.

When the fluid velocity is doubled the thermal time constant of a thermometer used for measuring the fluid temperature reduces by a factor of $$2$$

Biot number signifies

The heat transfer process between a body and its ambient is governed by an internal conductive resistance $$\left( {{\rm I}CR} \right)$$ and an external convective resistance $$(ECR).$$ The body can be considered to be a lumped heat capacity system if

A metal ball of diameter $$60mm$$ is initially at $${220^ \circ }C.$$ The ball is suddenly cooled by an air jet of $${20^ \circ }C.$$ The heat transfer coefficient is $$200\,W/{m^2}.K.$$ The specific heat, thermal conductivity and density of the metal ball are $$400\,\,J/kg.K,\,\,400\,\,W/m.K$$ and $$\,9000\,\,kg/{m^3},$$ respectively. The ball temperature (in $${}^ \circ C$$) after $$90$$ seconds will be approximately.

Two cylindrical shafts $$A$$ and $$B$$ at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of the shafts can be assumed to be negligible. The data related to shafts $$A$$ and $$B$$ is given in the following Table.

The temperature at the center-line of the shaft $$A$$ reaches $${400^ \circ }C$$ after two hours. The time required (in hours) for the center-line of the shaft $$B$$ to attain the temperature of $${400^ \circ }C$$ is ____________

A cylindrical steel rod, $$0.01$$ $$m$$ in diameter and $$0.2$$ $$m$$ in length is first heated to $${750^ \circ }C$$ and then immersed in a water bath at $${100^ \circ }C.$$ The heat transfer coefficient is $$250\,W/{m^2}$$-$$K.$$ The density, specific heat and thermal conductivity of steel are $$\rho = 7801\,\,kg/{m^3},$$ $$c = 473$$ $$J/kg$$-$$K,$$ and $$k = 43$$ $$W/m$$-$$K,$$ respectively. The time required for the rod to reach $${300^ \circ }C$$ is ________ seconds.

A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a water environment at $$300$$ $$K.$$ The convective heat transfer coefficient is $$1000\,\,W/{m^2}$$-$$K.$$ Thermal conductivity of steel is $$40$$ $$W/m$$-$$K.$$ The time constant for the cooling process $$\tau $$ is $$16s.$$ The time required (in $$s$$) to reach the final temperature is __________________.

A steel ball of diameter $$60$$ $$mm$$ is initially in thermal equilibrium at $${1030^ \circ }C$$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at $${30^ \circ }C$$ with convective heat transfer coefficient $$h = 20\,W/{m^2}K.$$ The thermo-physical properties of steel are: density $$\rho = 7800\,\,kg/{m^3},$$ , conductivity $$k = 40 W/mK$$ and specific heat $$c = 600 J/kgK.$$ The time required in seconds to cool the steel ball in air from $${1030^ \circ }C$$ to $${430^ \circ }C$$ is

A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ The heat transfer coefficient between the steel ball and the surrounding is $$5W/{m^2}K.$$ The thermal conductivity of steel is $$20$$ $$W/mK.$$ The temperature difference between the centre and the surface of steel ball is

A fin has $$5mm$$ diameter and $$100mm$$ length. The thermal conductivity of fin material is $$400W/m K.$$ One end of the fin is maintained at $${130^ \circ }C$$ and its remaining surface is exposed to ambient air at $${30^ \circ }C.$$ if the convective heat transfer coefficient is $$40W/{m^2}K,$$ the heat loss (in $$W$$) from the fin is

A small copper ball of $$5$$ $$mm$$ diameter at $$500$$ $$K$$ is dropped into an oil bath whose temperature is $$300$$ $$K.$$ the thermal conductivity of copper is $$400$$ $$W/m.$$ $$K,$$ its density $$9000\,\,kg/{m^3}$$ and its specific heat $$385\,J/kg.\,\,K.$$ if the heat transfer coefficient is $$250\,\,W/{m^2}K$$ and lumped analysis is assumed to be valid, the rate of fall of the temperature of the ball at the beginning of cooling will be, in $$K/s.$$

A spherical thermocouple junction of diameter $$0.706 mm$$ is to be used for the measurement of temperature of a gas stream. The convective heat transfer co-efficient on the bead surface is $$400W/{m^2}K.$$ Thermo-physical properties of thermocouple material are
$$k = 20W/mK,$$ $$C = 400J/kgK$$ and $$\rho = 8500\,\,kg/{m^3}.$$ If the thermocouple initially at $${30^ \circ }C$$ is placed in a hot stream of $${300^ \circ }C$$ the time taken by the bead to reach $${298^ \circ }C$$, is

Two rods, one of length $$L$$ and the other of length $$2L$$ are made of the same material and have the same diameter. The two ends of the longer rod are maintained at $${100^ \circ }C.$$ One end of the shorter end is maintained at $${100^ \circ }C.$$ while the other end is insulated. Both the rods are exposed to the same environment at $${40^ \circ }C.$$ The temperature at the insulated end of the shorter rod is measured to be $${55^ \circ }C.$$ The temperature at the mid-point of the longer rod would be

An iron rod $$\left( {K = 41.5W/mK} \right)$$ of $$15mm$$ diameter and $$160mm$$ long extends out of a hot surface of temp $${150^ \circ }C$$ into environment at $${36^ \circ }C.$$The free end of the rod is insulated. If the film heat transfer coefficient is $$25W/{m^2}K,$$ calculate the rate of heat flowing out of the hot surface through the rod and the temp at the insulated end of the rod.

The total efficiency, $${\eta _t}$$ for a finned surface may be defined as the ratio of the total heat transferred by the combined area of the fins, $${A_r},$$ and the exposed surface to that by the total area, $$A$$, if it were maintained at the base temp, $${T_0}.$$ Assuming uniform heat transfer coefficient over the entire surface, derive an expression for the relationship between efficiency and effectiveness of the fin.