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Cooling rate for relatively thin plates Calculator

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Heat Flow in Welded Joints Distortion in Weldments Heat Input in Welding Resistance spot welding parameters for mild steels

✖Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal Conductivity [k]			+10% -10%
✖The Density of Electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld.ⓘ Density of Electrode [ρ]			+10% -10%
✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [Q_c]			+10% -10%
✖Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set.ⓘ Thickness of Filler Metal [t]			+10% -10%
✖Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.ⓘ Net Heat Supplied Per Unit Length [H_net]			+10% -10%
✖Temperature for Cooling Rate is the temperature at which the cooling rate is calculated.ⓘ Temperature for Cooling Rate [T_c]			+10% -10%
✖Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.ⓘ Ambient Temperature [t_a]			+10% -10%

✖Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness.ⓘ Cooling rate for relatively thin plates [R_c]

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Cooling rate for relatively thin plates Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3)
R_c = 2*pi*k*ρ*Q_c*((t/H_net)^2)*((T_c-t_a)^3)
This formula uses 1 Constants, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Cooling Rate of Thin Plate - (Measured in Kelvin per Second) - Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance.
Density of Electrode - (Measured in Kilogram per Cubic Meter) - The Density of Electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Thickness of Filler Metal - (Measured in Meter) - Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set.
Net Heat Supplied Per Unit Length - (Measured in Joule per Meter) - Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.
Temperature for Cooling Rate - (Measured in Kelvin) - Temperature for Cooling Rate is the temperature at which the cooling rate is calculated.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.

STEP 1: Convert Input(s) to Base Unit

Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Density of Electrode: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
Thickness of Filler Metal: 5 Millimeter --> 0.005 Meter (Check conversion here)
Net Heat Supplied Per Unit Length: 1000 Joule per Millimeter --> 1000000 Joule per Meter (Check conversion here)
Temperature for Cooling Rate: 500 Celsius --> 773.15 Kelvin (Check conversion here)
Ambient Temperature: 37 Celsius --> 310.15 Kelvin (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_c = 2*pi*k*ρ*Q_c*((t/H_net)^2)*((T_c-t_a)^3) --> 2*pi*10.18*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3)

Evaluating ... ...

R_c = 0.662060171595046

STEP 3: Convert Result to Output's Unit

0.662060171595046 Kelvin per Second -->0.662060171595046 Celsius per Second (Check conversion here)

FINAL ANSWER

0.662060171595046 ≈ 0.66206 Celsius per Second <-- Cooling Rate of Thin Plate

(Calculation completed in 00.020 seconds)

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University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material

LaTeX Go Peak Temperature Reached at Some Distance = Ambient Temperature+(Net Heat Supplied Per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of Filler Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied Per Unit Length)

Position of Peak Temperature from Fusion Boundary

LaTeX Go Distance from the Fusion Boundary = ((Melting Temperature of Base Metal-Temperature Reached at Some Distance)*Net Heat Supplied Per Unit Length)/((Temperature Reached at Some Distance-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Electrode*Specific Heat Capacity*Thickness of Filler Metal)

Net Heat Supplied to Weld Area to Raise it to given Temperature from Fusion Boundary

LaTeX Go Net Heat Supplied Per Unit Length = ((Temperature Reached at Some Distance-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Electrode*Specific Heat Capacity*Thickness of Filler Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at Some Distance)

Cooling Rate for Relatively Thick Plates

LaTeX Go Cooling Rate of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length

Cooling rate for relatively thin plates Formula

LaTeX Go

How heat transfer takes place near heat affected zone ?

Heat transfer in a welded joint is a complex phenomenon involving three dimensional movement of a heat source. Heat from the weld zone is transferred more to the other parts of the base metal by means of conduction. Similarly heat is also lost to surroundings by convection from the surface, with radiation component being relatively small except near the weld pool. Thus the analytical treatment of the weld zone is extremely difficult.

How to Calculate Cooling rate for relatively thin plates?

Cooling rate for relatively thin plates calculator uses Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3) to calculate the Cooling Rate of Thin Plate, The Cooling Rate for Relatively Thin Plates formula is defined as the rate at which heat is lost to the surrounding from the weldment. Cooling Rate of Thin Plate is denoted by R_c symbol.

How to calculate Cooling rate for relatively thin plates using this online calculator? To use this online calculator for Cooling rate for relatively thin plates, enter Thermal Conductivity (k), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Thickness of Filler Metal (t), Net Heat Supplied Per Unit Length (H_net), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a) and hit the calculate button. Here is how the Cooling rate for relatively thin plates calculation can be explained with given input values -> 0.659999 = 2*pi*10.18*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3).

FAQ

What is Cooling rate for relatively thin plates?

The Cooling Rate for Relatively Thin Plates formula is defined as the rate at which heat is lost to the surrounding from the weldment and is represented as R_c = 2*pi*k*ρ*Q_c*((t/H_net)^2)*((T_c-t_a)^3) or Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3). Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance, The Density of Electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set, Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium, Temperature for Cooling Rate is the temperature at which the cooling rate is calculated & Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.

How to calculate Cooling rate for relatively thin plates?

The Cooling Rate for Relatively Thin Plates formula is defined as the rate at which heat is lost to the surrounding from the weldment is calculated using Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3). To calculate Cooling rate for relatively thin plates, you need Thermal Conductivity (k), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Thickness of Filler Metal (t), Net Heat Supplied Per Unit Length (H_net), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a). With our tool, you need to enter the respective value for Thermal Conductivity, Density of Electrode, Specific Heat Capacity, Thickness of Filler Metal, Net Heat Supplied Per Unit Length, Temperature for Cooling Rate & Ambient Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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