Power on exponential of temperature-time relation Calculator

✖Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.ⓘ Convection Heat Transfer Coefficient [h]			+10% -10%
✖The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.ⓘ Surface Area [A]			+10% -10%
✖Time elapsed after a particular task is started.ⓘ Time Elapsed [t]			+10% -10%
✖The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.ⓘ Density [ρ]			+10% -10%
✖Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Total volume [V_T]			+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 [C_o]			+10% -10%

✖Constant B is the number that has a fixed value in a given situation or universally or that is characteristic of some substance or instrument.ⓘ Power on exponential of temperature-time relation [b]

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Formula

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Power on exponential of temperature-time relation

Formula

`"b" = -("h"*"A"*"t")/("ρ"*"V"_{"T"}*"C"_{"o"})`

Example

`"-0.006222"=-("0.04W/m²*K"*"18m²"*"12s")/("5.51kg/m³"*"63m³"*"4J/(kg*K)")`

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Power on exponential of temperature-time relation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)
b = -(h*A*t)/(ρ*V_T*C_o)
This formula uses 7 Variables

Variables Used

Constant B - Constant B is the number that has a fixed value in a given situation or universally or that is characteristic of some substance or instrument.
Convection Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.
Surface Area - (Measured in Square Meter) - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
Time Elapsed - (Measured in Second) - Time elapsed after a particular task is started.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
Total volume - (Measured in Cubic Meter) - Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.
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.

STEP 1: Convert Input(s) to Base Unit

Convection Heat Transfer Coefficient: 0.04 Watt per Square Meter per Kelvin --> 0.04 Watt per Square Meter per Kelvin No Conversion Required
Surface Area: 18 Square Meter --> 18 Square Meter No Conversion Required
Time Elapsed: 12 Second --> 12 Second No Conversion Required
Density: 5.51 Kilogram per Cubic Meter --> 5.51 Kilogram per Cubic Meter No Conversion Required
Total volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific Heat Capacity: 4 Joule per Kilogram per K --> 4 Joule per Kilogram per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

b = -(h*A*t)/(ρ*V_T*C_o) --> -(0.04*18*12)/(5.51*63*4)

Evaluating ... ...

b = -0.00622245268343272

STEP 3: Convert Result to Output's Unit

-0.00622245268343272 --> No Conversion Required

FINAL ANSWER

-0.00622245268343272 ≈ -0.006222 <-- Constant B

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Transient Heat Conduction » Power on exponential of temperature-time relation

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Created by Ravi Khiyani

Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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< 13 Transient Heat Conduction Calculators

Instantaneous heat transfer rate

Go Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)))

Temperature after given time elapsed

Go Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature

Time taken to reach given temperature

Go Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area))

Change in Internal energy of Lumped body

Go Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))

Total Heat Transfer during Time Interval

Go Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))

Ratio of temperature difference for given time elapsed

Go Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))

Product of Biot and Fourier Number given System Properties

Go Product of Biot And Fourier Numbers = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)

Power on exponential of temperature-time relation

Go Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)

Time Constant in unsteady state heat transfer

Go Time Constant = (Density*Specific Heat Capacity*Total volume)/(Convection Heat Transfer Coefficient*Surface Area)

Thermal Diffusivity

Go Thermal Diffusivity = Thermal Conductivity/(Density*Specific Heat Capacity)

Thermal Capacitance

Go Thermal Capacitance = Density*Specific Heat Capacity*Volume

Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number

Go Temperature Ratio = exp(-(Biot Number*Fourier Number))

Power on Exponential of Temperature-time Relation given Biot and Fourier Number

Go Constant B = -(Biot Number*Fourier Number)

Power on exponential of temperature-time relation Formula

Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)
b = -(h*A*t)/(ρ*V_T*C_o)

What is Temperature-Time relation?

The temperature-time relationship of unsteady-state heat transfer helps to determine the rate of heat transfer that has been conducted in the lumped system in a given time period.

How to Calculate Power on exponential of temperature-time relation?

Power on exponential of temperature-time relation calculator uses Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity) to calculate the Constant B, Power on exponential of temperature-time relation formula calculates the value of power on exponential in the equation which makes the further calculation of lumped system easy. Constant B is denoted by b symbol.

How to calculate Power on exponential of temperature-time relation using this online calculator? To use this online calculator for Power on exponential of temperature-time relation, enter Convection Heat Transfer Coefficient (h), Surface Area (A), Time Elapsed (t), Density (ρ), Total volume (V_T) & Specific Heat Capacity (C_o) and hit the calculate button. Here is how the Power on exponential of temperature-time relation calculation can be explained with given input values -> -0.006222 = -(0.04*18*12)/(5.51*63*4).

FAQ

What is Power on exponential of temperature-time relation?

Power on exponential of temperature-time relation formula calculates the value of power on exponential in the equation which makes the further calculation of lumped system easy and is represented as b = -(h*A*t)/(ρ*V_T*C_o) or Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity). Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature, The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides, Time elapsed after a particular task is started, The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container & Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

How to calculate Power on exponential of temperature-time relation?

Power on exponential of temperature-time relation formula calculates the value of power on exponential in the equation which makes the further calculation of lumped system easy is calculated using Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity). To calculate Power on exponential of temperature-time relation, you need Convection Heat Transfer Coefficient (h), Surface Area (A), Time Elapsed (t), Density (ρ), Total volume (V_T) & Specific Heat Capacity (C_o). With our tool, you need to enter the respective value for Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Total volume & Specific Heat Capacity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Constant B?

In this formula, Constant B uses Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Total volume & Specific Heat Capacity. We can use 1 other way(s) to calculate the same, which is/are as follows -

Constant B = -(Biot Number*Fourier Number)

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