Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in a different field, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of ramped boundary conditions near a porous surface. The dynamical analysis of heat transfer is based on classical differentiation with no memory effects. The non-dimensional form of the governing equations of the model is developed. These are solved by the classical integral (Laplace) transform technique/method with the convolution theorem and closed-form solutions are attained for temperature, concentration, and velocity. The physical aspects of distinct parameters are discussed

In the literature, different theories are made to see the phenomenon of heat transfer analysis. Radiation, convection, and conduction are three modes of heat transfer. Convection can be defined as heat transfer by the substance motion which may be air or water. It plays a central role in creating the weather clause on the plant. Convection consists of forced and natural convection. It happens when the medium divides the heat energy and is on its move. Heat is disbursed when a fan pushes air, and sometimes heat advection is referred to the forced convection. Heat is animated to distress by means of itself hotness becomes the cause of natural convection by means of shifting source heat. Heat and mass are related to each other as heat transfer rate depends on mass transfer and mass transfer further depends upon concentration difference. Free convective flow is a self-reliant flow with the effect of heat transfer. In different industrial problems, the fluid flow phenomenon of free convection has achieved much consideration in recent years. The atmospheric, oceanic circulation, and emergency cooling system of advanced nuclear reactors is the most important application of free convection. The effect of heat transfer in non-Newtonian fluids plays a major role applying engineering such as drag reduction, the emergency cooling system of nuclear reactors, and thermal welding. In literature, different theories are made to see the phenomenon of heat transfer analysis. The convection heat transform between two heated cubes was discussed by Mousazadeh et al. [

Qi et al. [

Although the research on the Second grade model can be continued, we include here some related studies based on heat transfer, fractional models of fluids, magnetized fluids, and few others therein [

Consider the MHD Second grade fluid flow in a porous medium over an limitless vertical plate. Initially, the fluid is at rest at _{0}, the _{0}, it give constant velocity _{0} with temperature _{∞}. The fluid flow is one dimensional. The flow direction of radiative flux is negligible. Finally in energy equation, the dispersion term is neglected. The geometrical presentation of considered model is provided in

with appropriate conditions

where

Consider the different dimensionless quantities

After simplification, we have the set of dimensionless governing equations and their corresponding conditions are:

Applying Laplace transformation to get the solution of

The solution of above

using appropriate conditions are used to find the value of constant,

The inverse Laplace transformation of

where _{0}) represent a standard Heaviside function with _{0} =

To estimate the rate of heat transfer can be obtained as

Applying the Laplace transformation to

The required solution of second order differential

To obtain the exact solution, we take the inverse Laplace transformation, we have

using from literature

The solution of

by using the

where

where

Further,

where

Applying inverse Laplace transformation with convolution product on

Substituting all the above functions, the equation of velocity field becomes in the form

The following relation used to calculate the skin friction as

We recover the same result for velocity field in the absence of mass Grashof number _{m} = 0 obtained by Anwar et al. [_{r} = 0 and _{m} = 0, we get the same expression for velocity as discussed by Samiulhaq et al. [

This part is devoted for physical interpretation of heat transfer is executed on the motion of Second-grade fluid near a porous surface. The impact of thermal radiation, magnetic field, and ramped temperature conditions are also analyzed _{r}, _{r}, _{c}, _{m}, _{r}, _{r} on energy profile. It is seen that thermal layer and temperature decreases by large value of _{r}. As _{r} increase, the temperature profile reduce more rapidly. Physically, for less value of _{r} heat conductivity enhances. _{r}. By enhancing the value of _{r}, the required energy enhance. The domination of _{r}, enhanced due to transportation of energy.

In _{c} on concentration profile. It is noted that the greater value of _{c}, the concentration reduce as enhance the value of _{c}. Contribution of concentration component on the fluid motion is important and it cannot be ignored.

_{m}. It is the ratio of mass force to viscous force, which causes free convection. It is noted that the fluid velocity is increasing, if we increase the value of _{m}. _{r} for velocity field. The curve behavior of _{r} is same as _{m}. It is noted that the velocity field enhance by increasing in _{r}. Physically, when the _{r} is increased, then fluid flow increase due to the thermal effects.

_{r}. Specific heat and conductivity are depend on _{r}. The thickness of momentum and boundary layer is controled by prandtl number. It seen from the graph, decreasing the velocity, observed by increase the value of _{r}. The lower prandtl number enhance the thermal conductivity and increase the boundary layer. _{c} on fluid profile. It notices that the value of _{c} enhance, the velocity of fluid flow decreased.

This part is devoted for dynamical analysis of heat transfer on MHD Second-grade fluid near a porous surface. The impact of ramped temperature condition and magnetic effect are analyzed

It is noted that the decay in temperature for increasing value of _{r} while temperature is increasing as increase in _{r}.

The decay in concentration for growing the values of _{c}.

The fluid velocity decreases when the value of

Enhance the values of _{r}, _{m}, the required fluid velocity is increasing.

Enhance the values of

In case of large value of _{c} and magnetic field

Contribution of concentration component of fluid velocity on the fluid motion is important and it cannot be ignored.

The authors are highly thankful and grateful for generous support and facilities of this research work.